https://gdpark.blog/Recent content on gdpark.blogHugoenTue, 28 Jan 2025 00:00:00 +0000https://gdpark.blog/posts/cfa-l2-01-level-1-content-review/Sun, 22 Sep 2024 00:00:00 +0000https://gdpark.blog/posts/cfa-l2-01-level-1-content-review/We rebuild arithmetic vs geometric mean from scratch — and why using the wrong average on stock returns will quietly wreck your portfolio lol.https://gdpark.blog/posts/cfa-l1-01-balance-sheet/Wed, 31 Mar 2021 00:00:00 +0000https://gdpark.blog/posts/cfa-l1-01-balance-sheet/Kicking off the FRA grind from absolute zero — what Financial Reporting Analysis even is, why accounting matters, and a first peek at the balance sheet.https://gdpark.blog/posts/cfa-l1-01-introduction/Wed, 31 Mar 2021 00:00:00 +0000https://gdpark.blog/posts/cfa-l1-01-introduction/Kicking off a weekly series to transcribe my CFA class notes — maybe with a backtest or two — on a heroic 30-min-a-day schedule. Fighting!!!!https://gdpark.blog/posts/statistics-01-moment-generating-function/Mon, 13 Nov 2017 00:00:00 +0000https://gdpark.blog/posts/statistics-01-moment-generating-function/Turns out mean and variance are just the 1st and 2nd moments — and the MGF is the tool mathematicians built to pull any moment out, cleanly, anytime!https://gdpark.blog/posts/statistics-01-introduction/Sun, 12 Nov 2017 00:00:00 +0000https://gdpark.blog/posts/statistics-01-introduction/A casual dive into why sample variance divides by n-1 and how we use samples to estimate population parameters without measuring absolutely everyone.https://gdpark.blog/posts/special-relativity-01-introduction-to-special-relativity/Mon, 27 Feb 2017 00:00:00 +0000https://gdpark.blog/posts/special-relativity-01-introduction-to-special-relativity/A physics grad&rsquo;s enthusiastic deep-dive into special relativity — the wild theory of time travel and teleportation that made them major in physics in the first place!https://gdpark.blog/posts/corporate-finance-01-introduction-to-corporate-finance/Sat, 15 Oct 2016 00:00:00 +0000https://gdpark.blog/posts/corporate-finance-01-introduction-to-corporate-finance/A reluctant double-major&rsquo;s crash course in corporate finance — covering fund procurement, investment decisions, dividend policy, and the agency problem, all with honest student energy.https://gdpark.blog/posts/derivatives-01-introduction-to-derivatives/Thu, 13 Oct 2016 00:00:00 +0000https://gdpark.blog/posts/derivatives-01-introduction-to-derivatives/Kicking off a derivatives series with a skim of Hull Chapter 1 — futures vs. options, hedging vs. speculation, and the quiz-first study method.https://gdpark.blog/posts/financial-engineering-01-call-options-put-options/Thu, 01 Sep 2016 00:00:00 +0000https://gdpark.blog/posts/financial-engineering-01-call-options-put-options/A casual dive into call and put options — what they actually mean, why Black–Scholes blew the market wide open, and yes, there&rsquo;s a dropped-class backstory involved.https://gdpark.blog/posts/microeconomics-01-introduction-to-microeconomics/Sun, 03 Jul 2016 00:00:00 +0000https://gdpark.blog/posts/microeconomics-01-introduction-to-microeconomics/I lost faith in traditional economics after reading The Origin of Wealth, but I&rsquo;m studying micro anyway — someone has to know the old framework before they can fix it.https://gdpark.blog/posts/basic-investing-01-overview-of-basic-investing/Tue, 29 Mar 2016 00:00:00 +0000https://gdpark.blog/posts/basic-investing-01-overview-of-basic-investing/A no-fluff rundown of investing basics — what markets actually do, asset allocation vs. security selection, the EMH, and money market instruments like T-bills and CDs.https://gdpark.blog/posts/linear-algebra-01-prologue-heralding-the-beginning/Mon, 18 Jan 2016 00:00:00 +0000https://gdpark.blog/posts/linear-algebra-01-prologue-heralding-the-beginning/Stumbled onto a hidden-gem linear algebra course on educast.pro while cramming for quantum mechanics, and the pure love-of-learning vibe had me completely hooked.https://gdpark.blog/posts/linear-algebra-01-vector-spaces/Mon, 18 Jan 2016 00:00:00 +0000https://gdpark.blog/posts/linear-algebra-01-vector-spaces/Turns out &ldquo;linear&rdquo; literally just means line-shaped — lol — and here&rsquo;s why that embarrassingly simple idea is the backbone of basically all of math and STEM.https://gdpark.blog/posts/macroeconomics-01-goods-market-and-the-short-term-model/Sun, 10 Jan 2016 00:00:00 +0000https://gdpark.blog/posts/macroeconomics-01-goods-market-and-the-short-term-model/Finally diving into real macro — breaking down GDP composition, inventory vs. fixed investment, and the consumption function from Blanchard Chapter 3.https://gdpark.blog/posts/thermal-statistical-01-stirling-s-formula-and-stirling-s-approximation/Tue, 29 Dec 2015 00:00:00 +0000https://gdpark.blog/posts/thermal-statistical-01-stirling-s-formula-and-stirling-s-approximation/A physics student dives into proving Stirling&rsquo;s formula from scratch using the Gamma function — a key tool for the Thermal &amp; Statistical Mechanics journey ahead.https://gdpark.blog/posts/modern-physics-01-time-dilation-in-special-relativity/Thu, 20 Aug 2015 00:00:00 +0000https://gdpark.blog/posts/modern-physics-01-time-dilation-in-special-relativity/A fun dive into Einstein&rsquo;s special relativity — covering the two postulates and why time itself literally has to slow down to keep the speed of light constant. hehehttps://gdpark.blog/posts/quantum-mechanics-01-introduction-to-quantum-mechanics-on-probability/Mon, 10 Aug 2015 00:00:00 +0000https://gdpark.blog/posts/quantum-mechanics-01-introduction-to-quantum-mechanics-on-probability/Two weeks into quantum mechanics and already questioning my life choices — tackling the Schrödinger equation, wavefunctions, and why QM still has no &lsquo;owner&rsquo; lol.https://gdpark.blog/posts/money-banking-01-why-study-money-and-banking/Thu, 25 Jun 2015 00:00:00 +0000https://gdpark.blog/posts/money-banking-01-why-study-money-and-banking/Casually skimmed then carefully re-read Ch. 1–2 of money &amp; banking — vocab check on stocks, bonds, debt instruments, and short-term money market tools!https://gdpark.blog/posts/classical-mechanics-01-vectors-and-polar-coordinates/Thu, 18 Jun 2015 00:00:00 +0000https://gdpark.blog/posts/classical-mechanics-01-vectors-and-polar-coordinates/A casual walkthrough of university-level vector concepts — cross products, the BAC-CAB rule, and coordinate transformation matrices — with encouragement to derive it yourself!https://gdpark.blog/posts/modern-physics-01-rutherford-scattering-and-the-rutherford-scattering-formula/Sat, 02 May 2015 00:00:00 +0000https://gdpark.blog/posts/modern-physics-01-rutherford-scattering-and-the-rutherford-scattering-formula/Deriving the Rutherford scattering formula while stumbling through the wild history of how we went from Thomson&rsquo;s pudding model to discovering the atomic nucleus — scary math incoming lol.https://gdpark.blog/posts/differential-equations-01-introduction-to-the-differential-equations-special-series/Sun, 26 Apr 2015 00:00:00 +0000https://gdpark.blog/posts/differential-equations-01-introduction-to-the-differential-equations-special-series/A casual dive into first- and second-order linear differential equations, kicking things off with the integrating factor method — because this stuff shows up <em>everywhere</em> in nature!!https://gdpark.blog/posts/electromagnetism-01-electrostatics/Fri, 14 Nov 2014 00:00:00 +0000https://gdpark.blog/posts/electromagnetism-01-electrostatics/Kicking off electrostatics with a fun breakdown of what static electricity actually means and why Coulomb&rsquo;s law looks the way it does — nature first, explanations second!https://gdpark.blog/posts/cfa-l2-02-forward-pricing/Sun, 10 Nov 2024 00:00:00 +0000https://gdpark.blog/posts/cfa-l2-02-forward-pricing/A casual walkthrough of forward pricing for zero coupon bonds — showing how today&rsquo;s spot rates imply a locked-in future price, and why realized rates rarely match what we expected.https://gdpark.blog/posts/cfa-l1-02-income-statement-and-cash-flow-statement/Thu, 08 Apr 2021 00:00:00 +0000https://gdpark.blog/posts/cfa-l1-02-income-statement-and-cash-flow-statement/Quick rundown of the income statement — what it shows, why revenue ≠ profit, and why accountants split out discontinued operations so shareholders don&rsquo;t get played.https://gdpark.blog/posts/statistics-02-derivation-of-the-poisson-distribution/Tue, 14 Nov 2017 00:00:00 +0000https://gdpark.blog/posts/statistics-02-derivation-of-the-poisson-distribution/We kick off the distributions series by deriving the Poisson from scratch — starting with the binomial and cranking n to infinity to see what shakes out.https://gdpark.blog/posts/special-relativity-02-fundamental-understanding-of-special-relativity/Tue, 28 Feb 2017 00:00:00 +0000https://gdpark.blog/posts/special-relativity-02-fundamental-understanding-of-special-relativity/A fun, casual breakdown of special relativity — from inertial frames and Maxwell&rsquo;s equations to why light always clocks in at c no matter where you are lololol.https://gdpark.blog/posts/corporate-finance-02-time-value-of-money/Sat, 15 Oct 2016 00:00:00 +0000https://gdpark.blog/posts/corporate-finance-02-time-value-of-money/A fun, casual walkthrough of time value of money concepts — future value, present value, and the compound value interest factor (CVIF) explained with zero boring.https://gdpark.blog/posts/derivatives-02-structure-of-futures-markets/Thu, 13 Oct 2016 00:00:00 +0000https://gdpark.blog/posts/derivatives-02-structure-of-futures-markets/A Q&amp;A rundown of futures market basics — open interest, margin calls, stop vs. limit orders, and how hedgers and speculators get taxed differently.https://gdpark.blog/posts/financial-engineering-02-intrinsic-value-time-value-of-options/Thu, 01 Sep 2016 00:00:00 +0000https://gdpark.blog/posts/financial-engineering-02-intrinsic-value-time-value-of-options/Option value splits into two pieces — intrinsic value (the profit you&rsquo;d lock in right now) and time value (all that probabilistic could-happen-later stuff) — here&rsquo;s how they work.https://gdpark.blog/posts/microeconomics-02-endogenous-and-exogenous-variables/Sun, 03 Jul 2016 00:00:00 +0000https://gdpark.blog/posts/microeconomics-02-endogenous-and-exogenous-variables/A fun, breezy breakdown of endogenous vs. exogenous variables — think exam scores, study hours, and yes, a girlfriend shifting your efficiency curve upward by h.https://gdpark.blog/posts/basic-investing-02-stock-market-indices/Tue, 29 Mar 2016 00:00:00 +0000https://gdpark.blog/posts/basic-investing-02-stock-market-indices/Breaking down what stock market indices actually are — Dow Jones, S&amp;P 500, NYSE, NASDAQ — how they&rsquo;re calculated, and why the jump from a plain average to a weighted one matters.https://gdpark.blog/posts/linear-algebra-02-linear-dependence-and-linear-independence/Tue, 19 Jan 2016 00:00:00 +0000https://gdpark.blog/posts/linear-algebra-02-linear-dependence-and-linear-independence/Breaking down linear combinations, span, and what it actually means for vectors to be linearly independent — all in plain terms.https://gdpark.blog/posts/macroeconomics-02-financial-markets/Sun, 10 Jan 2016 00:00:00 +0000https://gdpark.blog/posts/macroeconomics-02-financial-markets/We dig into the financial market — breaking down money demand, interest rates, and why splitting it from the goods market makes sense before we smash it all back into AD.https://gdpark.blog/posts/thermal-statistical-02-chapter-3-practice-problems/Tue, 29 Dec 2015 00:00:00 +0000https://gdpark.blog/posts/thermal-statistical-02-chapter-3-practice-problems/Stumbling through heat, heat capacity, and all their flavors (constant-volume, constant-pressure&hellip;) with way too many question marks before tiptoeing into probability.https://gdpark.blog/posts/modern-physics-02-the-relativistic-doppler-effect/Thu, 20 Aug 2015 00:00:00 +0000https://gdpark.blog/posts/modern-physics-02-the-relativistic-doppler-effect/We connect the classic Doppler effect to time dilation, and it turns out moving really fast changes the frequency you perceive even when you&rsquo;re not getting closer or farther away!https://gdpark.blog/posts/quantum-mechanics-02-normalization/Mon, 10 Aug 2015 00:00:00 +0000https://gdpark.blog/posts/quantum-mechanics-02-normalization/Figuring out why a normalized wave function stays normalized over time — turns out the Schrödinger equation holds that secret all along!https://gdpark.blog/posts/money-banking-02-the-money-supply-process/Fri, 26 Jun 2015 00:00:00 +0000https://gdpark.blog/posts/money-banking-02-the-money-supply-process/A casual rundown of Chapter 15 — breaking down the Fed&rsquo;s balance sheet, monetary base, reserves, and how open market operations move the money supply!!!https://gdpark.blog/posts/classical-mechanics-02-work-energy-theorem-and-conservative-forces/Thu, 18 Jun 2015 00:00:00 +0000https://gdpark.blog/posts/classical-mechanics-02-work-energy-theorem-and-conservative-forces/Deriving the Work-Energy Theorem and potential energy straight from F=ma using the chain rule — turns out it&rsquo;s shockingly simple and kinda blew my mind!!!https://gdpark.blog/posts/electromagnetism-02-gauss-s-law/Fri, 14 Nov 2014 00:00:00 +0000https://gdpark.blog/posts/electromagnetism-02-gauss-s-law/A super easy breakdown of Gauss&rsquo;s law using a soy-sauce-flinging analogy, electric field lines, and flux — no scary math required (well, almost).https://gdpark.blog/posts/cfa-l2-03-par-rate/Mon, 11 Nov 2024 00:00:00 +0000https://gdpark.blog/posts/cfa-l2-03-par-rate/Par rate is just the YTM of a bond trading at face value — and once you get that, bootstrapping spot rates from the par curve is honestly just arithmetic.https://gdpark.blog/posts/cfa-l1-03-accrual-accounting/Sun, 11 Apr 2021 00:00:00 +0000https://gdpark.blog/posts/cfa-l1-03-accrual-accounting/A casual breakdown of why accrual accounting exists — from the &lsquo;does undelivered revenue count?&rsquo; dilemma to how GAAP, IFRS, and K-IFRS all fit together.https://gdpark.blog/posts/statistics-03-derivation-of-the-exponential-distribution/Wed, 15 Nov 2017 00:00:00 +0000https://gdpark.blog/posts/statistics-03-derivation-of-the-exponential-distribution/We skip the normal distribution to derive the exponential distribution — aka the waiting time until the first event — straight from the Poisson!https://gdpark.blog/posts/special-relativity-03-spacetime-and-lorentz-invariance/Thu, 20 Apr 2017 00:00:00 +0000https://gdpark.blog/posts/special-relativity-03-spacetime-and-lorentz-invariance/A casual dive into four-vectors and spacetime — why we need (t, x, y, z) once Einstein smashes simultaneity and each inertial frame gets its own time!https://gdpark.blog/posts/corporate-finance-03-capital-markets-and-financial-assets/Sun, 16 Oct 2016 00:00:00 +0000https://gdpark.blog/posts/corporate-finance-03-capital-markets-and-financial-assets/A casual breakdown of financial markets, covering capital vs. money markets, issuing markets, and the two main underwriting methods taught in financial management class.https://gdpark.blog/posts/derivatives-03-hedging-strategies-using-futures/Thu, 13 Oct 2016 00:00:00 +0000https://gdpark.blog/posts/derivatives-03-hedging-strategies-using-futures/A quiz-style walkthrough of futures hedging — short vs long hedges, basis risk, optimal hedge ratios, and beta reduction with index futures.https://gdpark.blog/posts/derivatives-03-linear-regression-in-finance/Thu, 13 Oct 2016 00:00:00 +0000https://gdpark.blog/posts/derivatives-03-linear-regression-in-finance/A from-scratch derivation of linear regression — why we square the errors, how to find the best-fit slope and intercept, and why this shows up everywhere in finance.https://gdpark.blog/posts/financial-engineering-03-put-call-parity/Wed, 07 Sep 2016 00:00:00 +0000https://gdpark.blog/posts/financial-engineering-03-put-call-parity/Before jumping into the binomial model, we lock in put-call parity — the neat reason knowing a European call&rsquo;s price automatically pins down its put, and vice versa.https://gdpark.blog/posts/microeconomics-03-demand-curve-and-supply-curve/Sun, 03 Jul 2016 00:00:00 +0000https://gdpark.blog/posts/microeconomics-03-demand-curve-and-supply-curve/We build the demand curve from scratch using red ginseng as our example market, then unpack the law of demand plus direct vs. derived demand — heh heh.https://gdpark.blog/posts/basic-investing-03-ipo-and-order-types/Sat, 02 Apr 2016 00:00:00 +0000https://gdpark.blog/posts/basic-investing-03-ipo-and-order-types/A breakdown of how IPOs actually work — from primary vs. secondary markets to road shows, bookbuilding, and why playing it cool at an IPO is a bad idea.https://gdpark.blog/posts/linear-algebra-03-basis/Tue, 19 Jan 2016 00:00:00 +0000https://gdpark.blog/posts/linear-algebra-03-basis/So a basis is literally the intersection of spanning sets and linearly independent sets — and there are TONS of them, plus order actually matters!!https://gdpark.blog/posts/macroeconomics-03-is-curve-and-lm-curve/Mon, 11 Jan 2016 00:00:00 +0000https://gdpark.blog/posts/macroeconomics-03-is-curve-and-lm-curve/Finally deriving the IS and LM curves for real — dropping the constant-investment assumption and sketching out equilibrium in both the goods and financial markets!https://gdpark.blog/posts/thermal-statistical-03-microstates-and-macrostates/Wed, 30 Dec 2015 00:00:00 +0000https://gdpark.blog/posts/thermal-statistical-03-microstates-and-macrostates/We kick things off with the Zeroth Law of Thermodynamics — what thermal equilibrium really means, why heat only flows one way, and how that leads us to thermometers!https://gdpark.blog/posts/modern-physics-03-length-contraction-in-special-relativity/Thu, 20 Aug 2015 00:00:00 +0000https://gdpark.blog/posts/modern-physics-03-length-contraction-in-special-relativity/Muons from cosmic rays should die way before reaching Earth — so why do we detect them?! It all comes down to length contraction and time dilation in special relativity!https://gdpark.blog/posts/quantum-mechanics-03-the-momentum-operator/Tue, 11 Aug 2015 00:00:00 +0000https://gdpark.blog/posts/quantum-mechanics-03-the-momentum-operator/Jumping into the math of differentiating <x> with respect to time — and watching it naturally lead us straight to the momentum operator!https://gdpark.blog/posts/money-banking-03-tools-of-monetary-policy/Fri, 26 Jun 2015 00:00:00 +0000https://gdpark.blog/posts/money-banking-03-tools-of-monetary-policy/Breaking down the 4 monetary policy tools the Fed uses to nail its target federal funds rate, and why it all plays out in the reserves market!https://gdpark.blog/posts/classical-mechanics-03-oscillations-and-damped-harmonic-motion/Fri, 19 Jun 2015 00:00:00 +0000https://gdpark.blog/posts/classical-mechanics-03-oscillations-and-damped-harmonic-motion/Springs are literally everywhere — turns out any potential looks like a spring up close, and that&rsquo;s why oscillations are SO important in physics!!https://gdpark.blog/posts/electromagnetism-03-electric-potential/Fri, 14 Nov 2014 00:00:00 +0000https://gdpark.blog/posts/electromagnetism-03-electric-potential/A casual breakdown of electric potential — from curl-zero fields and scalar potentials to Poisson&rsquo;s equation, with the kind of asides you wish your textbook had.https://gdpark.blog/posts/cfa-l2-04-rolling-down-the-yield-curve/Wed, 13 Nov 2024 00:00:00 +0000https://gdpark.blog/posts/cfa-l2-04-rolling-down-the-yield-curve/A casual breakdown of how buying longer-maturity bonds and selling early lets you squeeze out extra return by rolling down an upward-sloping yield curve.https://gdpark.blog/posts/cfa-l1-04-inventories-1-acquisition-cost/Fri, 16 Apr 2021 00:00:00 +0000https://gdpark.blog/posts/cfa-l1-04-inventories-1-acquisition-cost/We kick off our B/S line-item series with inventories — what they are, how acquisition cost first hits the books, and the cash-vs-credit purchase breakdown.https://gdpark.blog/posts/statistics-04-derivation-of-the-gamma-distribution/Thu, 16 Nov 2017 00:00:00 +0000https://gdpark.blog/posts/statistics-04-derivation-of-the-gamma-distribution/Deriving the Gamma distribution from scratch by connecting it to the Poisson process — turns out it&rsquo;s just waiting for the α-th event instead of the first!!!!https://gdpark.blog/posts/special-relativity-04-timelike-spacelike-and-null-intervals/Fri, 05 May 2017 00:00:00 +0000https://gdpark.blog/posts/special-relativity-04-timelike-spacelike-and-null-intervals/Picking up right where we cut off last time — we finally classify spacetime intervals as timelike, spacelike, or null, and yes, hyperbolas make a comeback!https://gdpark.blog/posts/corporate-finance-04-valuation-of-bonds-and-stocks/Sun, 16 Oct 2016 00:00:00 +0000https://gdpark.blog/posts/corporate-finance-04-valuation-of-bonds-and-stocks/Breaking down how to slap a price tag on bonds and stocks using present value formulas — and yes, yield to maturity is just as annoying to solve as it sounds.https://gdpark.blog/posts/derivatives-04-interest-rates/Thu, 13 Oct 2016 00:00:00 +0000https://gdpark.blog/posts/derivatives-04-interest-rates/A worked-through tour of the interest rate zoo — compounding conventions, LIBOR vs LIBID, spot and forward rates, FRAs, and bond pricing, all with quiz solutions.https://gdpark.blog/posts/financial-engineering-04-binomial-model-one-period/Mon, 03 Oct 2016 00:00:00 +0000https://gdpark.blog/posts/financial-engineering-04-binomial-model-one-period/The one-period binomial model in a nutshell — stock goes up or down, we build a risk-free portfolio, and derive the hedge ratio Δ and call option price.https://gdpark.blog/posts/microeconomics-04-equilibrium/Wed, 13 Jul 2016 00:00:00 +0000https://gdpark.blog/posts/microeconomics-04-equilibrium/Turns out economic equilibrium is a dynamic concept — and it clicks way easier once you see it&rsquo;s basically the same thing as thermal equilibrium in physics.https://gdpark.blog/posts/basic-investing-04-buying-on-margin-and-short-sales/Sun, 03 Apr 2016 00:00:00 +0000https://gdpark.blog/posts/basic-investing-04-buying-on-margin-and-short-sales/A casual breakdown of how buying on margin works — borrowing from your broker to buy stocks, why margin calls happen, and why losses hurt way more than gains feel good.https://gdpark.blog/posts/linear-algebra-04-matrices-and-matrix-multiplication/Wed, 20 Jan 2016 00:00:00 +0000https://gdpark.blog/posts/linear-algebra-04-matrices-and-matrix-multiplication/We dive into linear algebra by unpacking functions as set mappings, then zoom in on linear mappings and how they all secretly boil down to matrices.https://gdpark.blog/posts/macroeconomics-04-medium-term-analysis-labor-market/Mon, 11 Jan 2016 00:00:00 +0000https://gdpark.blog/posts/macroeconomics-04-medium-term-analysis-labor-market/We&rsquo;re done with the short-term goods and financial markets — now we crack open the medium term, which means the labor market and figuring out how wages actually get determined.https://gdpark.blog/posts/thermal-statistical-04-temperature/Thu, 31 Dec 2015 00:00:00 +0000https://gdpark.blog/posts/thermal-statistical-04-temperature/Diving into the statistical definition of temperature — microstates, the ergodic hypothesis, and the genuinely staggering conclusion that falls out of it all!https://gdpark.blog/posts/modern-physics-04-the-twin-paradox-in-special-relativity/Thu, 20 Aug 2015 00:00:00 +0000https://gdpark.blog/posts/modern-physics-04-the-twin-paradox-in-special-relativity/Finally cracking the twin paradox using length contraction — whoever changed direction was the one actually moving, and the math totally checks out hehe.https://gdpark.blog/posts/quantum-mechanics-04-the-time-independent-schr-dinger-equation/Tue, 11 Aug 2015 00:00:00 +0000https://gdpark.blog/posts/quantum-mechanics-04-the-time-independent-schr-dinger-equation/A fun, casual rundown of how the time-independent Schrödinger equation came to be — tracing the genius relay from Planck to Einstein to de Broglie to Schrödinger!https://gdpark.blog/posts/money-banking-04-conducting-monetary-policy-strategy-and-tactics/Fri, 26 Jun 2015 00:00:00 +0000https://gdpark.blog/posts/money-banking-04-conducting-monetary-policy-strategy-and-tactics/A breezy rundown of how central banks juggle inflation targeting, the time-inconsistency problem, and a whole laundry list of goals beyond just price stability!https://gdpark.blog/posts/classical-mechanics-04-forced-harmonic-oscillation-and-resonance/Sat, 20 Jun 2015 00:00:00 +0000https://gdpark.blog/posts/classical-mechanics-04-forced-harmonic-oscillation-and-resonance/A step-by-step walkthrough of forced harmonic oscillation — what happens when the driving frequency meets the oscillator&rsquo;s natural frequency and resonance kicks in.https://gdpark.blog/posts/electromagnetism-04-electric-potential-part-2/Fri, 14 Nov 2014 00:00:00 +0000https://gdpark.blog/posts/electromagnetism-04-electric-potential-part-2/We drag charges in one by one, crunch the work each step takes, and land on a neat double-sum formula for the total electric potential energy of a system.https://gdpark.blog/posts/cfa-l2-05-swap-rate-curve/Fri, 15 Nov 2024 00:00:00 +0000https://gdpark.blog/posts/cfa-l2-05-swap-rate-curve/Breaking down what swap rates actually are, why the swap curve matters as a benchmark, and how it stacks up against government bond yield curves.https://gdpark.blog/posts/cfa-l1-05-inventories-2-cost-flow-assumptions/Thu, 22 Apr 2021 00:00:00 +0000https://gdpark.blog/posts/cfa-l1-05-inventories-2-cost-flow-assumptions/When prices and quantities change every single time you buy, you need a cost flow assumption — here&rsquo;s the rundown on FIFO, LIFO, weighted average, and perpetual vs. periodic.https://gdpark.blog/posts/statistics-05-derivation-of-the-chi-squared-distribution/Fri, 17 Nov 2017 00:00:00 +0000https://gdpark.blog/posts/statistics-05-derivation-of-the-chi-squared-distribution/Chi-squared is just a gamma in disguise — we prove Z² follows it with 1 degree of freedom and show how sample variance ties in before jumping to the t-distribution.https://gdpark.blog/posts/special-relativity-05-hyperbolic-geometry-and-non-euclidean-geometry/Fri, 05 May 2017 00:00:00 +0000https://gdpark.blog/posts/special-relativity-05-hyperbolic-geometry-and-non-euclidean-geometry/We jump straight into Lorentz transformations and spacetime diagrams, playing with inertial frames and Einstein&rsquo;s brain-smashing assumption that light always travels at c!https://gdpark.blog/posts/corporate-finance-05-liquidity-management-and-capital-budgeting-overview/Sun, 16 Oct 2016 00:00:00 +0000https://gdpark.blog/posts/corporate-finance-05-liquidity-management-and-capital-budgeting-overview/A no-frills terminology dump on liquidity management, working capital, and financing policies — because these chapters sure aren&rsquo;t giving us any practical how-tos. T_Thttps://gdpark.blog/posts/derivatives-05-determining-forward-and-futures-prices/Sat, 15 Oct 2016 00:00:00 +0000https://gdpark.blog/posts/derivatives-05-determining-forward-and-futures-prices/A quiz-style rundown of how forward and futures prices actually work — short selling, convenience yield, cost of carry, and why copper isn&rsquo;t gold.https://gdpark.blog/posts/financial-engineering-05-binomial-model-two-period/Mon, 03 Oct 2016 00:00:00 +0000https://gdpark.blog/posts/financial-engineering-05-binomial-model-two-period/Extending the one-period binomial model to two periods — turns out it&rsquo;s the same trick applied twice, and the binomial weights just fall right out naturally.https://gdpark.blog/posts/microeconomics-05-types-of-elasticity/Wed, 13 Jul 2016 00:00:00 +0000https://gdpark.blog/posts/microeconomics-05-types-of-elasticity/Elasticity isn&rsquo;t the same as a derivative — here&rsquo;s why, plus a breakdown of price elasticity of demand and why the value can differ at every single point on the curve.https://gdpark.blog/posts/basic-investing-05-mutual-funds/Sun, 03 Apr 2016 00:00:00 +0000https://gdpark.blog/posts/basic-investing-05-mutual-funds/A casual breakdown of what investment companies actually are, how they&rsquo;re classified, and why mutual funds ended up eating unit investment trusts&rsquo; lunch.https://gdpark.blog/posts/linear-algebra-05-surjective-injective-and-bijective-functions/Wed, 20 Jan 2016 00:00:00 +0000https://gdpark.blog/posts/linear-algebra-05-surjective-injective-and-bijective-functions/We nail down surjective, injective, and bijective functions — and prove why same-dimension linear maps only need one condition to guarantee the other.https://gdpark.blog/posts/macroeconomics-05-wage-setting-and-price-setting/Tue, 12 Jan 2016 00:00:00 +0000https://gdpark.blog/posts/macroeconomics-05-wage-setting-and-price-setting/Picking up where we left off, we graph wage setting and price setting curves to nail down the natural unemployment rate — and yeah, it basically all comes down to markup.https://gdpark.blog/posts/thermal-statistical-05-chapter-4-practice-problems/Thu, 31 Dec 2015 00:00:00 +0000https://gdpark.blog/posts/thermal-statistical-05-chapter-4-practice-problems/Working through Chapter 4 problems on two-state systems, using the Boltzmann distribution and partition functions to nail expectation values and energy variance.https://gdpark.blog/posts/modern-physics-05-relativistic-mass-momentum-and-energy/Fri, 21 Aug 2015 00:00:00 +0000https://gdpark.blog/posts/modern-physics-05-relativistic-mass-momentum-and-energy/We crack open why mass isn&rsquo;t as intrinsic as you thought by watching two particles collide across reference frames to see how relativistic momentum really works.https://gdpark.blog/posts/quantum-mechanics-05-the-time-independent-schr-dinger-equation-part-2/Tue, 11 Aug 2015 00:00:00 +0000https://gdpark.blog/posts/quantum-mechanics-05-the-time-independent-schr-dinger-equation-part-2/We crack the time-independent Schrödinger equation by assuming ψ separates into x and t parts — basically the same separation-of-variables trick from electromagnetism!https://gdpark.blog/posts/money-banking-05-foreign-exchange-markets-and-exchange-rates/Sun, 28 Jun 2015 00:00:00 +0000https://gdpark.blog/posts/money-banking-05-foreign-exchange-markets-and-exchange-rates/A casual intro to foreign exchange markets — covering why exchange rates matter, spot vs. forward transactions, OTC trading, and how long/short-term rates are determined.https://gdpark.blog/posts/classical-mechanics-05-2d-and-3d-isotropic-harmonic-oscillators-and-lissajous-figur/Mon, 22 Jun 2015 00:00:00 +0000https://gdpark.blog/posts/classical-mechanics-05-2d-and-3d-isotropic-harmonic-oscillators-and-lissajous-figur/We&rsquo;re already at chapter 4 — diving into isotropic harmonic oscillators in 2D and 3D, where separating x and y equations leads to super cool Lissajous figures!https://gdpark.blog/posts/electromagnetism-05-electrostatics-in-conductors/Sat, 15 Nov 2014 00:00:00 +0000https://gdpark.blog/posts/electromagnetism-05-electrostatics-in-conductors/A breezy walkthrough of why E = 0 inside a conductor, how charges spread to the outer surface, and finding the potential for a nested conducting sphere problem!https://gdpark.blog/posts/cfa-l2-06-spread-measures/Sat, 16 Nov 2024 00:00:00 +0000https://gdpark.blog/posts/cfa-l2-06-spread-measures/A been-here-done-this rundown of swap spread, I-spread (yes, with that annoying linear interpolation), and Z-spread — basically Level 1 déjà vu, but let&rsquo;s power through it.https://gdpark.blog/posts/cfa-l1-06-inventories-3-lifo-reserve/Sun, 02 May 2021 00:00:00 +0000https://gdpark.blog/posts/cfa-l1-06-inventories-3-lifo-reserve/A casual walkthrough of how FIFO vs. LIFO choices ripple through key financial ratios — liquidity, solvency, and activity — before diving into the LIFO reserve.https://gdpark.blog/posts/statistics-06-derivation-of-the-student-s-t-distribution/Sat, 18 Nov 2017 00:00:00 +0000https://gdpark.blog/posts/statistics-06-derivation-of-the-student-s-t-distribution/Where the &lsquo;Student&rsquo; name came from, why we ditch the Z-stat when σ is unknown, and a full derivation of the t-distribution PDF — plus properties and a worked example.https://gdpark.blog/posts/special-relativity-06-time-dilation-and-length-contraction/Fri, 05 May 2017 00:00:00 +0000https://gdpark.blog/posts/special-relativity-06-time-dilation-and-length-contraction/Using spacetime&rsquo;s weird geometry — and a Pythagorean theorem I totally named myself lol — to show why time dilates and lengths contract when you&rsquo;re moving fast.https://gdpark.blog/posts/corporate-finance-06-cash-flow-estimation/Sun, 04 Dec 2016 00:00:00 +0000https://gdpark.blog/posts/corporate-finance-06-cash-flow-estimation/A casual walkthrough of cash flow estimation for investment evaluation — covering incremental flows, opportunity costs, sunk costs, depreciation, and more.https://gdpark.blog/posts/derivatives-06-interest-rate-futures/Wed, 19 Oct 2016 00:00:00 +0000https://gdpark.blog/posts/derivatives-06-interest-rate-futures/Working through quiz problems on T-bond accrued interest, conversion factors, Eurodollar futures P&amp;L, convexity adjustments, and duration-based portfolio hedging.https://gdpark.blog/posts/financial-engineering-06-binomial-model-generalized-n-period/Mon, 03 Oct 2016 00:00:00 +0000https://gdpark.blog/posts/financial-engineering-06-binomial-model-generalized-n-period/We tackle the scary-looking generalized n-period binomial formula and break it down piece by piece — p, u, d, sigma notation and all.https://gdpark.blog/posts/microeconomics-06-long-run-and-short-run-elasticity/Wed, 13 Jul 2016 00:00:00 +0000https://gdpark.blog/posts/microeconomics-06-long-run-and-short-run-elasticity/Elasticity isn&rsquo;t a fixed number — oil demand can be inelastic short-term but flip elastic long-run, and durable goods like airplanes can do the exact opposite.https://gdpark.blog/posts/basic-investing-06-types-of-portfolio-average-returns/Mon, 04 Apr 2016 00:00:00 +0000https://gdpark.blog/posts/basic-investing-06-types-of-portfolio-average-returns/A rundown of the different flavors of portfolio average return — arithmetic, geometric (time-weighted), and dollar-weighted — and when each one makes sense to use.https://gdpark.blog/posts/linear-algebra-06-kernel-and-image/Thu, 21 Jan 2016 00:00:00 +0000https://gdpark.blog/posts/linear-algebra-06-kernel-and-image/We nail down the kernel and image of a linear map, see what injective and surjective really mean, and lock in the theorem that links them all!!!!https://gdpark.blog/posts/macroeconomics-06-deriving-the-aggregate-demand-and-aggregate-supply-curves/Tue, 12 Jan 2016 00:00:00 +0000https://gdpark.blog/posts/macroeconomics-06-deriving-the-aggregate-demand-and-aggregate-supply-curves/Mashing together the short-run goods/financial markets and the medium-run labor market to derive the AD and AS curves — and spoiler: it still can&rsquo;t explain inflation lol.https://gdpark.blog/posts/thermal-statistical-06-chapter-4-practice-problems-part-2/Thu, 31 Dec 2015 00:00:00 +0000https://gdpark.blog/posts/thermal-statistical-06-chapter-4-practice-problems-part-2/Knocking out more Chapter 4 problems — Taylor expansion terms, how wildly Ω blows up when a photon gets absorbed, and grinding out ⟨E⟩ for a harmonic oscillator.https://gdpark.blog/posts/modern-physics-06-general-relativity/Fri, 21 Aug 2015 00:00:00 +0000https://gdpark.blog/posts/modern-physics-06-general-relativity/A fun casual intro to general relativity — from Einstein&rsquo;s 11-year Riemannian geometry grind to the wild idea that gravity actually bends light!https://gdpark.blog/posts/quantum-mechanics-06-the-infinite-square-well/Tue, 11 Aug 2015 00:00:00 +0000https://gdpark.blog/posts/quantum-mechanics-06-the-infinite-square-well/We dive into the infinite square well potential and nail down ψ(x) by slapping on boundary conditions — and honestly, it&rsquo;s basically the same math as electromagnetism lol.https://gdpark.blog/posts/money-banking-06-the-international-financial-system/Tue, 30 Jun 2015 00:00:00 +0000https://gdpark.blog/posts/money-banking-06-the-international-financial-system/We&rsquo;re diving into how central banks intervene in the forex market — buying or selling foreign reserves to move the monetary base, interest rates, and ultimately the exchange rate.https://gdpark.blog/posts/classical-mechanics-06-inertial-and-non-inertial-frames-and-the-galilean-transforma/Tue, 23 Jun 2015 00:00:00 +0000https://gdpark.blog/posts/classical-mechanics-06-inertial-and-non-inertial-frames-and-the-galilean-transforma/Struggling through chapter 5 of General Mechanics I, we dig into what inertial and non-inertial frames actually mean and why Newton&rsquo;s 1st law is sneakier than it looks.https://gdpark.blog/posts/electromagnetism-06-laplace-s-equation/Sat, 15 Nov 2014 00:00:00 +0000https://gdpark.blog/posts/electromagnetism-06-laplace-s-equation/Finally hitting real university-level physics — we dive into Poisson&rsquo;s and Laplace&rsquo;s equations and why differentiating beats integrating when dealing with electric potential.https://gdpark.blog/posts/cfa-l2-07-term-structure-theory/Sun, 17 Nov 2024 00:00:00 +0000https://gdpark.blog/posts/cfa-l2-07-term-structure-theory/A quick rundown of the theories that explain why the yield curve slopes the way it does — and the sneaky exam traps hiding in each one.https://gdpark.blog/posts/cfa-l1-07-inventories-4-lower-of-cost-or-market-lcm/Sun, 09 May 2021 00:00:00 +0000https://gdpark.blog/posts/cfa-l1-07-inventories-4-lower-of-cost-or-market-lcm/We plug the last inventory gap: when year-end hits, unsold stock on the B/S gets valued at whichever is lower — historical cost or market value — that&rsquo;s the LCM method.https://gdpark.blog/posts/statistics-07-derivation-of-the-f-distribution/Sat, 18 Nov 2017 00:00:00 +0000https://gdpark.blog/posts/statistics-07-derivation-of-the-f-distribution/We derive the F-distribution PDF from scratch — turns out it&rsquo;s basically next of kin to the t-distribution — then wrap up with how to actually read an F-table.https://gdpark.blog/posts/special-relativity-07-lorentz-transformation-and-lorentz-boosts/Fri, 05 May 2017 00:00:00 +0000https://gdpark.blog/posts/special-relativity-07-lorentz-transformation-and-lorentz-boosts/We finally wrap up the Lorentz transformation by using hyperbolic angles to assign ct&rsquo;, x&rsquo; coordinates to events in a relatively moving frame!https://gdpark.blog/posts/corporate-finance-07-economic-feasibility-evaluation-of-investment-projects/Mon, 19 Dec 2016 00:00:00 +0000https://gdpark.blog/posts/corporate-finance-07-economic-feasibility-evaluation-of-investment-projects/A rundown of the 6 methods for evaluating investment cash flows — from ARR and payback period to NPV — complete with worked examples and each method&rsquo;s sneaky strengths and weaknesses.https://gdpark.blog/posts/derivatives-07-fundamentals-of-interest-rate-swaps/Wed, 19 Oct 2016 00:00:00 +0000https://gdpark.blog/posts/derivatives-07-fundamentals-of-interest-rate-swaps/A casual walkthrough of how interest rate swaps actually work — fixed vs. floating rates, notional principal, and why companies would sign up for this in the first place.https://gdpark.blog/posts/financial-engineering-07-american-options/Mon, 03 Oct 2016 00:00:00 +0000https://gdpark.blog/posts/financial-engineering-07-american-options/Breaking down the one chunky difference between American and European options — early exercise — and how it flips the whole binomial pricing tree on its head.https://gdpark.blog/posts/microeconomics-07-estimating-demand-and-supply-curves/Thu, 14 Jul 2016 00:00:00 +0000https://gdpark.blog/posts/microeconomics-07-estimating-demand-and-supply-curves/Using elasticity plus a few starred averages pulled from real data, we cook up an approximate linear demand (or supply) curve without having to derive it from scratch.https://gdpark.blog/posts/basic-investing-07-statistical-theory-risk-and-risk-premium/Mon, 04 Apr 2016 00:00:00 +0000https://gdpark.blog/posts/basic-investing-07-statistical-theory-risk-and-risk-premium/A casual dive into the stats behind investment returns — scenarios, expected value, variance, and why the Gaussian is kind of a big deal.https://gdpark.blog/posts/linear-algebra-07-isomorphism-and-the-dimension-theorem/Thu, 21 Jan 2016 00:00:00 +0000https://gdpark.blog/posts/linear-algebra-07-isomorphism-and-the-dimension-theorem/Kernel and image lead us to isomorphism — two vector spaces with the same dimension and a bijective map between them are literally just the same space in disguise!!!!https://gdpark.blog/posts/macroeconomics-07-aggregate-supply-aggregate-demand-analysis/Wed, 13 Jan 2016 00:00:00 +0000https://gdpark.blog/posts/macroeconomics-07-aggregate-supply-aggregate-demand-analysis/A deep dive into AS-AD analysis — tracing exactly what happens to equilibrium when M drops, G rises, or firms jack up their markup, step by step.https://gdpark.blog/posts/thermal-statistical-07-velocity-distribution-function-of-gas-molecules/Thu, 31 Dec 2015 00:00:00 +0000https://gdpark.blog/posts/thermal-statistical-07-velocity-distribution-function-of-gas-molecules/We finally get to handle something real — gases! Starting from a simple ideal gas model, we derive the velocity distribution using the Boltzmann distribution.https://gdpark.blog/posts/modern-physics-07-the-rayleigh-jeans-formula-and-blackbody-radiation/Mon, 24 Aug 2015 00:00:00 +0000https://gdpark.blog/posts/modern-physics-07-the-rayleigh-jeans-formula-and-blackbody-radiation/Diving into Chapter 2 with blackbody radiation — what a black body even is, how to fake one in a lab, and why standing waves are the secret behind that glowing-sword spectrum!https://gdpark.blog/posts/quantum-mechanics-07-the-harmonic-oscillator-and-ladder-operators/Thu, 13 Aug 2015 00:00:00 +0000https://gdpark.blog/posts/quantum-mechanics-07-the-harmonic-oscillator-and-ladder-operators/Turns out spring systems are everywhere in physics because any potential looks like one near its minimum — now let&rsquo;s tackle the quantum harmonic oscillator with ladder operators.https://gdpark.blog/posts/money-banking-07-quantity-theory-of-money-inflation-and-money-demand-keynes-a/Tue, 30 Jun 2015 00:00:00 +0000https://gdpark.blog/posts/money-banking-07-quantity-theory-of-money-inflation-and-money-demand-keynes-a/From Irving Fisher&rsquo;s velocity of money to Keynes&rsquo;s Liquidity Preference Theory — a casual breakdown of how money supply, interest rates, and GDP all connect.https://gdpark.blog/posts/classical-mechanics-07-rotating-reference-frames-coriolis-transverse-and-centrifuga/Wed, 24 Jun 2015 00:00:00 +0000https://gdpark.blog/posts/classical-mechanics-07-rotating-reference-frames-coriolis-transverse-and-centrifuga/We figure out what happens when your coordinate system won&rsquo;t stop spinning — hello Coriolis, centrifugal, and transverse forces!https://gdpark.blog/posts/electromagnetism-07-the-method-of-images/Sun, 16 Nov 2014 00:00:00 +0000https://gdpark.blog/posts/electromagnetism-07-the-method-of-images/We tackle the method of images — a sneaky trick where you swap out a grounded conductor for a phantom charge to nail the potential without breaking a sweat.https://gdpark.blog/posts/cfa-l2-08-yield-curve-risks-and-economic-factors-nelson-siegel-model/Mon, 18 Nov 2024 00:00:00 +0000https://gdpark.blog/posts/cfa-l2-08-yield-curve-risks-and-economic-factors-nelson-siegel-model/Why effective duration falls flat for non-parallel yield curve shifts — and how key rate duration and the Nelson-Siegel model actually fix that.https://gdpark.blog/posts/cfa-l1-08-property-plant-and-equipment-1-acquisition/Sun, 16 May 2021 00:00:00 +0000https://gdpark.blog/posts/cfa-l1-08-property-plant-and-equipment-1-acquisition/We kick off long-lived assets by diving into PP&amp;E acquisition — what counts as an asset, why it&rsquo;s not just an expense, and how initial recognition works.https://gdpark.blog/posts/statistics-08-hypothesis-testing/Tue, 21 Nov 2017 00:00:00 +0000https://gdpark.blog/posts/statistics-08-hypothesis-testing/A casual walkthrough of hypothesis testing basics — null vs. alternative hypotheses, Z-statistics, and how to decide when to reject what the data&rsquo;s telling you.https://gdpark.blog/posts/special-relativity-08-four-vectors/Sat, 06 May 2017 00:00:00 +0000https://gdpark.blog/posts/special-relativity-08-four-vectors/Closing out the special-relativity series with a look at four-vectors — their notation, basis vectors, and how spacetime intervals set them apart from plain 3D vectors!https://gdpark.blog/posts/corporate-finance-08-risk-and-project-selection-dominance-principle-and-return-ri/Mon, 19 Dec 2016 00:00:00 +0000https://gdpark.blog/posts/corporate-finance-08-risk-and-project-selection-dominance-principle-and-return-ri/A chill walkthrough of how risk is actually just quantified volatility — using probability distributions, expected returns, and variance to figure out which projects are worth picking.https://gdpark.blog/posts/derivatives-08-swaps/Mon, 21 Nov 2016 00:00:00 +0000https://gdpark.blog/posts/derivatives-08-swaps/A casual breakdown of how interest rate swaps work — exchanging fixed and floating payments on a notional principal, and why anyone would actually do that.https://gdpark.blog/posts/financial-engineering-08-wiener-process/Mon, 03 Oct 2016 00:00:00 +0000https://gdpark.blog/posts/financial-engineering-08-wiener-process/Can&rsquo;t derive Black-Scholes and not even gonna try — instead we&rsquo;re just coding it up while taking a detour through Brownian motion and Geometric Brownian Motion.https://gdpark.blog/posts/microeconomics-08-preferences/Thu, 14 Jul 2016 00:00:00 +0000https://gdpark.blog/posts/microeconomics-08-preferences/A casual intro to consumer choice theory — breaking down what a &lsquo;basket&rsquo; is, why we pretend only two goods exist, and the &lsquo;more is better&rsquo; axiom.https://gdpark.blog/posts/basic-investing-08-inflation-indexed-bonds-tips/Mon, 04 Apr 2016 00:00:00 +0000https://gdpark.blog/posts/basic-investing-08-inflation-indexed-bonds-tips/Real vs. nominal interest rates, the Fisher equation, and a quick intro to TIPS — the inflation-protected bond that hands you the truly risk-free rate.https://gdpark.blog/posts/linear-algebra-08-change-of-basis/Fri, 22 Jan 2016 00:00:00 +0000https://gdpark.blog/posts/linear-algebra-08-change-of-basis/Same linear map, totally different matrix depending on your basis — let&rsquo;s dig into why that happens and how A and A&rsquo; are actually related.https://gdpark.blog/posts/macroeconomics-08-the-phillips-curve-unemployment-and-inflation/Wed, 13 Jan 2016 00:00:00 +0000https://gdpark.blog/posts/macroeconomics-08-the-phillips-curve-unemployment-and-inflation/Diving into the Phillips curve — why the unemployment-inflation trade-off was such a big deal, how we derive it from scratch, and why it totally fell apart in the 70s.https://gdpark.blog/posts/thermal-statistical-08-maxwell-boltzmann-speed-distribution/Thu, 31 Dec 2015 00:00:00 +0000https://gdpark.blog/posts/thermal-statistical-08-maxwell-boltzmann-speed-distribution/We ditch direction entirely and dive into velocity space to figure out the Maxwell-Boltzmann speed distribution — because who cares which way the gas is flying lol.https://gdpark.blog/posts/modern-physics-08-the-photoelectric-effect/Mon, 24 Aug 2015 00:00:00 +0000https://gdpark.blog/posts/modern-physics-08-the-photoelectric-effect/Ever wonder why Einstein won the Nobel Prize for the photoelectric effect and not relativity?! Let&rsquo;s dig into the experiment that changed everything!https://gdpark.blog/posts/quantum-mechanics-08-ladder-operators/Thu, 13 Aug 2015 00:00:00 +0000https://gdpark.blog/posts/quantum-mechanics-08-ladder-operators/We dig into how the normalization constants Aₙ behave each time the raising operator is applied, so we can express every excited state ψₙ neatly in terms of n!https://gdpark.blog/posts/money-banking-08-the-is-curve/Wed, 01 Jul 2015 00:00:00 +0000https://gdpark.blog/posts/money-banking-08-the-is-curve/Breaking down the IS curve — which maps the real interest rate to national income in goods-market equilibrium — because you&rsquo;d better know this one well!https://gdpark.blog/posts/classical-mechanics-08-kepler-s-laws-ellipse-law-equal-area-law-and-harmonic-law-pa/Thu, 25 Jun 2015 00:00:00 +0000https://gdpark.blog/posts/classical-mechanics-08-kepler-s-laws-ellipse-law-equal-area-law-and-harmonic-law-pa/Newton slickly combined Galileo&rsquo;s earthly motion with Kepler&rsquo;s celestial laws into universal gravitation, and yes — you really can treat a planet as a point mass!!https://gdpark.blog/posts/electromagnetism-08-separation-of-variables/Mon, 17 Nov 2014 00:00:00 +0000https://gdpark.blog/posts/electromagnetism-08-separation-of-variables/Learn the separation of variables trick for solving the Laplace equation — assume V = X(x)·Y(y), plug in, and hunt down those coefficients with boundary conditions!https://gdpark.blog/posts/cfa-l2-09-yield-curve-volatility-and-term-premium/Wed, 20 Nov 2024 00:00:00 +0000https://gdpark.blog/posts/cfa-l2-09-yield-curve-volatility-and-term-premium/Finally wrapping up Chapter 1 — yield curve volatility, term premium, and how the curve twists with expansions, recessions, and flight-to-quality~https://gdpark.blog/posts/cfa-l1-09-property-plant-and-equipment-2-depreciation/Sun, 23 May 2021 00:00:00 +0000https://gdpark.blog/posts/cfa-l1-09-property-plant-and-equipment-2-depreciation/A casual breakdown of accounting depreciation for PPE — turns out it&rsquo;s about spreading costs over useful life, not just saying an asset lost value.https://gdpark.blog/posts/statistics-09-a-hasty-conclusion/Tue, 21 Nov 2017 00:00:00 +0000https://gdpark.blog/posts/statistics-09-a-hasty-conclusion/Hastily wrapping up the stats fundamentals series because the math foundation got too shaky — no promises on when the next part&rsquo;s coming, lol.https://gdpark.blog/posts/corporate-finance-09-portfolio-variance-and-covariance-matrix/Mon, 19 Dec 2016 00:00:00 +0000https://gdpark.blog/posts/corporate-finance-09-portfolio-variance-and-covariance-matrix/We level up from single-stock picking to full portfolio selection — figuring out how to compute a portfolio&rsquo;s μ and σ using the covariance matrix.https://gdpark.blog/posts/derivatives-09-swaps-practice-problems/Tue, 22 Nov 2016 00:00:00 +0000https://gdpark.blog/posts/derivatives-09-swaps-practice-problems/Working through classic swap design problems — comparative advantage, LIBOR discounting, and currency swaps — with the actual numbers worked out step by step.https://gdpark.blog/posts/financial-engineering-09-monte-carlo-method/Thu, 20 Oct 2016 00:00:00 +0000https://gdpark.blog/posts/financial-engineering-09-monte-carlo-method/Stumbled into a stats lecture and finally got it — turns out if you scatter enough random dots and do a little ratio math, you can actually calculate π. Wild, right?https://gdpark.blog/posts/microeconomics-09-indifference-curves-and-utility-functions/Thu, 14 Jul 2016 00:00:00 +0000https://gdpark.blog/posts/microeconomics-09-indifference-curves-and-utility-functions/We get into indifference curves and utility functions — why some baskets make you equally happy, and why piling on more stuff gives you less of a kick each time.https://gdpark.blog/posts/basic-investing-09-capital-allocation-line-cal/Tue, 05 Apr 2016 00:00:00 +0000https://gdpark.blog/posts/basic-investing-09-capital-allocation-line-cal/How slicing your cash between the spicy risky stuff and the boring risk-free stuff moves your expected return and volatility — that&rsquo;s the Capital Allocation Line.https://gdpark.blog/posts/linear-algebra-09-systems-of-linear-equations-and-gaussian-elimination/Fri, 22 Jan 2016 00:00:00 +0000https://gdpark.blog/posts/linear-algebra-09-systems-of-linear-equations-and-gaussian-elimination/A casual walkthrough of systems of linear equations — from middle-school basics all the way up to matrix form, homogeneous vs. non-homogeneous, and Gaussian elimination.https://gdpark.blog/posts/macroeconomics-09-okun-s-law/Thu, 14 Jan 2016 00:00:00 +0000https://gdpark.blog/posts/macroeconomics-09-okun-s-law/We finally tackle Okun&rsquo;s Law — the bridge between economic growth and unemployment that sets us up to fix the inflation gap in our AD-AS model.https://gdpark.blog/posts/thermal-statistical-09-proofs-of-integrals-commonly-used-in-thermal-and-statistical/Thu, 31 Dec 2015 00:00:00 +0000https://gdpark.blog/posts/thermal-statistical-09-proofs-of-integrals-commonly-used-in-thermal-and-statistical/Starting from the Gaussian integral, I keep differentiating with respect to α to build up all those handy x^n·e^(-αx²) formulas you keep needing in thermal and stat mech.https://gdpark.blog/posts/modern-physics-09-x-rays/Tue, 25 Aug 2015 00:00:00 +0000https://gdpark.blog/posts/modern-physics-09-x-rays/X-rays are basically the reverse of the photoelectric effect — slam electrons into a plate with insane voltage and boom, mystery radiation appears (hence the &lsquo;x&rsquo;!).https://gdpark.blog/posts/quantum-mechanics-09-algebraic-solution-to-the-harmonic-oscillator/Fri, 14 Aug 2015 00:00:00 +0000https://gdpark.blog/posts/quantum-mechanics-09-algebraic-solution-to-the-harmonic-oscillator/Jumping straight into brute-force solving the quantum harmonic oscillator, simplifying the Schrödinger equation with a substitution and chasing down energy quantization~~~~https://gdpark.blog/posts/money-banking-09-the-mp-curve-and-the-ad-curve/Wed, 01 Jul 2015 00:00:00 +0000https://gdpark.blog/posts/money-banking-09-the-mp-curve-and-the-ad-curve/We&rsquo;re diving into the MP curve — how central banks fiddle with nominal rates to steer real interest rates — then combining it with the IS curve to derive the AD curve!!https://gdpark.blog/posts/classical-mechanics-09-kepler-s-laws-ellipse-law-equal-area-law-and-harmonic-law-pa/Thu, 25 Jun 2015 00:00:00 +0000https://gdpark.blog/posts/classical-mechanics-09-kepler-s-laws-ellipse-law-equal-area-law-and-harmonic-law-pa/We derive the polar-coordinate equation of an ellipse from scratch to confirm, in proper &lsquo;Ahhhh~~~~&rsquo; fashion, that the orbit equation from last time really is an ellipse.https://gdpark.blog/posts/electromagnetism-09-multipole-expansion/Mon, 17 Nov 2014 00:00:00 +0000https://gdpark.blog/posts/electromagnetism-09-multipole-expansion/A casual dive into multipole expansion — how charge distributions look like point charges from far away, and why potential falls off faster for dipoles and quadrupoles~!https://gdpark.blog/posts/cfa-l2-10-the-arbitrage-free-valuation-framework/Wed, 27 Nov 2024 00:00:00 +0000https://gdpark.blog/posts/cfa-l2-10-the-arbitrage-free-valuation-framework/Chapter 2 kicks off with arbitrage-free bond valuation — value additivity, dominance, and the binomial interest rate tree where volatility is the secret sauce!https://gdpark.blog/posts/cfa-l1-10-property-plant-and-equipment-3-revaluation-model/Sat, 29 May 2021 00:00:00 +0000https://gdpark.blog/posts/cfa-l1-10-property-plant-and-equipment-3-revaluation-model/IFRS lets you pick the Revaluation Model for PPE — and here&rsquo;s why that&rsquo;s a big deal (and a headache) compared to just sticking with the Cost Model.https://gdpark.blog/posts/corporate-finance-10-minimum-variance-portfolio/Tue, 20 Dec 2016 00:00:00 +0000https://gdpark.blog/posts/corporate-finance-10-minimum-variance-portfolio/Walks through how diversifying stocks makes individual risk basically vanish while covariance dominates, with a hands-on two-stock example using correlation coefficients 0, 1, and -1.https://gdpark.blog/posts/derivatives-10-options/Mon, 28 Nov 2016 00:00:00 +0000https://gdpark.blog/posts/derivatives-10-options/A casual intro to options — call vs. put, why theoretical prices even matter, and how Black-Scholes blew the whole market wide open.https://gdpark.blog/posts/financial-engineering-10-black-scholes-formula/Thu, 20 Oct 2016 00:00:00 +0000https://gdpark.blog/posts/financial-engineering-10-black-scholes-formula/Can&rsquo;t derive it (lmao), but we can totally code it up — walking through the Black-Scholes pricing formula and computing actual call and put prices.https://gdpark.blog/posts/microeconomics-10-marginal-rate-of-substitution/Thu, 14 Jul 2016 00:00:00 +0000https://gdpark.blog/posts/microeconomics-10-marginal-rate-of-substitution/MRS is basically something we already know deep down — here&rsquo;s why ∆y is always negative on the indifference curve, plus a Coke vs. Pepsi reality check on diminishing MRS.https://gdpark.blog/posts/basic-investing-10-diversification/Fri, 15 Apr 2016 00:00:00 +0000https://gdpark.blog/posts/basic-investing-10-diversification/More stocks = less risk, but only up to a point — turns out there&rsquo;s this pesky market risk that no amount of diversification can ever kill.https://gdpark.blog/posts/linear-algebra-10-elementary-row-operation-matrices-erom/Sat, 23 Jan 2016 00:00:00 +0000https://gdpark.blog/posts/linear-algebra-10-elementary-row-operation-matrices-erom/Back at it with the general solution of AX = B — recapping RREF, breaking down dependent vs. independent variables, and chasing down X_0 and ker A.https://gdpark.blog/posts/macroeconomics-10-stylized-facts-of-economic-growth/Thu, 14 Jan 2016 00:00:00 +0000https://gdpark.blog/posts/macroeconomics-10-stylized-facts-of-economic-growth/We&rsquo;re finally zooming out to the long run — why do some countries keep winning? Enter Solow&rsquo;s aggregate production function Y = F(K, N), and the real fun begins.https://gdpark.blog/posts/thermal-statistical-10-expected-speed-expected-energy-and-statistical-analysis-of-i/Thu, 31 Dec 2015 00:00:00 +0000https://gdpark.blog/posts/thermal-statistical-10-expected-speed-expected-energy-and-statistical-analysis-of-i/We ditch talking distributions and actually calculate averages — finding the expected speed and energy of an ideal gas molecule using integrals and odd-function tricks.https://gdpark.blog/posts/modern-physics-10-the-compton-effect/Tue, 25 Aug 2015 00:00:00 +0000https://gdpark.blog/posts/modern-physics-10-the-compton-effect/Compton&rsquo;s wild experiment pits X-ray photons head-on against electrons and uses conservation of momentum &amp; energy to prove light really does act like a particle.https://gdpark.blog/posts/quantum-mechanics-10-the-free-particle/Mon, 17 Aug 2015 00:00:00 +0000https://gdpark.blog/posts/quantum-mechanics-10-the-free-particle/We tackle the free particle (V=0) case of the Schrödinger equation, discover why normalization is a headache, and unpack what wave numbers actually mean — brace yourself for a mini mental meltdown!https://gdpark.blog/posts/money-banking-10-the-as-curve-aggregate-supply-curve/Wed, 01 Jul 2015 00:00:00 +0000https://gdpark.blog/posts/money-banking-10-the-as-curve-aggregate-supply-curve/A casual, student-eye-view breakdown of the AS curve — why output and inflation move together and what short-run vs. long-run aggregate supply actually means.https://gdpark.blog/posts/classical-mechanics-10-the-orbit-equation-via-energy-methods/Thu, 25 Jun 2015 00:00:00 +0000https://gdpark.blog/posts/classical-mechanics-10-the-orbit-equation-via-energy-methods/We rederive the orbit equation using energy conservation — kinetic plus potential — then sneak in angular momentum and the u=1/r substitution to nail the same result.https://gdpark.blog/posts/electromagnetism-10-polarization/Tue, 18 Nov 2014 00:00:00 +0000https://gdpark.blog/posts/electromagnetism-10-polarization/We&rsquo;re diving into electrostatic fields inside matter — atoms polarize in an external E field, giving us dipole moments, atomic polarizability α, and polarization density P!https://gdpark.blog/posts/cfa-l2-11-binomial-trees-part-2/Mon, 16 Dec 2024 00:00:00 +0000https://gdpark.blog/posts/cfa-l2-11-binomial-trees-part-2/This time we build the interest rate tree from scratch — calibration, e^{2σ} forward-rate spacing, and all — then value it via backward induction or pathwise.https://gdpark.blog/posts/cfa-l2-11-valuing-option-free-bonds-with-the-binomial-model/Sat, 14 Dec 2024 00:00:00 +0000https://gdpark.blog/posts/cfa-l2-11-valuing-option-free-bonds-with-the-binomial-model/A quick walkthrough of valuing option-free bonds using backward induction on a binomial tree, plus why pathwise valuation matters when cash flows are path-dependent.https://gdpark.blog/posts/cfa-l1-11-property-plant-and-equipment-4-impairment/Sat, 29 May 2021 00:00:00 +0000https://gdpark.blog/posts/cfa-l1-11-property-plant-and-equipment-4-impairment/Breaks down PPE impairment — what &lsquo;gone bad&rsquo; actually means, how US-GAAP&rsquo;s two-step recovery test works, and where IFRS handles things differently.https://gdpark.blog/posts/statistics-11-gauss-markov-theorem-and-the-proof-of-blue/Sun, 12 Nov 2017 00:00:00 +0000https://gdpark.blog/posts/statistics-11-gauss-markov-theorem-and-the-proof-of-blue/Digging into what OLS actually guarantees — the 5 assumptions behind linear regression and why they make your estimates BLUE according to the Gauss-Markov theorem.https://gdpark.blog/posts/corporate-finance-11-efficient-frontier-markowitz/Wed, 21 Dec 2016 00:00:00 +0000https://gdpark.blog/posts/corporate-finance-11-efficient-frontier-markowitz/We dive into the Markowitz efficient frontier — plotting every possible portfolio combo in expected return vs. standard deviation space to find the best bang for your risk buck.https://gdpark.blog/posts/derivatives-11-properties-of-stock-options/Mon, 28 Nov 2016 00:00:00 +0000https://gdpark.blog/posts/derivatives-11-properties-of-stock-options/Breaking down every variable that moves option prices — S, K, T, σ, r, and D — and why European vs. American options handle time to expiration differently.https://gdpark.blog/posts/financial-engineering-11-volatility/Thu, 20 Oct 2016 00:00:00 +0000https://gdpark.blog/posts/financial-engineering-11-volatility/Breaking down historical and implied volatility — what they are, why we care, and how to actually compute historical vol from weekly price data in VBA.https://gdpark.blog/posts/microeconomics-11-special-utility-functions/Fri, 15 Jul 2016 00:00:00 +0000https://gdpark.blog/posts/microeconomics-11-special-utility-functions/We dive into the &lsquo;special cases&rsquo; where diminishing marginal utility just doesn&rsquo;t apply — perfect substitutes and perfect complements, with all their quirks!https://gdpark.blog/posts/basic-investing-11-sources-of-various-risks/Sat, 16 Apr 2016 00:00:00 +0000https://gdpark.blog/posts/basic-investing-11-sources-of-various-risks/Excess return broken down into three buckets: market vibes (β), totally-unpredictable company drama (e), and that mysterious security alpha (α).https://gdpark.blog/posts/linear-algebra-11-the-rank-theorem/Sat, 23 Jan 2016 00:00:00 +0000https://gdpark.blog/posts/linear-algebra-11-the-rank-theorem/We poke at whether RREF is unique, then laser in on invertible matrices to show their RREF has to be the identity — and that&rsquo;s the Rank Theorem taking shape!https://gdpark.blog/posts/macroeconomics-11-the-relationship-between-savings-rate-and-output/Fri, 15 Jan 2016 00:00:00 +0000https://gdpark.blog/posts/macroeconomics-11-the-relationship-between-savings-rate-and-output/We dig into how the savings rate connects to capital per person — and why that matters for output, with a quick detour through flow vs. stock.https://gdpark.blog/posts/thermal-statistical-11-ideal-gas-equation-of-state-and-pressure/Fri, 01 Jan 2016 00:00:00 +0000https://gdpark.blog/posts/thermal-statistical-11-ideal-gas-equation-of-state-and-pressure/Diving into Chapter 6 to microscopically derive PV=nRT, kicking things off with the definition of pressure and then wrestling with the surprisingly weird world of solid angles.https://gdpark.blog/posts/modern-physics-11-wave-properties-of-particles/Tue, 25 Aug 2015 00:00:00 +0000https://gdpark.blog/posts/modern-physics-11-wave-properties-of-particles/If light can act like a particle, why not flip it — turns out matter has wave properties too, and that wild idea leads straight to de Broglie wavelengths and Schrödinger&rsquo;s equation!https://gdpark.blog/posts/quantum-mechanics-11-the-delta-function-potential/Mon, 17 Aug 2015 00:00:00 +0000https://gdpark.blog/posts/quantum-mechanics-11-the-delta-function-potential/Diving into the delta-function potential — with a quick pit stop on bound vs. scattering states and why Dirac made the delta function actually make sense~!!https://gdpark.blog/posts/money-banking-11-aggregate-supply-and-aggregate-demand/Thu, 02 Jul 2015 00:00:00 +0000https://gdpark.blog/posts/money-banking-11-aggregate-supply-and-aggregate-demand/We&rsquo;re throwing AD and AS together on one graph, diving into equilibrium, output gaps, and how the self-correcting mechanism handles demand and supply shocks!!https://gdpark.blog/posts/classical-mechanics-11-orbital-stability/Thu, 25 Jun 2015 00:00:00 +0000https://gdpark.blog/posts/classical-mechanics-11-orbital-stability/Why does a circular orbit stay stable instead of flying off after a tiny shock?! Spoiler: there&rsquo;s a sneaky spring constant hiding in the equation of motion!https://gdpark.blog/posts/electromagnetism-11-bound-charge-density/Tue, 18 Nov 2014 00:00:00 +0000https://gdpark.blog/posts/electromagnetism-11-bound-charge-density/Working out the intuition behind σ_b = P·n̂ and ρ_b = -∇·P by thinking of P as opposite charges piled up on either side of a unit volume.https://gdpark.blog/posts/cfa-l2-12-term-structure-models-cir-vasicek-ho-lee-and-kwk/Mon, 16 Dec 2024 00:00:00 +0000https://gdpark.blog/posts/cfa-l2-12-term-structure-models-cir-vasicek-ho-lee-and-kwk/A rundown of CIR, Vasicek, Ho-Lee, and KWK — what makes each term structure model tick and the key characteristics you actually need to nail for the exam.https://gdpark.blog/posts/cfa-l1-12-investment-property/Sun, 06 Jun 2021 00:00:00 +0000https://gdpark.blog/posts/cfa-l1-12-investment-property/Investment property is just rental real estate — not speculation — and here&rsquo;s how it differs from PPE under IFRS (spoiler: US GAAP doesn&rsquo;t even have this account).https://gdpark.blog/posts/statistics-12-python-poisson-exponential-and-gamma-distributions/Sun, 15 Sep 2019 00:00:00 +0000https://gdpark.blog/posts/statistics-12-python-poisson-exponential-and-gamma-distributions/Just plotted the Poisson, Exponential, and Gamma distributions in Python straight from Wikipedia&rsquo;s parameters — skipped the random-variable cross-checks and kept it chill this time.https://gdpark.blog/posts/corporate-finance-12-capital-asset-pricing-model-capm/Wed, 21 Dec 2016 00:00:00 +0000https://gdpark.blog/posts/corporate-finance-12-capital-asset-pricing-model-capm/We pick up where Markowitz left off, toss in a risk-free asset, find the one tangent point that becomes the Market Portfolio, and see why the S&amp;P 500 basically fits the bill.https://gdpark.blog/posts/derivatives-12-options-practice-problems/Mon, 28 Nov 2016 00:00:00 +0000https://gdpark.blog/posts/derivatives-12-options-practice-problems/Working through options pricing problems — lower bounds on calls and puts, why American options always beat intrinsic value, and when put-call parity breaks down.https://gdpark.blog/posts/financial-engineering-12-midterm-exam-review/Thu, 17 Nov 2016 00:00:00 +0000https://gdpark.blog/posts/financial-engineering-12-midterm-exam-review/A visual midterm exam review covering options Greeks like delta and gamma, dynamic delta hedging strategies, and related VBA concepts.https://gdpark.blog/posts/microeconomics-12-utility-maximization/Fri, 15 Jul 2016 00:00:00 +0000https://gdpark.blog/posts/microeconomics-12-utility-maximization/Mr. Nodap&rsquo;s got 10,000 won and a choice between booze and smokes — here&rsquo;s how utility curves and the budget line team up to nail the one combo that maxes him out.https://gdpark.blog/posts/basic-investing-12-efficient-market-hypothesis-emh/Wed, 11 May 2016 00:00:00 +0000https://gdpark.blog/posts/basic-investing-12-efficient-market-hypothesis-emh/How economists took Kendall&rsquo;s &lsquo;prices are random&rsquo; bombshell and flipped it into the EMH — keeping the &lsquo;humans are rational&rsquo; assumption perfectly intact.https://gdpark.blog/posts/linear-algebra-12-multilinear-forms-alternating-forms-and-the-epsilon-symbol/Sun, 24 Jan 2016 00:00:00 +0000https://gdpark.blog/posts/linear-algebra-12-multilinear-forms-alternating-forms-and-the-epsilon-symbol/We finally tackle <em>how</em> to tell if a matrix is invertible by wading through multilinear forms, alternating forms, and the epsilon symbol — all the groundwork for determinants!https://gdpark.blog/posts/macroeconomics-12-the-cobb-douglas-production-function/Fri, 15 Jan 2016 00:00:00 +0000https://gdpark.blog/posts/macroeconomics-12-the-cobb-douglas-production-function/We finally pin down that vague f(K/N) with the Cobb-Douglas production function and crank through the math to get a concrete steady-state output formula.https://gdpark.blog/posts/thermal-statistical-12-chapter-6-practice-problems/Fri, 01 Jan 2016 00:00:00 +0000https://gdpark.blog/posts/thermal-statistical-12-chapter-6-practice-problems/Working through Chapter 6 practice problems on ideal gas volume at STP, kinetic energy density, and what happens to the air in your room when you turn up the heat.https://gdpark.blog/posts/modern-physics-12-atomic-models-and-the-bohr-model/Tue, 25 Aug 2015 00:00:00 +0000https://gdpark.blog/posts/modern-physics-12-atomic-models-and-the-bohr-model/We dig into why the old orbital atomic model is totally wrong — spinning electrons radiate energy and collapse — and set the stage for Bohr&rsquo;s fix.https://gdpark.blog/posts/quantum-mechanics-12-delta-function-potential-scattering-states-and-quantum-tunne/Mon, 17 Aug 2015 00:00:00 +0000https://gdpark.blog/posts/quantum-mechanics-12-delta-function-potential-scattering-states-and-quantum-tunne/Picking up where we left off, we tackle the E &gt; 0 scattering states of the delta-function potential and work through boundary conditions to uncover quantum tunneling!https://gdpark.blog/posts/money-banking-12-monetary-policy-theory/Thu, 02 Jul 2015 00:00:00 +0000https://gdpark.blog/posts/money-banking-12-monetary-policy-theory/A casual breakdown of the activist vs. nonactivist debate in monetary policy — why deflation is scarier than it sounds, and how central banks chase that ~1–3% inflation sweet spot.https://gdpark.blog/posts/classical-mechanics-12-series-quick-reference-overview/Thu, 25 Jun 2015 00:00:00 +0000https://gdpark.blog/posts/classical-mechanics-12-series-quick-reference-overview/A handy visual quick-reference overview of the series, covering all the key info you need at a glance.https://gdpark.blog/posts/electromagnetism-12-electric-displacement/Wed, 19 Nov 2014 00:00:00 +0000https://gdpark.blog/posts/electromagnetism-12-electric-displacement/We meet the D vector — electric displacement — and see how it lets us handle electric fields inside dielectrics without worrying about the polarization effects!https://gdpark.blog/posts/cfa-l2-13-bonds-with-embedded-options/Wed, 25 Dec 2024 00:00:00 +0000https://gdpark.blog/posts/cfa-l2-13-bonds-with-embedded-options/A quick rundown of callable vs. putable bonds — who holds the option, why callables are cheaper, and how to back out the embedded option value from the straight bond price.https://gdpark.blog/posts/cfa-l1-13-intangible-assets/Sat, 12 Jun 2021 00:00:00 +0000https://gdpark.blog/posts/cfa-l1-13-intangible-assets/A breakdown of intangible assets — what they are, how they stack up against PP&amp;E, and the surprisingly messy rules for getting them onto the B/S.https://gdpark.blog/posts/machine-learning-13-logistic-regression-part-3/Sat, 23 Nov 2019 00:00:00 +0000https://gdpark.blog/posts/machine-learning-13-logistic-regression-part-3/We bend our binary logistic regression into a multi-class classifier using the one-vs-rest trick, then try it out on sklearn&rsquo;s iris dataset.https://gdpark.blog/posts/statistics-13-python-chi-squared-student-s-t-and-f-distributions/Sat, 28 Sep 2019 00:00:00 +0000https://gdpark.blog/posts/statistics-13-python-chi-squared-student-s-t-and-f-distributions/Wrapped up derivations of the chi-squared, t-, and F-distributions — and honestly it&rsquo;s just reminded me how shaky my stats fundamentals still are lol.https://gdpark.blog/posts/corporate-finance-13-cost-of-capital/Wed, 21 Dec 2016 00:00:00 +0000https://gdpark.blog/posts/corporate-finance-13-cost-of-capital/Before diving into capital structure theory, let&rsquo;s get the basics straight — cost of debt, cost of equity, and why k is the discount rate that actually matters.https://gdpark.blog/posts/derivatives-13-options-trading-strategies-part-1-spreads-bull-spread-bear-s/Wed, 14 Dec 2016 00:00:00 +0000https://gdpark.blog/posts/derivatives-13-options-trading-strategies-part-1-spreads-bull-spread-bear-s/We finally stop staring at one lonely option and start building real portfolios — covered calls, protective puts, and every spread you&rsquo;d want to know.https://gdpark.blog/posts/financial-engineering-13-implied-volatility/Fri, 09 Dec 2016 00:00:00 +0000https://gdpark.blog/posts/financial-engineering-13-implied-volatility/Flip the BS formula backwards — plug in the real market price, leave σ blank, and whatever volatility makes it work? That&rsquo;s implied volatility, baby.https://gdpark.blog/posts/microeconomics-13-utility-maximization-with-special-utility-functions/Fri, 15 Jul 2016 00:00:00 +0000https://gdpark.blog/posts/microeconomics-13-utility-maximization-with-special-utility-functions/We knock out utility maximization for two funky non-Cobb-Douglas functions — one with a surprising shape and one for perfect substitutes — and spoiler: both consumers go all-in on x!https://gdpark.blog/posts/basic-investing-13-behavioral-finance/Thu, 12 May 2016 00:00:00 +0000https://gdpark.blog/posts/basic-investing-13-behavioral-finance/Behavioral finance argues human irrationality — forecast errors, overconfidence, conservatism bias — actually moves markets in ways the efficient market hypothesis can&rsquo;t explain.https://gdpark.blog/posts/linear-algebra-13-similar-matrices/Sun, 24 Jan 2016 00:00:00 +0000https://gdpark.blog/posts/linear-algebra-13-similar-matrices/Before we can actually crunch a determinant, we load up on similar matrices — plus why det A = 0 is the snap-decision test for invertibility.https://gdpark.blog/posts/macroeconomics-13-solow-residual-a-macroeconomic-approach-to-technological-pro/Sat, 16 Jan 2016 00:00:00 +0000https://gdpark.blog/posts/macroeconomics-13-solow-residual-a-macroeconomic-approach-to-technological-pro/We finally stop pinning labor productivity A at 1, bundle it with N into &rsquo;effective labor&rsquo; AN, and roll into the Solow residual framework for thinking about tech progress.https://gdpark.blog/posts/thermal-statistical-13-graham-s-law-of-effusion/Fri, 01 Jan 2016 00:00:00 +0000https://gdpark.blog/posts/thermal-statistical-13-graham-s-law-of-effusion/We derive Graham&rsquo;s Law of effusion from first principles using flux and the Maxwell-Boltzmann distribution — turns out it&rsquo;s way easier than it sounds!https://gdpark.blog/posts/quantum-mechanics-13-the-finite-square-well/Mon, 17 Aug 2015 00:00:00 +0000https://gdpark.blog/posts/quantum-mechanics-13-the-finite-square-well/Powering through the finite square well — tackling bound and scattering states, boundary conditions, and wave functions one painful step at a time.https://gdpark.blog/posts/money-banking-13-money-and-banking-at-a-glance-series-overview/Thu, 02 Jul 2015 00:00:00 +0000https://gdpark.blog/posts/money-banking-13-money-and-banking-at-a-glance-series-overview/A visual series overview covering the essentials of money and banking — everything you need to get up to speed fast.https://gdpark.blog/posts/electromagnetism-13-linear-dielectrics/Wed, 19 Nov 2014 00:00:00 +0000https://gdpark.blog/posts/electromagnetism-13-linear-dielectrics/We dig into linear dielectrics (P = ε₀χₑE), untangle chi vs. epsilon, and see why the displacement field D = εE saves us from an infinite E↔P feedback loop.https://gdpark.blog/posts/classical-mechanics-13-center-of-mass-cm/Fri, 07 Nov 2014 00:00:00 +0000https://gdpark.blog/posts/classical-mechanics-13-center-of-mass-cm/Center of mass is basically lumping all your particles into one spot — a weighted average of positions that makes multi-particle dynamics way less of a headache!https://gdpark.blog/posts/cfa-l2-14-valuing-bonds-with-embedded-options-part-1/Wed, 25 Dec 2024 00:00:00 +0000https://gdpark.blog/posts/cfa-l2-14-valuing-bonds-with-embedded-options-part-1/We finally put the Binomial Tree Framework to work pricing callable and putable bonds, walking through how cash flows shift at every node as rates move.https://gdpark.blog/posts/cfa-l1-14-income-tax-expense/Sat, 19 Jun 2021 00:00:00 +0000https://gdpark.blog/posts/cfa-l1-14-income-tax-expense/Breaking down how corporate tax expense actually works — from taxable income reconciliation to current vs. deferred tax — purely from the CFA angle, heh.https://gdpark.blog/posts/corporate-finance-14-capital-structure-theory-and-the-modigliani-miller-theorem/Thu, 22 Dec 2016 00:00:00 +0000https://gdpark.blog/posts/corporate-finance-14-capital-structure-theory-and-the-modigliani-miller-theorem/We break down capital structure theory — from the traditional approach to MM (1958) and modified MM (1963) — and why minimizing WACC is the whole game.https://gdpark.blog/posts/derivatives-14-options-trading-strategies-part-2-combinations-and-practice/Wed, 14 Dec 2016 00:00:00 +0000https://gdpark.blog/posts/derivatives-14-options-trading-strategies-part-2-combinations-and-practice/Wrapping up options combinations — straddles, strangles, strips, and straps — and figuring out which one to pick depending on your vol view and your wallet.https://gdpark.blog/posts/financial-engineering-14-bisection-method-weighted-bisection-method/Sun, 11 Dec 2016 00:00:00 +0000https://gdpark.blog/posts/financial-engineering-14-bisection-method-weighted-bisection-method/A super chill walkthrough of the bisection method — arguably the simplest root-finding algorithm ever — plus a weighted twist, with Python code and visuals.https://gdpark.blog/posts/microeconomics-14-utility-maximization-with-coupons-and-subsidies/Fri, 15 Jul 2016 00:00:00 +0000https://gdpark.blog/posts/microeconomics-14-utility-maximization-with-coupons-and-subsidies/Walking through how government housing subsidies mess with your budget line — turns out it&rsquo;s not as scary as it sounds, just a little funky shaped.https://gdpark.blog/posts/basic-investing-14-debt-securities/Tue, 24 May 2016 00:00:00 +0000https://gdpark.blog/posts/basic-investing-14-debt-securities/A casual grand tour of bond basics — types, coupons, bearer bonds, and why YTM is the number issuers actually care about.https://gdpark.blog/posts/modern-physics-14-a-basic-understanding-of-the-photolithography-process/Tue, 22 Mar 2016 00:00:00 +0000https://gdpark.blog/posts/modern-physics-14-a-basic-understanding-of-the-photolithography-process/A casual breakdown of the photolithography process — from photoresist types to clean rooms — by someone genuinely shocked engineering is this hard.https://gdpark.blog/posts/linear-algebra-14-determinants/Mon, 25 Jan 2016 00:00:00 +0000https://gdpark.blog/posts/linear-algebra-14-determinants/We finally crack the determinant open — from 2x2 all the way to 4x4 — by tracing it straight back to where it really came from: the Alternating Form, lol.https://gdpark.blog/posts/macroeconomics-14-the-real-interest-rate/Sat, 16 Jan 2016 00:00:00 +0000https://gdpark.blog/posts/macroeconomics-14-the-real-interest-rate/Breaking down why expectations run the whole economy, then working through how nominal and real interest rates actually connect — spoiler: bread prices are doing a lot of work.https://gdpark.blog/posts/thermal-statistical-14-chapter-7-practice-problems/Fri, 01 Jan 2016 00:00:00 +0000https://gdpark.blog/posts/thermal-statistical-14-chapter-7-practice-problems/Working through Chapter 7 problems on particle flux for nitrogen at STP and the average kinetic energy of molecules escaping through a tiny hole.https://gdpark.blog/posts/quantum-mechanics-14-formalism-hilbert-space/Mon, 17 Aug 2015 00:00:00 +0000https://gdpark.blog/posts/quantum-mechanics-14-formalism-hilbert-space/A casual romp through how quantum mechanics got its math — from Heisenberg rage-quitting to the beach to the Hilbert space formalism that makes it all click.https://gdpark.blog/posts/electromagnetism-14-linear-dielectrics-part-2/Mon, 22 Dec 2014 00:00:00 +0000https://gdpark.blog/posts/electromagnetism-14-linear-dielectrics-part-2/Part 2 of linear dielectrics — why stuffing a dielectric in your capacitor boosts capacitance, plus the dielectric constant explained with Spider-Man analogies!https://gdpark.blog/posts/classical-mechanics-14-momentum-of-a-system-of-particles/Fri, 07 Nov 2014 00:00:00 +0000https://gdpark.blog/posts/classical-mechanics-14-momentum-of-a-system-of-particles/We walk through how a system&rsquo;s total momentum equals m·v_cm, and why zero external force means momentum stays constant — aka conservation of linear momentum!https://gdpark.blog/posts/cfa-l2-15-interest-rate-volatility-rate-level-and-yield-curve-changes/Wed, 25 Dec 2024 00:00:00 +0000https://gdpark.blog/posts/cfa-l2-15-interest-rate-volatility-rate-level-and-yield-curve-changes/Here&rsquo;s the breakdown on how volatility, rate levels, and yield curve shape each hit the value of embedded options in callable and putable bonds — exam staples, all three.https://gdpark.blog/posts/cfa-l1-15-effective-interest-rate-method-a-complete-accounting-guide/Sat, 03 Jul 2021 00:00:00 +0000https://gdpark.blog/posts/cfa-l1-15-effective-interest-rate-method-a-complete-accounting-guide/Breaking down the effective interest rate method and amortized cost from the issuer&rsquo;s side — because honestly, I had to fully get it myself before I could explain it!https://gdpark.blog/posts/derivatives-15-binomial-option-pricing-model-basics/Wed, 14 Dec 2016 00:00:00 +0000https://gdpark.blog/posts/derivatives-15-binomial-option-pricing-model-basics/A copy-paste deep dive into the binomial option pricing model — covering one-period basics, risk-free portfolios, and how to pin down a call option&rsquo;s theoretical price.https://gdpark.blog/posts/financial-engineering-15-newton-raphson-method/Mon, 12 Dec 2016 00:00:00 +0000https://gdpark.blog/posts/financial-engineering-15-newton-raphson-method/We ditch bisection and let Newton-Raphson chase down implied volatility by hopping along tangent lines until it zeros in on the answer.https://gdpark.blog/posts/microeconomics-15-utility-maximization-under-a-membership-scheme/Fri, 15 Jul 2016 00:00:00 +0000https://gdpark.blog/posts/microeconomics-15-utility-maximization-under-a-membership-scheme/A fun walkthrough of how a membership fee shifts your budget line — and why some people are actually better off never joining in the first place.https://gdpark.blog/posts/basic-investing-15-bond-valuation-and-risk/Tue, 24 May 2016 00:00:00 +0000https://gdpark.blog/posts/basic-investing-15-bond-valuation-and-risk/We actually price a bond this time — figuring out what it&rsquo;s worth today by adding up the present value of all those future coupon payments.https://gdpark.blog/posts/linear-algebra-15-the-adjoint-matrix/Tue, 26 Jan 2016 00:00:00 +0000https://gdpark.blog/posts/linear-algebra-15-the-adjoint-matrix/We dig into triangular and Vandermonde matrices, crack their determinants, then build up to the adjoint matrix — which is about to become super important for what&rsquo;s coming next.https://gdpark.blog/posts/macroeconomics-15-short-run-and-medium-run-analysis-with-the-real-interest-rat/Sun, 17 Jan 2016 00:00:00 +0000https://gdpark.blog/posts/macroeconomics-15-short-run-and-medium-run-analysis-with-the-real-interest-rat/We patch up the IS-LM model to use r instead of i, then show why the medium-run always lands at Wicksell&rsquo;s natural real interest rate r(n).https://gdpark.blog/posts/thermal-statistical-15-mean-free-path-between-molecules/Sat, 02 Jan 2016 00:00:00 +0000https://gdpark.blog/posts/thermal-statistical-15-mean-free-path-between-molecules/A casual, self-reconstructed walkthrough of mean free path derivation — expect some controversy, but the author breaks down molecular collisions and relative velocity in their own way.https://gdpark.blog/posts/quantum-mechanics-15-formalism-observables-and-hermitian-operators/Mon, 17 Aug 2015 00:00:00 +0000https://gdpark.blog/posts/quantum-mechanics-15-formalism-observables-and-hermitian-operators/Why do quantum measurements always spit out real numbers? Turns out the measuring operator can&rsquo;t be just any matrix — it has to be Hermitian, and here&rsquo;s the proof!https://gdpark.blog/posts/classical-mechanics-15-angular-momentum-of-a-system-of-particles/Sat, 17 Jan 2015 00:00:00 +0000https://gdpark.blog/posts/classical-mechanics-15-angular-momentum-of-a-system-of-particles/Spinning into rotational mechanics — we break down angular momentum for particle systems, torque, conservation laws, and how to re-express everything around the center of mass!https://gdpark.blog/posts/electromagnetism-15-lorentz-force-and-magnetostatics/Tue, 23 Dec 2014 00:00:00 +0000https://gdpark.blog/posts/electromagnetism-15-lorentz-force-and-magnetostatics/We&rsquo;re jumping into magnetostatics — where moving charges create steady magnetic fields — and meeting the Lorentz force that ties electricity and magnetism together!https://gdpark.blog/posts/cfa-l2-16-option-adjusted-spread-oas/Fri, 27 Dec 2024 00:00:00 +0000https://gdpark.blog/posts/cfa-l2-16-option-adjusted-spread-oas/OAS is the constant spread you add to every node of a risk-free binomial tree until your callable bond price matches the market — and spoiler: it has nothing to do with options.https://gdpark.blog/posts/cfa-l1-16-bonds/Sun, 25 Jul 2021 00:00:00 +0000https://gdpark.blog/posts/cfa-l1-16-bonds/Cruising through bonds for CFA prep — par, discount, and premium bonds, how market interest rates set the price, and how it all lands on the financial statements.https://gdpark.blog/posts/derivatives-16-deriving-the-black-scholes-formula-from-the-binomial-model/Thu, 15 Dec 2016 00:00:00 +0000https://gdpark.blog/posts/derivatives-16-deriving-the-black-scholes-formula-from-the-binomial-model/Turns out if you just crank n to infinity in the binomial model, the Black-Scholes formula pops right out — so let&rsquo;s do exactly that instead of going the hard way.https://gdpark.blog/posts/financial-engineering-16-differentiation-fundamentals-for-finite-difference-methods/Mon, 12 Dec 2016 00:00:00 +0000https://gdpark.blog/posts/financial-engineering-16-differentiation-fundamentals-for-finite-difference-methods/Before we can tackle FDM and crack open the Black-Scholes PDE numerically, we need to get our differentiation fundamentals straight — so let&rsquo;s run through it.https://gdpark.blog/posts/microeconomics-16-utility-maximization-with-savings-and-loans/Sat, 16 Jul 2016 00:00:00 +0000https://gdpark.blog/posts/microeconomics-16-utility-maximization-with-savings-and-loans/We tackle the last weird budget line — loans let you borrow against next year&rsquo;s income, savings stack up interest, and the slope ties it all together.https://gdpark.blog/posts/basic-investing-16-duration-and-modified-duration/Tue, 24 May 2016 00:00:00 +0000https://gdpark.blog/posts/basic-investing-16-duration-and-modified-duration/We crack open basic calculus to see exactly how bond prices react when interest rates move — and that&rsquo;s what leads us straight to the definition of duration.https://gdpark.blog/posts/linear-algebra-16-block-matrices/Wed, 27 Jan 2016 00:00:00 +0000https://gdpark.blog/posts/linear-algebra-16-block-matrices/A casual dive into diagonalization — what it means to turn a matrix diagonal, why that&rsquo;s such a big deal in physics, and how blocking gets the whole thing started.https://gdpark.blog/posts/macroeconomics-16-expected-present-discounted-value/Sun, 17 Jan 2016 00:00:00 +0000https://gdpark.blog/posts/macroeconomics-16-expected-present-discounted-value/So what&rsquo;s a future stream of payments actually worth right now? We walk through present value, discount factors, and interest rates — the stuff you kinda already know.https://gdpark.blog/posts/thermal-statistical-16-the-first-law-of-thermodynamics-state-functions-and-exact-vs/Sat, 02 Jan 2016 00:00:00 +0000https://gdpark.blog/posts/thermal-statistical-16-the-first-law-of-thermodynamics-state-functions-and-exact-vs/We dig into what heat actually IS, why state functions don&rsquo;t care about the path you took, and the difference between exact and inexact differentials — hehe.https://gdpark.blog/posts/quantum-mechanics-16-formalism-determinate-states/Mon, 17 Aug 2015 00:00:00 +0000https://gdpark.blog/posts/quantum-mechanics-16-formalism-determinate-states/Unpacking what a &lsquo;determinate state&rsquo; actually means in QM — turns out σ_Q = 0 leads straight to eigenvalues, and yeah degenerate spectra are a thing lolol.https://gdpark.blog/posts/classical-mechanics-16-rigid-body-dynamics-and-the-center-of-mass-of-a-rigid-body/Sat, 17 Jan 2015 00:00:00 +0000https://gdpark.blog/posts/classical-mechanics-16-rigid-body-dynamics-and-the-center-of-mass-of-a-rigid-body/We dig into what a rigid body actually is (spoiler: it&rsquo;s an idealized fake lol) and grind through center of mass integrals for 3D solids and 2D plates, hemisphere included.https://gdpark.blog/posts/electromagnetism-16-the-biot-savart-law/Thu, 25 Dec 2014 00:00:00 +0000https://gdpark.blog/posts/electromagnetism-16-the-biot-savart-law/We finally answer how strong the magnetic field around a current-carrying wire actually is — meet the Biot-Savart law and let&rsquo;s calculate some fields together, hehe!https://gdpark.blog/posts/cfa-l2-17-key-rate-duration-partial-duration/Sat, 28 Dec 2024 00:00:00 +0000https://gdpark.blog/posts/cfa-l2-17-key-rate-duration-partial-duration/A casual walkthrough of duration — modified, effective, and key rate — and why assuming a parallel yield curve shift doesn&rsquo;t always cut it.https://gdpark.blog/posts/cfa-l1-17-leases/Sat, 31 Jul 2021 00:00:00 +0000https://gdpark.blog/posts/cfa-l1-17-leases/A quick rundown of lease types and lessor/lessee basics you need to know — even though leases are basically gone from CFA Level 1 now, heh heh heh.https://gdpark.blog/posts/derivatives-17-black-scholes-formula-practice-problems/Fri, 16 Dec 2016 00:00:00 +0000https://gdpark.blog/posts/derivatives-17-black-scholes-formula-practice-problems/Working through Chapter 13 Black-Scholes practice problems — from log-normal returns and Geometric Brownian Motion to actually pricing European call options.https://gdpark.blog/posts/financial-engineering-17-explicit-finite-difference-method-fdm/Tue, 13 Dec 2016 00:00:00 +0000https://gdpark.blog/posts/financial-engineering-17-explicit-finite-difference-method-fdm/Can&rsquo;t solve Black-Scholes analytically? No sweat — we slice the (t, S) plane into a grid, lock down the boundary values, and sneak our way to the rest one point at a time.https://gdpark.blog/posts/microeconomics-17-price-consumption-curve-and-demand-curve/Sat, 16 Jul 2016 00:00:00 +0000https://gdpark.blog/posts/microeconomics-17-price-consumption-curve-and-demand-curve/We trace what happens when the price of good x keeps dropping, connect all the utility-maximizing bundles into a price consumption curve, and boom — that&rsquo;s literally where the demand curve comes from.https://gdpark.blog/posts/linear-algebra-17-introduction-to-diagonalization-eigenvalues-and-eigenvectors/Thu, 28 Jan 2016 00:00:00 +0000https://gdpark.blog/posts/linear-algebra-17-introduction-to-diagonalization-eigenvalues-and-eigenvectors/Finally cracking how to diagonalize a matrix without hunting for the right basis — turns out eigenvalues and eigenvectors are the secret the whole time!https://gdpark.blog/posts/thermal-statistical-17-chapter-11-practice-problems/Sun, 03 Jan 2016 00:00:00 +0000https://gdpark.blog/posts/thermal-statistical-17-chapter-11-practice-problems/Working through Chapter 11 thermo problems — isothermal expansion of a monatomic ideal gas and showing those Cv/Cp identities with γ, step by step.https://gdpark.blog/posts/quantum-mechanics-17-the-uncertainty-principle/Tue, 18 Aug 2015 00:00:00 +0000https://gdpark.blog/posts/quantum-mechanics-17-the-uncertainty-principle/Let&rsquo;s actually prove Heisenberg&rsquo;s uncertainty principle mathematically instead of just taking it on faith — using variances, Schwarz&rsquo;s inequality, and some operator magic.https://gdpark.blog/posts/classical-mechanics-17-moment-of-inertia-perpendicular-axis-theorem-and-parallel-ax/Sun, 18 Jan 2015 00:00:00 +0000https://gdpark.blog/posts/classical-mechanics-17-moment-of-inertia-perpendicular-axis-theorem-and-parallel-ax/We spin up a planar rigid body, derive the moment of inertia from scratch, then work through the perpendicular and parallel axis theorems step by step!https://gdpark.blog/posts/electromagnetism-17-amp-re-s-law/Fri, 26 Dec 2014 00:00:00 +0000https://gdpark.blog/posts/electromagnetism-17-amp-re-s-law/If electrostatics has Gauss&rsquo;s law, magnetostatics has Ampère&rsquo;s law — the line integral of B around any closed loop just gives μ₀i_in, no matter the path!https://gdpark.blog/posts/cfa-l2-18-capped-and-floored-floaters/Sun, 29 Dec 2024 00:00:00 +0000https://gdpark.blog/posts/cfa-l2-18-capped-and-floored-floaters/Capped floaters put a ceiling on the coupon (great for the issuer), floored floaters set a minimum (great for you), and you value both by tweaking a binomial tree and working backward.https://gdpark.blog/posts/cfa-l1-18-pension/Sat, 07 Aug 2021 00:00:00 +0000https://gdpark.blog/posts/cfa-l1-18-pension/Quick intro to post-employment benefits and why you can&rsquo;t just slap a retirement payout on the I/S all at once — matching principle, retirement allowance systems, and more.https://gdpark.blog/posts/derivatives-18-stock-index-options-and-currency-options/Fri, 16 Dec 2016 00:00:00 +0000https://gdpark.blog/posts/derivatives-18-stock-index-options-and-currency-options/Extending Black-Scholes to handle dividends, stock index options, and currency options — turns out it&rsquo;s basically the same trick each time.https://gdpark.blog/posts/financial-engineering-18-implicit-finite-difference-method-fdm/Tue, 13 Dec 2016 00:00:00 +0000https://gdpark.blog/posts/financial-engineering-18-implicit-finite-difference-method-fdm/A walkthrough of Implicit FDM and how swapping to a forward time difference turns the Black-Scholes PDE into a system you solve backwards — algebra included, sanity optional.https://gdpark.blog/posts/microeconomics-18-engel-curve-and-income-consumption-curve/Sat, 16 Jul 2016 00:00:00 +0000https://gdpark.blog/posts/microeconomics-18-engel-curve-and-income-consumption-curve/We derive the income consumption curve and Engel curve step by step, then use their shapes to figure out whether a good is normal or inferior — think ramen vs. electricity.https://gdpark.blog/posts/linear-algebra-18-characteristic-polynomials-and-the-cayley-hamilton-theorem/Fri, 29 Jan 2016 00:00:00 +0000https://gdpark.blog/posts/linear-algebra-18-characteristic-polynomials-and-the-cayley-hamilton-theorem/We chase down which matrices can actually be diagonalized — starting with characteristic polynomials, hitting complex eigenvalues, and landing on the Cayley–Hamilton theorem.https://gdpark.blog/posts/thermal-statistical-18-isothermal-expansion-and-contraction-adiabatic-expansion-and/Sun, 03 Jan 2016 00:00:00 +0000https://gdpark.blog/posts/thermal-statistical-18-isothermal-expansion-and-contraction-adiabatic-expansion-and/We revisit isothermal and adiabatic processes under the reversible + ideal gas assumptions, and get clear on what &lsquo;reversible&rsquo; actually means before the real fun begins!https://gdpark.blog/posts/quantum-mechanics-18-two-level-systems/Tue, 18 Aug 2015 00:00:00 +0000https://gdpark.blog/posts/quantum-mechanics-18-two-level-systems/We tackle a quantum system stuck between just two states, slap a Hermitian Hamiltonian on it, and chase down what state it&rsquo;s actually in at time t!https://gdpark.blog/posts/classical-mechanics-18-radius-of-gyration/Sun, 18 Jan 2015 00:00:00 +0000https://gdpark.blog/posts/classical-mechanics-18-radius-of-gyration/A casual breakdown of the radius of gyration — what it really means to divide moment of inertia by total mass and slap a root on it to get an average distance feel.https://gdpark.blog/posts/electromagnetism-18-amp-re-s-law-part-2/Sat, 27 Dec 2014 00:00:00 +0000https://gdpark.blog/posts/electromagnetism-18-amp-re-s-law-part-2/Time to actually solve problems with Ampère&rsquo;s law — because symmetry is your best friend when finding magnetic fields from wires and surface currents!https://gdpark.blog/posts/cfa-l2-19-convertible-bonds/Sun, 29 Dec 2024 00:00:00 +0000https://gdpark.blog/posts/cfa-l2-19-convertible-bonds/A casual breakdown of convertible bond terminology — conversion ratio, conversion price, conversion value, straight value, and why CBs trade above their theoretical floor.https://gdpark.blog/posts/cfa-l1-19-financial-ratios-1-financial-analysis-techniques/Fri, 13 Aug 2021 00:00:00 +0000https://gdpark.blog/posts/cfa-l1-19-financial-ratios-1-financial-analysis-techniques/A breezy intro to why financial ratios are surprisingly tricky — cross-company comparisons, IFRS vs US-GAAP headaches, the Samsung problem, and whether a 200% debt ratio is even bad.https://gdpark.blog/posts/derivatives-19-stock-index-options-and-currency-options-practice-problems/Sat, 17 Dec 2016 00:00:00 +0000https://gdpark.blog/posts/derivatives-19-stock-index-options-and-currency-options-practice-problems/Practice problems on currency and stock index options — lower bounds, put-call parity, Black-Scholes puts, and hedging a portfolio with index puts.https://gdpark.blog/posts/financial-engineering-19-lu-decomposition/Wed, 14 Dec 2016 00:00:00 +0000https://gdpark.blog/posts/financial-engineering-19-lu-decomposition/Starting from middle-school bike problems and building up to Gaussian elimination, we crack open LU decomposition — because computing A⁻¹ is just painful.https://gdpark.blog/posts/microeconomics-19-substitution-effect-income-effect-inferior-goods-and-giffen/Sat, 16 Jul 2016 00:00:00 +0000https://gdpark.blog/posts/microeconomics-19-substitution-effect-income-effect-inferior-goods-and-giffen/We break down what actually happens when a price drops — splitting that bump in consumption into the substitution effect and the income effect, then going deep on inferior and Giffen goods.https://gdpark.blog/posts/linear-algebra-19-number-theory-and-polynomial-background-for-the-decompositio/Sat, 30 Jan 2016 00:00:00 +0000https://gdpark.blog/posts/linear-algebra-19-number-theory-and-polynomial-background-for-the-decompositio/A casual walk through naturals, integers, divisibility, and the division algorithm, building up to why any subset of Z closed under +, −, and × must look like nZ.https://gdpark.blog/posts/thermal-statistical-19-chapter-12-practice-problems/Mon, 04 Jan 2016 00:00:00 +0000https://gdpark.blog/posts/thermal-statistical-19-chapter-12-practice-problems/Chapter 12 practice problems working through adiabatic expansion, ideal gas state equations, and partial derivative relations for heat capacity — some surprisingly simple!https://gdpark.blog/posts/quantum-mechanics-19-the-schr-dinger-equation-in-spherical-coordinates-3d/Wed, 19 Aug 2015 00:00:00 +0000https://gdpark.blog/posts/quantum-mechanics-19-the-schr-dinger-equation-in-spherical-coordinates-3d/We&rsquo;re finally getting to the good stuff — extending the Schrödinger equation to 3D for the hydrogen atom, and finding out why Cartesian coords just won&rsquo;t cut it.https://gdpark.blog/posts/classical-mechanics-19-physical-pendulum-and-center-of-oscillation/Sun, 18 Jan 2015 00:00:00 +0000https://gdpark.blog/posts/classical-mechanics-19-physical-pendulum-and-center-of-oscillation/We hang a rigid body and let it swing to derive its period, and it turns out it&rsquo;s basically the same as the simple pendulum you memorized in high school — with k²/l sneaking right in!https://gdpark.blog/posts/electromagnetism-19-magnetic-vector-potential/Sun, 28 Dec 2014 00:00:00 +0000https://gdpark.blog/posts/electromagnetism-19-magnetic-vector-potential/Trying to make sense of why ∇×A = B using a tiny pinwheel analogy — wherever it spins inside field A, that spinning IS the magnetic field B!https://gdpark.blog/posts/cfa-l2-20-credit-valuation-adjustment-cva/Sun, 29 Dec 2024 00:00:00 +0000https://gdpark.blog/posts/cfa-l2-20-credit-valuation-adjustment-cva/Diving into CVA — that shave-off amount on OTC derivative valuations that accounts for counterparty default risk, because zero-risk counterparties just don&rsquo;t exist.https://gdpark.blog/posts/cfa-l1-20-financial-ratios-2-financial-analysis-techniques/Sat, 21 Aug 2021 00:00:00 +0000https://gdpark.blog/posts/cfa-l1-20-financial-ratios-2-financial-analysis-techniques/Part 2 of financial ratios — breaking down liquidity ratios like the Current, Quick, Cash, and Defensive Interval ratios with actual intuition, not just exam memorization.https://gdpark.blog/posts/financial-engineering-20-implicit-finite-difference-method-fdm-part-2/Sun, 18 Dec 2016 00:00:00 +0000https://gdpark.blog/posts/financial-engineering-20-implicit-finite-difference-method-fdm-part-2/We put our Ax=b solver to work and actually price a European call with Implicit FDM, walking through how the matrix equations generalize as we slice the grid into more pieces!https://gdpark.blog/posts/derivatives-20-the-greeks/Sat, 17 Dec 2016 00:00:00 +0000https://gdpark.blog/posts/derivatives-20-the-greeks/A casual walkthrough of why hedging exists and a few &lsquo;dumb&rsquo; strategies before the real stuff — delta hedging — explained like chatting with someone in the field.https://gdpark.blog/posts/microeconomics-20-backward-bending-labor-supply-curve/Sat, 16 Jul 2016 00:00:00 +0000https://gdpark.blog/posts/microeconomics-20-backward-bending-labor-supply-curve/As wages rise you work more — until you don&rsquo;t: here&rsquo;s why the labor supply curve bends backward once you&rsquo;d rather enjoy your money than grind 24/7.https://gdpark.blog/posts/linear-algebra-20-the-first-decomposition-theorem/Sun, 31 Jan 2016 00:00:00 +0000https://gdpark.blog/posts/linear-algebra-20-the-first-decomposition-theorem/We revisit diagonalization up close — eigenvalues, kernels, and how a 2D space splits into two 1D invariant subspaces — as a warm-up for the full Decomposition Theorem.https://gdpark.blog/posts/thermal-statistical-20-the-second-law-of-thermodynamics-and-the-clausius-inequality/Mon, 04 Jan 2016 00:00:00 +0000https://gdpark.blog/posts/thermal-statistical-20-the-second-law-of-thermodynamics-and-the-clausius-inequality/We dive into the second law of thermodynamics, unpacking how Clausius and Kelvin&rsquo;s seemingly different statements are actually the same thing — and why the Carnot engine is the key!https://gdpark.blog/posts/quantum-mechanics-20-the-hydrogen-atom/Wed, 19 Aug 2015 00:00:00 +0000https://gdpark.blog/posts/quantum-mechanics-20-the-hydrogen-atom/We finally plug hydrogen&rsquo;s real electric potential into the radial equation, solve for R(r), and normalize it cleanly — this time it&rsquo;s actually hydrogen!!https://gdpark.blog/posts/classical-mechanics-20-rigid-body-in-planar-motion/Mon, 19 Jan 2015 00:00:00 +0000https://gdpark.blog/posts/classical-mechanics-20-rigid-body-in-planar-motion/We level up from fixed-axis rotation to planar motion where the axis moves too, and figure out that sneaky extra term that pops up in the torque equation T_Thttps://gdpark.blog/posts/electromagnetism-20-magnetic-fields-in-matter/Mon, 29 Dec 2014 00:00:00 +0000https://gdpark.blog/posts/electromagnetism-20-magnetic-fields-in-matter/Chapter 6 is basically Chapter 4&rsquo;s magnetic twin — once you survived polarization and electric dipoles, magnetic dipole moments and multipole expansions are a total breeze!https://gdpark.blog/posts/cfa-l2-21-risk-neutral-probability-of-default/Sun, 29 Dec 2024 00:00:00 +0000https://gdpark.blog/posts/cfa-l2-21-risk-neutral-probability-of-default/Risk-neutral (aka implied) default probability is just the PD that calibrates you to market prices — so you can discount everything at the risk-free rate, no guesswork needed.https://gdpark.blog/posts/cfa-l1-21-dupont-analysis/Fri, 27 Aug 2021 00:00:00 +0000https://gdpark.blog/posts/cfa-l1-21-dupont-analysis/DuPont Analysis is basically about ripping ROE apart into three pieces — Net Profit Margin, Asset Turnover, and Financial Leverage — so each one actually means something.https://gdpark.blog/posts/financial-engineering-21-crank-nicolson-finite-difference-method-fdm/Sun, 18 Dec 2016 00:00:00 +0000https://gdpark.blog/posts/financial-engineering-21-crank-nicolson-finite-difference-method-fdm/Wrapping up the FDM trilogy with Crank-Nicolson — the most efficient of the three, averaging Explicit and Implicit to cut positional error in Black-Scholes approximations.https://gdpark.blog/posts/derivatives-21-the-greeks-practice-problems/Sat, 17 Dec 2016 00:00:00 +0000https://gdpark.blog/posts/derivatives-21-the-greeks-practice-problems/Working through Greeks practice problems — stop-loss strategies, futures option deltas, and hedging a short call position on silver futures.https://gdpark.blog/posts/microeconomics-21-compensating-variation-and-equivalent-variation/Sun, 17 Jul 2016 00:00:00 +0000https://gdpark.blog/posts/microeconomics-21-compensating-variation-and-equivalent-variation/We dig into compensating and equivalent variation — two ways to pin down how much a price change is worth by pretending it was an income change instead.https://gdpark.blog/posts/linear-algebra-21-minimal-polynomials-companion-matrices-and-more/Mon, 01 Feb 2016 00:00:00 +0000https://gdpark.blog/posts/linear-algebra-21-minimal-polynomials-companion-matrices-and-more/Diving into minimal polynomials and their sneaky relationship with characteristic polynomials — turns out it&rsquo;s the same divisor-hunting logic we used back in number theory!!!!https://gdpark.blog/posts/thermal-statistical-21-chapter-13-practice-problems/Tue, 05 Jan 2016 00:00:00 +0000https://gdpark.blog/posts/thermal-statistical-21-chapter-13-practice-problems/Working through Chapter 13 problems on refrigerator efficiency, Carnot engines, and why perpetual motion machines just don&rsquo;t exist in this universe.https://gdpark.blog/posts/quantum-mechanics-21-angular-momentum/Sun, 20 Dec 2015 00:00:00 +0000https://gdpark.blog/posts/quantum-mechanics-21-angular-momentum/Kicking off 2nd semester QM by turning the classical angular momentum L = r × p into a proper quantum operator using our existing momentum operator tools.https://gdpark.blog/posts/classical-mechanics-21-three-dimensional-motion-of-a-rigid-body/Mon, 19 Jan 2015 00:00:00 +0000https://gdpark.blog/posts/classical-mechanics-21-three-dimensional-motion-of-a-rigid-body/We level up from planar rigid bodies to full 3D — think spinning a sweet potato on an arbitrary axis — and grind through the inertia tensor using direction cosines and cross products.https://gdpark.blog/posts/electromagnetism-21-the-auxiliary-field-h/Mon, 29 Dec 2014 00:00:00 +0000https://gdpark.blog/posts/electromagnetism-21-the-auxiliary-field-h/Just like D tidies up the electric side, H does the same for magnetics—letting us work with free currents only and ignore the messy bound current stuff.https://gdpark.blog/posts/cfa-l2-22-credit-scores-and-credit-ratings/Mon, 30 Dec 2024 00:00:00 +0000https://gdpark.blog/posts/cfa-l2-22-credit-scores-and-credit-ratings/A quick breakdown of how credit scores differ from credit ratings, why subordinated bonds get notched down, and what credit migration does to bond prices.https://gdpark.blog/posts/cfa-l1-22-financial-assets-and-accounts-receivable/Sun, 19 Sep 2021 00:00:00 +0000https://gdpark.blog/posts/cfa-l1-22-financial-assets-and-accounts-receivable/Back to the B/S! We dig into financial assets, break down non-derivative instruments, and learn why the classic maturity-date rule for debt vs. equity doesn&rsquo;t always hold up.https://gdpark.blog/posts/financial-engineering-22-cholesky-decomposition-correlated-random-variables/Sun, 18 Dec 2016 00:00:00 +0000https://gdpark.blog/posts/financial-engineering-22-cholesky-decomposition-correlated-random-variables/A casual walkthrough of Cholesky decomposition — from real and Hermitian matrices to positive definite covariance matrices — and why it all matters in financial engineering.https://gdpark.blog/posts/microeconomics-22-market-demand-and-network-externalities/Sun, 17 Jul 2016 00:00:00 +0000https://gdpark.blog/posts/microeconomics-22-market-demand-and-network-externalities/We stack up individual demand curves to get the market demand curve, watch it flatten under perfect competition, then kick off network externalities with real-life examples.https://gdpark.blog/posts/linear-algebra-22-is-further-block-decomposition-always-possible/Tue, 02 Feb 2016 00:00:00 +0000https://gdpark.blog/posts/linear-algebra-22-is-further-block-decomposition-always-possible/Poking at a special case where the minimal and characteristic polynomials match as a power of an irreducible polynomial, and what that tells us about block decomposition.https://gdpark.blog/posts/thermal-statistical-22-entropy-thermodynamic-and-statistical-mechanical-perspective/Tue, 05 Jan 2016 00:00:00 +0000https://gdpark.blog/posts/thermal-statistical-22-entropy-thermodynamic-and-statistical-mechanical-perspective/Nobody really knows what entropy is (not even the pros lol), but let&rsquo;s stumble through Clausius&rsquo; definition and the second law of thermodynamics together anyway.https://gdpark.blog/posts/quantum-mechanics-22-spin/Mon, 21 Dec 2015 00:00:00 +0000https://gdpark.blog/posts/quantum-mechanics-22-spin/Finally diving into spin — the quantum concept physicists urgently cooked up to explain the Zeeman effect, and spoiler: the electron isn&rsquo;t literally rotating.https://gdpark.blog/posts/electromagnetism-22-electrodynamics/Tue, 21 Jul 2015 00:00:00 +0000https://gdpark.blog/posts/electromagnetism-22-electrodynamics/Diving into electrodynamics together — breaking down current density, conductivity, and the Lorentz force as we work our way toward Maxwell&rsquo;s equations!https://gdpark.blog/posts/classical-mechanics-22-the-inertia-tensor/Tue, 20 Jan 2015 00:00:00 +0000https://gdpark.blog/posts/classical-mechanics-22-the-inertia-tensor/Still fuzzy on what a tensor really <em>is</em>, but studying the moment-of-inertia tensor this time actually made things click — let&rsquo;s muddle through it together!https://gdpark.blog/posts/cfa-l2-23-structural-and-reduced-form-credit-models/Mon, 30 Dec 2024 00:00:00 +0000https://gdpark.blog/posts/cfa-l2-23-structural-and-reduced-form-credit-models/A casual walkthrough of structural vs. reduced-form credit models — just enough to nail the pros and cons without drowning in the math.https://gdpark.blog/posts/cfa-l1-23-equity/Sun, 26 Sep 2021 00:00:00 +0000https://gdpark.blog/posts/cfa-l1-23-equity/A casual (expectations: low!) walkthrough of equity on the balance sheet — paid-in capital, par value, share premium, and just enough accounting cycle to get by for the CFA exam.https://gdpark.blog/posts/financial-engineering-23-estimating-pi-using-the-monte-carlo-method-in-python/Thu, 26 Sep 2019 00:00:00 +0000https://gdpark.blog/posts/financial-engineering-23-estimating-pi-using-the-monte-carlo-method-in-python/Toss enough random darts at a unit square, count the ones inside the circle, and — boom — you&rsquo;ve got π, courtesy of the Monte Carlo method and a bit of Python.https://gdpark.blog/posts/microeconomics-23-average-and-marginal-product-of-labor/Sun, 17 Jul 2016 00:00:00 +0000https://gdpark.blog/posts/microeconomics-23-average-and-marginal-product-of-labor/We flip to the supplier side and dig into how output Q responds to labor L (with K fixed) — including why piling on more workers eventually starts hurting.https://gdpark.blog/posts/thermal-statistical-23-reciprocal-theorem-and-reciprocity-theorem/Wed, 06 Jan 2016 00:00:00 +0000https://gdpark.blog/posts/thermal-statistical-23-reciprocal-theorem-and-reciprocity-theorem/A quick walkthrough proving the reciprocal and reciprocity theorems by substituting partial derivative expressions and matching coefficients — simpler than it sounds!https://gdpark.blog/posts/quantum-mechanics-23-larmor-precession-and-the-stern-gerlach-experiment/Mon, 21 Dec 2015 00:00:00 +0000https://gdpark.blog/posts/quantum-mechanics-23-larmor-precession-and-the-stern-gerlach-experiment/A deep-dive into two super important Griffiths examples — Larmor precession and the Stern-Gerlach experiment — all about how electrons behave inside a magnetic field!https://gdpark.blog/posts/electromagnetism-23-motional-emf/Thu, 23 Jul 2015 00:00:00 +0000https://gdpark.blog/posts/electromagnetism-23-motional-emf/A casual walkthrough of how yanking a circuit through a magnetic field pushes charges around and why the rate of flux change is the key to EMF!https://gdpark.blog/posts/classical-mechanics-23-principal-axes-of-a-rigid-body/Wed, 21 Jan 2015 00:00:00 +0000https://gdpark.blog/posts/classical-mechanics-23-principal-axes-of-a-rigid-body/We finally dig into principal axes — the special axes on a rigid body where all the products of inertia vanish, plus all the notation conventions that come with them!https://gdpark.blog/posts/cfa-l2-24-credit-spread-analysis-and-term-structure-of-credit-spreads/Mon, 30 Dec 2024 00:00:00 +0000https://gdpark.blog/posts/cfa-l2-24-credit-spread-analysis-and-term-structure-of-credit-spreads/VND, CVA, and why credit spreads have their own term structure — plus what credit quality, the economy, liquidity, and equity vol do to the curve shape.https://gdpark.blog/posts/cfa-l1-24-statement-of-changes-in-equity-and-non-recurring-items/Sat, 02 Oct 2021 00:00:00 +0000https://gdpark.blog/posts/cfa-l1-24-statement-of-changes-in-equity-and-non-recurring-items/A breezy tour of the Statement of Changes in Equity, then a quick rundown on bad debt and warranty expense — and how both quietly create DTAs on the B/S.https://gdpark.blog/posts/microeconomics-24-isoquants/Sun, 17 Jul 2016 00:00:00 +0000https://gdpark.blog/posts/microeconomics-24-isoquants/We bring K back into the picture, plot the whole Q = f(L, K) surface in 3D, then slice it to see what isoquants actually are — infinite (L, K) combos that spit out the same output.https://gdpark.blog/posts/thermal-statistical-24-free-expansion-joule-expansion-and-entropy-of-mixing/Wed, 06 Jan 2016 00:00:00 +0000https://gdpark.blog/posts/thermal-statistical-24-free-expansion-joule-expansion-and-entropy-of-mixing/A casual walkthrough of Joule (free) expansion and entropy of mixing, showing why both processes increase entropy even when internal energy stays zero.https://gdpark.blog/posts/quantum-mechanics-24-addition-of-angular-momenta/Mon, 21 Dec 2015 00:00:00 +0000https://gdpark.blog/posts/quantum-mechanics-24-addition-of-angular-momenta/We finally drag the proton&rsquo;s spin into the picture and tackle how to add two spin-1/2 systems together — welcome to the wild world of addition of angular momenta!https://gdpark.blog/posts/electromagnetism-24-faraday-s-law-induced-electric-field/Thu, 23 Jul 2015 00:00:00 +0000https://gdpark.blog/posts/electromagnetism-24-faraday-s-law-induced-electric-field/Using Stokes&rsquo; theorem to connect changing magnetic flux and the electric field, we derive ∇×E = −∂B/∂t and apply it to a worked example!https://gdpark.blog/posts/classical-mechanics-24-euler-s-equations-of-motion-for-a-rigid-body/Thu, 22 Jan 2015 00:00:00 +0000https://gdpark.blog/posts/classical-mechanics-24-euler-s-equations-of-motion-for-a-rigid-body/We finally put inertia tensors and principal axes to work deriving Euler&rsquo;s equations of motion for a rigid body, with a spinning sweet potato thrown in for good measure.https://gdpark.blog/posts/cfa-l2-25-credit-default-swaps-cds-and-cds-premium/Mon, 30 Dec 2024 00:00:00 +0000https://gdpark.blog/posts/cfa-l2-25-credit-default-swaps-cds-and-cds-premium/CDS isn&rsquo;t your typical derivative — it&rsquo;s basically bond insurance, and this post breaks down the structure, settlement types, and why you don&rsquo;t even need to own the bond.https://gdpark.blog/posts/cfa-l1-25-cash-flow-statement/Mon, 11 Oct 2021 00:00:00 +0000https://gdpark.blog/posts/cfa-l1-25-cash-flow-statement/We finally made it to the cash flow statement — why it exists, why accrual alone isn&rsquo;t enough, and how CFO/CFI/CFF each tell a different part of the story.https://gdpark.blog/posts/cfa-l1-25-earnings-per-share-eps/Sun, 03 Oct 2021 00:00:00 +0000https://gdpark.blog/posts/cfa-l1-25-earnings-per-share-eps/Breaking down EPS the CFA way — weighted average shares, preferred stock deductions, and why dilutive securities make the whole thing a little messy.https://gdpark.blog/posts/microeconomics-25-isoquants-the-uneconomic-region-of-production/Mon, 18 Jul 2016 00:00:00 +0000https://gdpark.blog/posts/microeconomics-25-isoquants-the-uneconomic-region-of-production/That weird backward-bending chunk of the isoquant has a name — it&rsquo;s the uneconomic region, and here&rsquo;s exactly why it exists and why no sane firm would ever go there.https://gdpark.blog/posts/thermal-statistical-25-entropy-practice-problems/Thu, 07 Jan 2016 00:00:00 +0000https://gdpark.blog/posts/thermal-statistical-25-entropy-practice-problems/Working through entropy practice problems—cooling tea and bathtub heat sources—to confirm the second law of thermodynamics (dS ≥ 0) holds up in real scenarios!https://gdpark.blog/posts/quantum-mechanics-25-clebsch-gordan-coefficients/Tue, 22 Dec 2015 00:00:00 +0000https://gdpark.blog/posts/quantum-mechanics-25-clebsch-gordan-coefficients/A casual walkthrough of how to read Clebsch-Gordan coefficient tables — because thankfully some genius already worked out all those messy spin-coupling combos for us.https://gdpark.blog/posts/electromagnetism-25-inductance/Thu, 23 Jul 2015 00:00:00 +0000https://gdpark.blog/posts/electromagnetism-25-inductance/We finally dive into inductance — kicking things off with mutual inductance, Biot-Savart, and even pulling in the vector potential to tie it all together!https://gdpark.blog/posts/classical-mechanics-25-euler-angles/Fri, 23 Jan 2015 00:00:00 +0000https://gdpark.blog/posts/classical-mechanics-25-euler-angles/Breaking down Euler angles — those three tricky angles (Θ, Φ, ψ) that link a fixed coordinate system to a rotating one — using a spinning top as our guide.https://gdpark.blog/posts/cfa-l2-26-credit-default-swaps-cds-part-2/Tue, 31 Dec 2024 00:00:00 +0000https://gdpark.blog/posts/cfa-l2-26-credit-default-swaps-cds-part-2/A casual breakdown of single-name vs. index CDS, how credit correlation drives pricing, and why expected loss is the number that really matters.https://gdpark.blog/posts/cfa-l1-26-cash-flow-statement-and-ebitda/Sat, 16 Oct 2021 00:00:00 +0000https://gdpark.blog/posts/cfa-l1-26-cash-flow-statement-and-ebitda/Working through a real B/S and I/S to build a Cash Flow Statement step by step — tagging every line item as O, I, or F and smashing out CFI, CFF, and CFO the direct way.https://gdpark.blog/posts/microeconomics-26-marginal-rate-of-technical-substitution/Mon, 18 Jul 2016 00:00:00 +0000https://gdpark.blog/posts/microeconomics-26-marginal-rate-of-technical-substitution/We crack what the isoquant slope actually means — it&rsquo;s the MRTS — and work out mathematically why that labor-for-capital swap rate keeps shrinking as you slide along the curve.https://gdpark.blog/posts/thermal-statistical-26-gibbs-expression-for-the-entropy/Thu, 07 Jan 2016 00:00:00 +0000https://gdpark.blog/posts/thermal-statistical-26-gibbs-expression-for-the-entropy/A casual (and slightly reluctant) walkthrough of Gibbs&rsquo; entropy formula, showing how entropy gets re-expressed through probability over macrostates and microstates.https://gdpark.blog/posts/quantum-mechanics-26-two-particle-systems-and-the-exchange-force/Tue, 22 Dec 2015 00:00:00 +0000https://gdpark.blog/posts/quantum-mechanics-26-two-particle-systems-and-the-exchange-force/Chapter 5 kicks off with identical particles — turns out in QM you literally can&rsquo;t tell two electrons apart, and that changes everything about how we write wave functions!https://gdpark.blog/posts/electromagnetism-26-maxwell-s-equations/Tue, 28 Jul 2015 00:00:00 +0000https://gdpark.blog/posts/electromagnetism-26-maxwell-s-equations/We review all the basic relations we&rsquo;ve built up so far — curl E, div B, D, H, and all that — and finally head toward Maxwell&rsquo;s equations~~https://gdpark.blog/posts/classical-mechanics-26-euler-angles-part-2/Sat, 24 Jan 2015 00:00:00 +0000https://gdpark.blog/posts/classical-mechanics-26-euler-angles-part-2/Picking up right where we left off — breaking down what ψ̇, θ̇, and φ̇ actually mean physically for a spinning top, then working out their vector directions step by step.https://gdpark.blog/posts/cfa-l2-27-fra-orientation-and-overview/Sun, 05 Jan 2025 00:00:00 +0000https://gdpark.blog/posts/cfa-l2-27-fra-orientation-and-overview/A quick orientation on CFA Level 2 FRA — ditching the shallow-but-wide Level 1 style to go deeper on 5 big themes, kicking off with intercorporate investments.https://gdpark.blog/posts/cfa-l1-27-free-cash-flow-and-fra-wrap-up/Sun, 17 Oct 2021 00:00:00 +0000https://gdpark.blog/posts/cfa-l1-27-free-cash-flow-and-fra-wrap-up/Finally putting a period on FRA with a casual-but-essential look at FCFF and FCFE — what they are, how to build them from net income, and why WACC is the right discount rate.https://gdpark.blog/posts/classical-mechanics-27-angle-between-the-ellipse-axis-and-the-x-axis/Mon, 06 Nov 2017 00:00:00 +0000https://gdpark.blog/posts/classical-mechanics-27-angle-between-the-ellipse-axis-and-the-x-axis/Finally nailed the derivation for the angle ψ that an ellipse&rsquo;s major axis makes with the x-axis — posting it because nobody else seems to have one up.https://gdpark.blog/posts/microeconomics-27-types-of-isoquants-linear-l-shaped-and-cobb-douglas/Mon, 18 Jul 2016 00:00:00 +0000https://gdpark.blog/posts/microeconomics-27-types-of-isoquants-linear-l-shaped-and-cobb-douglas/A chill rundown of linear, L-shaped, and Cobb-Douglas isoquants — and why their shapes directly tell you everything about σ, the elasticity of substitution.https://gdpark.blog/posts/thermal-statistical-27-enthalpy-helmholtz-free-energy-and-gibbs-free-energy/Fri, 08 Jan 2016 00:00:00 +0000https://gdpark.blog/posts/thermal-statistical-27-enthalpy-helmholtz-free-energy-and-gibbs-free-energy/Starting from dU = TdS - pdV, we add clever terms to both sides to cook up enthalpy, Helmholtz, and Gibbs — basically just a change of variables to make life easier.https://gdpark.blog/posts/quantum-mechanics-27-time-independent-perturbation-theory/Wed, 23 Dec 2015 00:00:00 +0000https://gdpark.blog/posts/quantum-mechanics-27-time-independent-perturbation-theory/A casual dive into time-independent perturbation theory — why the world isn&rsquo;t as clean as an infinite square well, and how we handle slightly off-kilter systems.https://gdpark.blog/posts/electromagnetism-27-the-poynting-vector/Wed, 29 Jul 2015 00:00:00 +0000https://gdpark.blog/posts/electromagnetism-27-the-poynting-vector/We&rsquo;re uncovering the Poynting vector — a quick dive into electromagnetic field energy and conservation laws before jumping into electromagnetic waves!https://gdpark.blog/posts/cfa-l2-28-investments-in-financial-assets/Sun, 05 Jan 2025 00:00:00 +0000https://gdpark.blog/posts/cfa-l2-28-investments-in-financial-assets/A casual breakdown of the three types of intercorporate investments — financial assets, associates, and subsidiaries — and how to tell them apart on exams and in real life.https://gdpark.blog/posts/cfa-l1-28-what-is-a-bond-the-fundamental-difference-from-equity/Sun, 24 Oct 2021 00:00:00 +0000https://gdpark.blog/posts/cfa-l1-28-what-is-a-bond-the-fundamental-difference-from-equity/Kicking off Fixed Income for CFA Level 1 — what a bond actually is, why interest is called a coupon, and how it&rsquo;s fundamentally different from a stock.https://gdpark.blog/posts/microeconomics-28-returns-to-scale/Mon, 18 Jul 2016 00:00:00 +0000https://gdpark.blog/posts/microeconomics-28-returns-to-scale/We dig into the 3D production function to figure out why doubling a factory isn&rsquo;t the same as building a new one — and how increasing, decreasing, and constant returns to scale all shake out.https://gdpark.blog/posts/thermal-statistical-28-maxwell-relations/Fri, 08 Jan 2016 00:00:00 +0000https://gdpark.blog/posts/thermal-statistical-28-maxwell-relations/We dig into state functions and path-independence, invoke Stokes&rsquo; theorem to prove a key condition, and then finally get to deriving the Maxwell Relations!https://gdpark.blog/posts/quantum-mechanics-28-the-feynman-hellmann-theorem/Thu, 24 Dec 2015 00:00:00 +0000https://gdpark.blog/posts/quantum-mechanics-28-the-feynman-hellmann-theorem/Working through the virial theorem proof step by step before tackling hydrogen&rsquo;s fine structure — commutators, expectation values, and all.https://gdpark.blog/posts/electromagnetism-28-electromagnetic-waves-wave-basics/Wed, 29 Jul 2015 00:00:00 +0000https://gdpark.blog/posts/electromagnetism-28-electromagnetic-waves-wave-basics/Before diving into EM waves, let&rsquo;s nail down what a wave actually is — and derive the 1D wave equation from a taut rope using Newtonian mechanics!https://gdpark.blog/posts/cfa-l2-29-equity-method-accounting-fundamentals/Mon, 06 Jan 2025 00:00:00 +0000https://gdpark.blog/posts/cfa-l2-29-equity-method-accounting-fundamentals/A breakdown of why associate stocks skip fair-value measurement and how the equity method pipes B&rsquo;s net income straight into A&rsquo;s books to close the dividend-manipulation loophole.https://gdpark.blog/posts/cfa-l1-29-types-of-bonds/Sun, 31 Oct 2021 00:00:00 +0000https://gdpark.blog/posts/cfa-l1-29-types-of-bonds/A quick rundown of bond types by how they pay interest — floaters, inverse floaters, PIK bonds, index-linked, and the contingency provisions baked right in.https://gdpark.blog/posts/microeconomics-29-technological-progress/Tue, 19 Jul 2016 00:00:00 +0000https://gdpark.blog/posts/microeconomics-29-technological-progress/We sort technological progress on the K-L plane into three buckets — labor-saving, capital-saving, and neutral — by comparing MRTS slopes on isoquants over time.https://gdpark.blog/posts/thermal-statistical-29-isobaric-expansivity-adiabatic-expansivity-isothermal-compre/Sat, 09 Jan 2016 00:00:00 +0000https://gdpark.blog/posts/thermal-statistical-29-isobaric-expansivity-adiabatic-expansivity-isothermal-compre/Wrapping up the chapter with a casual intro to susceptibility — covering isochoric/isobaric heat capacities and all four flavors of expansivity and compressibility.https://gdpark.blog/posts/quantum-mechanics-29-kramers-relation/Thu, 24 Dec 2015 00:00:00 +0000https://gdpark.blog/posts/quantum-mechanics-29-kramers-relation/Proving ⟨1/r³⟩ for the hydrogen atom using Kramers&rsquo; relation — brutal-looking but apparently the least painful option, thanks Uncle Griffiths T_Thttps://gdpark.blog/posts/electromagnetism-29-electromagnetic-waves/Mon, 03 Aug 2015 00:00:00 +0000https://gdpark.blog/posts/electromagnetism-29-electromagnetic-waves/We stumble through Maxwell&rsquo;s equations, take a random curl or two, and somehow end up deriving the wave equations for E and B — hehehe!https://gdpark.blog/posts/cfa-l2-30-equity-method-accounting-advanced-topics/Tue, 07 Jan 2025 00:00:00 +0000https://gdpark.blog/posts/cfa-l2-30-equity-method-accounting-advanced-topics/Real-life equity-method: BV ≠ FV, a control premium gets stapled on top, and you&rsquo;ve gotta reconstruct income from an FV lens — exactly what the CFA exam tests.https://gdpark.blog/posts/cfa-l1-30-key-fixed-income-terminology/Sun, 05 Dec 2021 00:00:00 +0000https://gdpark.blog/posts/cfa-l1-30-key-fixed-income-terminology/A casual rundown of fixed income exam keywords — LIBOR, bond issuance methods, underwritten vs. best efforts offerings, primary dealers, and shelf registration.https://gdpark.blog/posts/microeconomics-30-opportunity-cost-vs-sunk-cost/Tue, 19 Jul 2016 00:00:00 +0000https://gdpark.blog/posts/microeconomics-30-opportunity-cost-vs-sunk-cost/Breaking down opportunity cost and sunk cost with a hilariously relatable uni-picking analogy — because sometimes your &lsquo;best&rsquo; choice becomes a sunk cost real fast.https://gdpark.blog/posts/thermal-statistical-30-chapter-16-practice-problems/Sat, 09 Jan 2016 00:00:00 +0000https://gdpark.blog/posts/thermal-statistical-30-chapter-16-practice-problems/Working through Chapter 16 problems on the four thermodynamic potentials, Maxwell relations, and general identities using the reciprocity theorem.https://gdpark.blog/posts/quantum-mechanics-30-relativistic-correction-and-the-fine-structure-of-hydrogen/Fri, 25 Dec 2015 00:00:00 +0000https://gdpark.blog/posts/quantum-mechanics-30-relativistic-correction-and-the-fine-structure-of-hydrogen/We&rsquo;re back to hydrogen again?! Using perturbation theory, we dig into fine structure — relativistic corrections, spin-orbit coupling, and the Lamb shift.https://gdpark.blog/posts/electromagnetism-30-electromagnetic-waves-in-matter/Tue, 04 Aug 2015 00:00:00 +0000https://gdpark.blog/posts/electromagnetism-30-electromagnetic-waves-in-matter/EM waves in a linear medium work out basically the same as in vacuum — just swap ε₀μ₀ for εμ, and that&rsquo;s literally how the index of refraction n pops out!https://gdpark.blog/posts/cfa-l2-31-equity-method-accounting-intercompany-transactions-and-impai/Wed, 08 Jan 2025 00:00:00 +0000https://gdpark.blog/posts/cfa-l2-31-equity-method-accounting-intercompany-transactions-and-impai/A casual breakdown of how intercompany transactions mess with your equity-method income — upstream, downstream, unrealized profits, and when impairment comes knocking.https://gdpark.blog/posts/cfa-l1-31-bond-valuation/Sun, 12 Dec 2021 00:00:00 +0000https://gdpark.blog/posts/cfa-l1-31-bond-valuation/Bond valuation is just PV of future cash flows — once you lock in why price adjusts to match required return, the rest of fixed income stops wrecking your mental health. heh heh!!https://gdpark.blog/posts/microeconomics-31-cost-and-cost-minimization/Tue, 19 Jul 2016 00:00:00 +0000https://gdpark.blog/posts/microeconomics-31-cost-and-cost-minimization/We dig into the cost minimization problem — and spoiler, it&rsquo;s basically the same deal as utility maximization, just swap the budget line for an isocost line.https://gdpark.blog/posts/thermal-statistical-31-equipartition-theorem/Thu, 21 Apr 2016 00:00:00 +0000https://gdpark.blog/posts/thermal-statistical-31-equipartition-theorem/Turns out when energy is proportional to a square, the average only depends on degrees of freedom — let&rsquo;s verify it step by step using the Boltzmann distribution!https://gdpark.blog/posts/quantum-mechanics-31-spin-orbit-coupling-ls-coupling-and-the-fine-structure-of-hy/Fri, 25 Dec 2015 00:00:00 +0000https://gdpark.blog/posts/quantum-mechanics-31-spin-orbit-coupling-ls-coupling-and-the-fine-structure-of-hy/We flip to the electron&rsquo;s frame, crank through Biot-Savart and magnetic moments, and nail down the spin-orbit Hamiltonian correction behind hydrogen&rsquo;s fine structure.https://gdpark.blog/posts/electromagnetism-31-reflection-and-transmission-of-normally-incident-electromagn/Tue, 04 Aug 2015 00:00:00 +0000https://gdpark.blog/posts/electromagnetism-31-reflection-and-transmission-of-normally-incident-electromagn/We dig into what happens when an EM wave hits the boundary between two linear media, using Maxwell&rsquo;s boundary conditions to work out reflection and transmission!https://gdpark.blog/posts/cfa-l2-32-proportionate-consolidation/Thu, 09 Jan 2025 00:00:00 +0000https://gdpark.blog/posts/cfa-l2-32-proportionate-consolidation/A quick breakdown of proportionate consolidation — folding in assets, liabilities, revenues, and expenses at your exact ownership %, and why accounting standards don&rsquo;t actually use it.https://gdpark.blog/posts/cfa-l1-32-yield-measures/Sun, 19 Dec 2021 00:00:00 +0000https://gdpark.blog/posts/cfa-l1-32-yield-measures/Breaking down why coupon rate isn&rsquo;t your bond&rsquo;s &rsquo;true&rsquo; yield, and how payment frequency changes everything when you&rsquo;re comparing bonds apple to apple.https://gdpark.blog/posts/microeconomics-32-expansion-path/Tue, 19 Jul 2016 00:00:00 +0000https://gdpark.blog/posts/microeconomics-32-expansion-path/Unlike demand theory, firms chasing a fixed output level have zero income effect — just pure substitution — and tracing those cost-minimizing combos as output rises draws out the expansion path.https://gdpark.blog/posts/thermal-statistical-32-limits-of-the-equipartition-theorem/Thu, 21 Apr 2016 00:00:00 +0000https://gdpark.blog/posts/thermal-statistical-32-limits-of-the-equipartition-theorem/Turns out the equipartition theorem quietly assumes energy is continuous — a big no-no once quantum mechanics enters the picture, unless kT ≫ ℏω saves the day!https://gdpark.blog/posts/quantum-mechanics-32-perturbation-theory-practice-problems/Fri, 25 Dec 2015 00:00:00 +0000https://gdpark.blog/posts/quantum-mechanics-32-perturbation-theory-practice-problems/Working through classic perturbation theory homework problems — delta-function bumps in infinite square wells and harmonic oscillator perturbations, step by step.https://gdpark.blog/posts/electromagnetism-32-refraction-of-obliquely-incident-electromagnetic-waves/Wed, 05 Aug 2015 00:00:00 +0000https://gdpark.blog/posts/electromagnetism-32-refraction-of-obliquely-incident-electromagnetic-waves/Tackling oblique-incidence EM wave refraction by ripping E and B fields into normal and parallel boundary components, then matching all four boundary conditions.https://gdpark.blog/posts/cfa-l2-33-full-consolidation-the-acquisition-method/Fri, 10 Jan 2025 00:00:00 +0000https://gdpark.blog/posts/cfa-l2-33-full-consolidation-the-acquisition-method/A casual breakdown of why full consolidation wins over proportionate consolidation, how NCI keeps the balance sheet balanced, and what it does to your ROE and ROA.https://gdpark.blog/posts/cfa-l1-33-understanding-geometric-mean-return-for-the-yield-curve/Sat, 25 Dec 2021 00:00:00 +0000https://gdpark.blog/posts/cfa-l1-33-understanding-geometric-mean-return-for-the-yield-curve/Finally tackling the yield curve — but first, why geometric mean return (not arithmetic mean) is the only correct way to think about % gains over time.https://gdpark.blog/posts/microeconomics-33-labor-demand-curve/Wed, 20 Jul 2016 00:00:00 +0000https://gdpark.blog/posts/microeconomics-33-labor-demand-curve/We derive the labor demand curve by tracing how a firm&rsquo;s optimal labor choice shifts each time the wage ticks up — first with graphs, then with a Cobb-Douglas proof.https://gdpark.blog/posts/thermal-statistical-33-the-partition-function/Fri, 22 Apr 2016 00:00:00 +0000https://gdpark.blog/posts/thermal-statistical-33-the-partition-function/A casual deep-dive into what the partition function Z actually means — from its German roots to why dividing by Z magically turns Boltzmann weights into real probabilities.https://gdpark.blog/posts/quantum-mechanics-33-van-der-waals-interaction-and-the-stark-effect/Fri, 25 Dec 2015 00:00:00 +0000https://gdpark.blog/posts/quantum-mechanics-33-van-der-waals-interaction-and-the-stark-effect/A walkthrough of Griffiths Problem 6.31, deriving the weak van der Waals attraction between two polarizable atoms using perturbation theory and Taylor series.https://gdpark.blog/posts/electromagnetism-33-electromagnetic-waves-in-conductors-absorption-and-dispersio/Fri, 07 Aug 2015 00:00:00 +0000https://gdpark.blog/posts/electromagnetism-33-electromagnetic-waves-in-conductors-absorption-and-dispersio/We crack open Maxwell&rsquo;s equations inside conductors (J ≠ 0 this time!) and mix in Ohm&rsquo;s law with the continuity equation to see what happens to free charge density.https://gdpark.blog/posts/cfa-l2-34-goodwill-full-and-partial-and-bargain-purchases/Sat, 11 Jan 2025 00:00:00 +0000https://gdpark.blog/posts/cfa-l2-34-goodwill-full-and-partial-and-bargain-purchases/Breaking down how goodwill pops out of consolidation accounting, how NCI gets booked, and what happens with partial goodwill and bargain purchases — CFA-style.https://gdpark.blog/posts/cfa-l1-34-yield-curve/Sat, 25 Dec 2021 00:00:00 +0000https://gdpark.blog/posts/cfa-l1-34-yield-curve/Finally cracking open the yield curve — spot rates, zero coupon bonds, and why discounting everything at one single yield is kinda ridiculous.https://gdpark.blog/posts/microeconomics-34-short-run-analysis/Wed, 20 Jul 2016 00:00:00 +0000https://gdpark.blog/posts/microeconomics-34-short-run-analysis/In the short run capital is locked in at K̄, so cost minimization means working around that constraint — which shifts your expansion path and nudges total cost up.https://gdpark.blog/posts/thermal-statistical-34-relationship-between-the-partition-function-and-state-functi/Sat, 23 Apr 2016 00:00:00 +0000https://gdpark.blog/posts/thermal-statistical-34-relationship-between-the-partition-function-and-state-functi/We derive thermodynamic state functions like U, F, and S straight from the partition function Z — turns out one sneaky differential trick does all the heavy lifting!https://gdpark.blog/posts/quantum-mechanics-34-the-variational-principle/Fri, 25 Dec 2015 00:00:00 +0000https://gdpark.blog/posts/quantum-mechanics-34-the-variational-principle/The variational principle is basically quantum gambling — guess a trial wavefunction, and your calculated energy is always ≥ the true ground state energy.https://gdpark.blog/posts/electromagnetism-34-electromagnetic-waves-in-conductors-absorption-and-dispersio/Fri, 07 Aug 2015 00:00:00 +0000https://gdpark.blog/posts/electromagnetism-34-electromagnetic-waves-in-conductors-absorption-and-dispersio/We tackle boundary conditions at a conductor surface, cheer over vanishing free currents, and set up incident/reflected wave equations for normal incidence into a conductor!https://gdpark.blog/posts/cfa-l2-35-special-purpose-entities-spe-and-variable-interest-entities/Sun, 12 Jan 2025 00:00:00 +0000https://gdpark.blog/posts/cfa-l2-35-special-purpose-entities-spe-and-variable-interest-entities/VIEs always get consolidated — no exceptions — and here&rsquo;s the wild history of how Korea&rsquo;s IMF crisis, ABS, and IFRS killed off-balance-sheet SPC financing for good.https://gdpark.blog/posts/cfa-l1-35-yield-spread/Fri, 31 Dec 2021 00:00:00 +0000https://gdpark.blog/posts/cfa-l1-35-yield-spread/A casual breakdown of yield spreads — what G-spread and I-spread actually mean, why swap rates beat LIBOR as the private-sector risk-free rate, and how traders decide if a bond is cheap or rich.https://gdpark.blog/posts/microeconomics-35-cost-minimization-with-three-variables/Wed, 20 Jul 2016 00:00:00 +0000https://gdpark.blog/posts/microeconomics-35-cost-minimization-with-three-variables/Adding a third input M sounds fancy, but once you pin K as a fixed cost the whole 3D problem just collapses back into the same old 2D setup — same playbook, every time.https://gdpark.blog/posts/thermal-statistical-35-partition-functions-for-a-two-level-system-and-the-harmonic/Sun, 24 Apr 2016 00:00:00 +0000https://gdpark.blog/posts/thermal-statistical-35-partition-functions-for-a-two-level-system-and-the-harmonic/We check that the partition function formulas for U, C, and S actually make physical sense using a simple two-level system — and yep, at 0 K everything ends up in the ground state. Ohong~!https://gdpark.blog/posts/quantum-mechanics-35-the-wkb-approximation-wentzel-kramers-brillouin/Sat, 26 Dec 2015 00:00:00 +0000https://gdpark.blog/posts/quantum-mechanics-35-the-wkb-approximation-wentzel-kramers-brillouin/Ch8 is all about WKB — the go-to approximation when V(x) varies slowly, letting you tackle bound states and tunneling without solving Schrödinger exactly.https://gdpark.blog/posts/electromagnetism-35-frequency-dependence-of-the-permittivity/Sat, 08 Aug 2015 00:00:00 +0000https://gdpark.blog/posts/electromagnetism-35-frequency-dependence-of-the-permittivity/Turns out permittivity isn&rsquo;t just a constant — it changes with frequency, and we dig into why using a good ol&rsquo; spring-mass atomic model instead of scary orbitals.https://gdpark.blog/posts/cfa-l2-36-defined-benefit-pension-plans-accounting-treatment/Sat, 25 Jan 2025 00:00:00 +0000https://gdpark.blog/posts/cfa-l2-36-defined-benefit-pension-plans-accounting-treatment/A breakdown of how severance pay and DB/DC pension plans hit the financial statements — and why stashing money outside the company matters when things go south.https://gdpark.blog/posts/cfa-l1-36-price-risk-reinvestment-risk-and-duration/Sat, 08 Jan 2022 00:00:00 +0000https://gdpark.blog/posts/cfa-l1-36-price-risk-reinvestment-risk-and-duration/YTM secretly assumes you reinvest every coupon at YTM itself — and that hidden assumption is exactly where price risk and reinvestment risk come from.https://gdpark.blog/posts/microeconomics-36-total-cost-marginal-cost-and-average-cost/Wed, 20 Jul 2016 00:00:00 +0000https://gdpark.blog/posts/microeconomics-36-total-cost-marginal-cost-and-average-cost/Wait, cost curves again?! Nope — this time we&rsquo;re plotting minimum TC against Q, then eyeballing derivatives to build the marginal and average cost curves from scratch.https://gdpark.blog/posts/thermal-statistical-36-density-of-states-and-statistical-mechanics-of-the-ideal-gas/Mon, 25 Apr 2016 00:00:00 +0000https://gdpark.blog/posts/thermal-statistical-36-density-of-states-and-statistical-mechanics-of-the-ideal-gas/We finally tackle the ideal gas and why we can actually compute Z for it — turns out independent subsystems make partition functions way more manageable lol.https://gdpark.blog/posts/quantum-mechanics-36-wkb-connection-formulas/Sun, 27 Dec 2015 00:00:00 +0000https://gdpark.blog/posts/quantum-mechanics-36-wkb-connection-formulas/When potential walls aren&rsquo;t vertical, WKB blows up at the turning point — so here&rsquo;s how we patch the two regions together using a Taylor expansion near x=0.https://gdpark.blog/posts/electromagnetism-36-gauge-transformations-coulomb-gauge-lorenz-gauge-and-the-d-a/Sat, 08 Aug 2015 00:00:00 +0000https://gdpark.blog/posts/electromagnetism-36-gauge-transformations-coulomb-gauge-lorenz-gauge-and-the-d-a/Diving into Chapter 10 — we finally tie scalar and vector potentials together, see how Maxwell&rsquo;s equations allow gauge freedom, and meet the Coulomb and Lorenz gauges.https://gdpark.blog/posts/cfa-l2-37-defined-benefit-pension-plans-analytical-perspective/Sun, 26 Jan 2025 00:00:00 +0000https://gdpark.blog/posts/cfa-l2-37-defined-benefit-pension-plans-analytical-perspective/Even though it got yanked from the 2024 CFA L2 curriculum, here&rsquo;s how analysts reclassify pension F/S and compute TPPC — both ways — from an economic lens.https://gdpark.blog/posts/cfa-l1-37-credit-analysis-and-credit-ratings/Sun, 23 Jan 2022 00:00:00 +0000https://gdpark.blog/posts/cfa-l1-37-credit-analysis-and-credit-ratings/A breezy skim through credit analysis — cash flow, bond indentures, and why credit loss is basically just lottery math but for money you might lose.https://gdpark.blog/posts/microeconomics-37-long-run-cost-minimization-with-cobb-douglas/Wed, 20 Jul 2016 00:00:00 +0000https://gdpark.blog/posts/microeconomics-37-long-run-cost-minimization-with-cobb-douglas/We pin down TC, MC, and AC for a Cobb-Douglas production function and find they all collapse to the same constant α — constant returns to scale is why.https://gdpark.blog/posts/thermal-statistical-37-density-of-states-another-perspective/Mon, 25 Apr 2016 00:00:00 +0000https://gdpark.blog/posts/thermal-statistical-37-density-of-states-another-perspective/Why stress over weird container shapes? Since boundary conditions don&rsquo;t actually matter in stat mech, we just pick periodic BCs so we can use clean plane waves instead of messy sines and cosines.https://gdpark.blog/posts/quantum-mechanics-37-wkb-approximation-practice-problems/Sun, 27 Dec 2015 00:00:00 +0000https://gdpark.blog/posts/quantum-mechanics-37-wkb-approximation-practice-problems/Working through WKB approximation problems — matching connection formulas at turning points x1 and x2 to nail down the quantization condition for bound states!https://gdpark.blog/posts/electromagnetism-37-jefimenko-s-equations/Sat, 08 Aug 2015 00:00:00 +0000https://gdpark.blog/posts/electromagnetism-37-jefimenko-s-equations/We build on the Lorentz gauge, introduce retarded time, and finally nail that causality the Coulomb gauge was missing — hello, retarded potentials!https://gdpark.blog/posts/cfa-l2-38-share-based-compensation/Sun, 26 Jan 2025 00:00:00 +0000https://gdpark.blog/posts/cfa-l2-38-share-based-compensation/Picking up with post-employment benefits and share-based comp — breaking down the actuarial stuff, stock options, SARs, and the vesting quirks you actually need to know.https://gdpark.blog/posts/cfa-l1-38-asset-backed-securities-abs-and-the-global-financial-crisis/Sat, 05 Feb 2022 00:00:00 +0000https://gdpark.blog/posts/cfa-l1-38-asset-backed-securities-abs-and-the-global-financial-crisis/ABS, MBS, maturity mismatches, and yes — the full 2008 meltdown with AIG and everything. Buckle up, it&rsquo;s the grand finale of the Fixed Income series!https://gdpark.blog/posts/microeconomics-38-economies-of-scale-and-diseconomies-of-scale/Thu, 21 Jul 2016 00:00:00 +0000https://gdpark.blog/posts/microeconomics-38-economies-of-scale-and-diseconomies-of-scale/We poke at what happens to TC when factor prices move, work through output elasticity of cost, and land on exactly what economies vs. diseconomies of scale actually mean.https://gdpark.blog/posts/thermal-statistical-38-quantum-concentration-and-thermal-de-broglie-wavelength/Tue, 26 Apr 2016 00:00:00 +0000https://gdpark.blog/posts/thermal-statistical-38-quantum-concentration-and-thermal-de-broglie-wavelength/We grind through the ideal gas partition function integral step by step, then dig into what the result actually tells us about quantum concentration and the thermal de Broglie wavelength.https://gdpark.blog/posts/quantum-mechanics-38-time-dependent-perturbation-theory/Sun, 27 Dec 2015 00:00:00 +0000https://gdpark.blog/posts/quantum-mechanics-38-time-dependent-perturbation-theory/So the perturb term now depends on time, meaning probability itself changes as time flows — which is how we start making sense of emission, absorption, and lasers!https://gdpark.blog/posts/electromagnetism-38-li-nard-wiechert-potentials-electromagnetic-fields-of-a-movi/Mon, 10 Aug 2015 00:00:00 +0000https://gdpark.blog/posts/electromagnetism-38-li-nard-wiechert-potentials-electromagnetic-fields-of-a-movi/We tackle the EM field of a moving point charge using Liénard–Wiechert potentials — supposedly easier than Jefimenko, but still a complete freaking disaster lol.https://gdpark.blog/posts/cfa-l2-39-multinational-operations/Mon, 27 Jan 2025 00:00:00 +0000https://gdpark.blog/posts/cfa-l2-39-multinational-operations/A quick breakdown of transaction exposure — how FX rate changes hit your AR and what counts as realized vs. unrealized in multinational accounting.https://gdpark.blog/posts/cfa-l1-39-fixed-income-wrap-up/Sun, 13 Feb 2022 00:00:00 +0000https://gdpark.blog/posts/cfa-l1-39-fixed-income-wrap-up/Wrapping up the whole Fixed Income series with a keyword-by-keyword tour of securitization, covered bonds, RMBS vs. CMBS, and call protection mechanics.https://gdpark.blog/posts/microeconomics-39-short-run-total-average-and-marginal-cost-curves-stc-sac-smc/Thu, 21 Jul 2016 00:00:00 +0000https://gdpark.blog/posts/microeconomics-39-short-run-total-average-and-marginal-cost-curves-stc-sac-smc/We flip from long-run to short-run, lock K down as a constant, and split total cost into TFC + TVC to build the STC curve — which, unlike long-run TC, doesn&rsquo;t pass through (0,0)!https://gdpark.blog/posts/thermal-statistical-39-partition-function-for-indistinguishable-particles/Wed, 27 Apr 2016 00:00:00 +0000https://gdpark.blog/posts/thermal-statistical-39-partition-function-for-indistinguishable-particles/Turns out Z_sys = (Z_1)^n only works for distinguishable particles — we break down why indistinguishable ones mess up the math using a simple two-level system.https://gdpark.blog/posts/quantum-mechanics-39-absorption-emission-and-stimulated-emission/Sun, 27 Dec 2015 00:00:00 +0000https://gdpark.blog/posts/quantum-mechanics-39-absorption-emission-and-stimulated-emission/We crack open sinusoidal perturbation Hamiltonians and trace how Cb(t) captures absorption, emission, and stimulated emission in a two-level system.https://gdpark.blog/posts/electromagnetism-39-derivation-of-the-maxwell-stress-tensor-appendix/Sun, 29 Mar 2015 00:00:00 +0000https://gdpark.blog/posts/electromagnetism-39-derivation-of-the-maxwell-stress-tensor-appendix/Couldn&rsquo;t stand just memorizing it, so I brute-forced my way through a full step-by-step derivation of the Maxwell stress tensor starting from the infinitesimal Lorentz force on a charge density.https://gdpark.blog/posts/cfa-l2-40-foreign-currency-translation-types-of-currency/Mon, 27 Jan 2025 00:00:00 +0000https://gdpark.blog/posts/cfa-l2-40-foreign-currency-translation-types-of-currency/A quick breakdown of the three currency types you need for translation — local, functional, and presentation — using Samsung as the running example.https://gdpark.blog/posts/microeconomics-40-graphing-ac-mc-sac-and-smc-together/Thu, 21 Jul 2016 00:00:00 +0000https://gdpark.blog/posts/microeconomics-40-graphing-ac-mc-sac-and-smc-together/We finally plot AC, MC, SAC, and SMC all on one graph and trace exactly how they intersect and relate as capital K gets pinned at different levels — it all snaps into place!https://gdpark.blog/posts/thermal-statistical-40-the-grand-canonical-ensemble/Sun, 01 May 2016 00:00:00 +0000https://gdpark.blog/posts/thermal-statistical-40-the-grand-canonical-ensemble/Chapter 22 extends our model to allow particle exchange alongside energy flow, diving into the grand canonical ensemble where both energy and particle number can fluctuate.https://gdpark.blog/posts/electromagnetism-40-the-hall-effect/Sat, 05 Mar 2016 00:00:00 +0000https://gdpark.blog/posts/electromagnetism-40-the-hall-effect/A student&rsquo;s casual write-up of a Hall effect lab report, covering the basics of Hall voltage, charge carriers, and Lorentz force in a way anyone can follow.https://gdpark.blog/posts/quantum-mechanics-40-fermi-s-golden-rule-and-selection-rules/Mon, 28 Dec 2015 00:00:00 +0000https://gdpark.blog/posts/quantum-mechanics-40-fermi-s-golden-rule-and-selection-rules/We take our monochromatic-light transition probability and extend it to polychromatic light by integrating over all ω — and that&rsquo;s how Fermi&rsquo;s Golden Rule pops out~!https://gdpark.blog/posts/cfa-l2-41-the-current-rate-method/Tue, 28 Jan 2025 00:00:00 +0000https://gdpark.blog/posts/cfa-l2-41-the-current-rate-method/A quick rundown of the Current Rate Method — when to use it, how to translate I/S before B/S, and how to make sense of AOCI without overcomplicating it!!https://gdpark.blog/posts/microeconomics-41-average-variable-cost-and-average-fixed-cost-avc-afc/Thu, 21 Jul 2016 00:00:00 +0000https://gdpark.blog/posts/microeconomics-41-average-variable-cost-and-average-fixed-cost-avc-afc/Breaking STC into FC + VC, then dividing by Q, shows SAC decomposes neatly into AFC + AVC — and why SMC passes through the minimum of AVC too.https://gdpark.blog/posts/thermal-statistical-41-the-grand-partition-function/Sat, 18 Jun 2016 00:00:00 +0000https://gdpark.blog/posts/thermal-statistical-41-the-grand-partition-function/We let particles flow freely and ask what happens to the partition function — turns out there&rsquo;s a grand version Z_G derived straight from entropy!https://gdpark.blog/posts/quantum-mechanics-41-spontaneous-emission-and-einstein-coefficients/Mon, 28 Dec 2015 00:00:00 +0000https://gdpark.blog/posts/quantum-mechanics-41-spontaneous-emission-and-einstein-coefficients/Breaking down Einstein&rsquo;s A &amp; B coefficients — spontaneous emission, absorption, and stimulated emission — and how they all click at thermal equilibrium.https://gdpark.blog/posts/cfa-l2-42-the-temporal-method/Tue, 28 Jan 2025 00:00:00 +0000https://gdpark.blog/posts/cfa-l2-42-the-temporal-method/Breaking down the Temporal Method — when to use it, which assets get translated at what rate, and how to snap to a gain/loss answer fast on the CFA.https://gdpark.blog/posts/microeconomics-42-perfectly-competitive-markets/Thu, 21 Jul 2016 00:00:00 +0000https://gdpark.blog/posts/microeconomics-42-perfectly-competitive-markets/A casual breakdown of perfectly competitive markets — why we bother studying a model that doesn&rsquo;t exist, plus a walkthrough of its four core assumptions.https://gdpark.blog/posts/thermal-statistical-42-grand-potential/Sun, 19 Jun 2016 00:00:00 +0000https://gdpark.blog/posts/thermal-statistical-42-grand-potential/We define the grand potential Φ_G = -k_BT·ln(Z_G) by building on how F works in the canonical ensemble — because the partition function holds all the power, hehehe!https://gdpark.blog/posts/quantum-mechanics-42-chapter-9-practice-problems/Tue, 29 Dec 2015 00:00:00 +0000https://gdpark.blog/posts/quantum-mechanics-42-chapter-9-practice-problems/Working through Chapter 9 practice problems on time-dependent perturbation theory, using the Dirac delta function to solve for transition coefficients Ca and Cb.https://gdpark.blog/posts/microeconomics-43-short-run-supply-curve/Thu, 21 Jul 2016 00:00:00 +0000https://gdpark.blog/posts/microeconomics-43-short-run-supply-curve/We derive the short-run supply curve in a perfectly competitive market — turns out it&rsquo;s just the SMC curve above AVC, and here&rsquo;s exactly why that matters.https://gdpark.blog/posts/thermal-statistical-43-chemical-potential-of-an-ideal-gas/Mon, 20 Jun 2016 00:00:00 +0000https://gdpark.blog/posts/thermal-statistical-43-chemical-potential-of-an-ideal-gas/We derive μ = k_BT ln(nλ_th³) for an ideal gas via the canonical ensemble and Helmholtz free energy — a relation we&rsquo;ll keep pulling out freely from here on.https://gdpark.blog/posts/quantum-mechanics-43-the-meaning-of-planck-s-constant-and-the-photoelectric-effec/Thu, 10 Mar 2016 00:00:00 +0000https://gdpark.blog/posts/quantum-mechanics-43-the-meaning-of-planck-s-constant-and-the-photoelectric-effec/Roughly chicken-scratched but hopefully clear: a casual dive into Planck&rsquo;s constant and the photoelectric effect, tracing the historical flow of quantum mechanics.https://gdpark.blog/posts/microeconomics-44-short-run-supply-curve-part-2/Thu, 21 Jul 2016 00:00:00 +0000https://gdpark.blog/posts/microeconomics-44-short-run-supply-curve-part-2/We split fixed costs into sunk vs. non-sunk and trace out exactly when a firm decides to keep producing — or bail — in the short run.https://gdpark.blog/posts/thermal-statistical-44-chemical-potential-as-gibbs-free-energy-per-particle/Tue, 21 Jun 2016 00:00:00 +0000https://gdpark.blog/posts/thermal-statistical-44-chemical-potential-as-gibbs-free-energy-per-particle/We dig into what happens to Gibbs free energy and entropy once we let particles flow in and out, and see why chemical potential turns out to be G per particle!https://gdpark.blog/posts/quantum-mechanics-44-the-pauli-exclusion-principle/Fri, 11 Mar 2016 00:00:00 +0000https://gdpark.blog/posts/quantum-mechanics-44-the-pauli-exclusion-principle/Why don&rsquo;t electrons just stop when metals cool down? Turns out the Pauli exclusion principle guarantees high-energy electrons always stick around, no matter how cold it gets!https://gdpark.blog/posts/microeconomics-45-chapter-2-3-practice-problems/Tue, 03 Jan 2017 00:00:00 +0000https://gdpark.blog/posts/microeconomics-45-chapter-2-3-practice-problems/A collection of practice problems covering the material from Chapters 2 and 3, all laid out for you to work through.https://gdpark.blog/posts/thermal-statistical-45-chemical-potential-of-photons/Tue, 21 Jun 2016 00:00:00 +0000https://gdpark.blog/posts/thermal-statistical-45-chemical-potential-of-photons/Turns out when a system doesn&rsquo;t conserve particle number — like photons — the chemical potential just goes to zero at equilibrium, and that&rsquo;s actually a huge deal!!https://gdpark.blog/posts/microeconomics-46-chapter-4-practice-problems/Wed, 04 Jan 2017 00:00:00 +0000https://gdpark.blog/posts/microeconomics-46-chapter-4-practice-problems/Work through the Chapter 4 practice problems to test your understanding and sharpen your skills.https://gdpark.blog/posts/thermal-statistical-46-pressure-dependence-of-chemical-potential/Wed, 22 Jun 2016 00:00:00 +0000https://gdpark.blog/posts/thermal-statistical-46-pressure-dependence-of-chemical-potential/Wrapping up chemical potential once and for all by rewriting μ in terms of pressure using the ideal-gas relation, and linking it to the Gibbs function per particle.https://gdpark.blog/posts/microeconomics-47-chapter-5-practice-problems/Fri, 06 Jan 2017 00:00:00 +0000https://gdpark.blog/posts/microeconomics-47-chapter-5-practice-problems/Grinding through Chapter 5 consumer theory problems — price-consumption curves, Giffen goods, and utility optimization — one painful step at a time.https://gdpark.blog/posts/thermal-statistical-47-le-chatelier-s-principle/Thu, 23 Jun 2016 00:00:00 +0000https://gdpark.blog/posts/thermal-statistical-47-le-chatelier-s-principle/A casual deep-dive into Le Chatelier&rsquo;s Principle through the lens of Gibbs free energy, explaining why reactions reach dynamic equilibrium and how the system responds to disturbances.https://gdpark.blog/posts/microeconomics-48-chapter-6-practice-problems/Sat, 07 Jan 2017 00:00:00 +0000https://gdpark.blog/posts/microeconomics-48-chapter-6-practice-problems/Working through Chapter 6 problems on production functions — filling tables, sketching graphs, and hunting down where average product, marginal product, and total product each hit their max.https://gdpark.blog/posts/thermal-statistical-48-bose-einstein-and-fermi-dirac-distributions/Fri, 24 Jun 2016 00:00:00 +0000https://gdpark.blog/posts/thermal-statistical-48-bose-einstein-and-fermi-dirac-distributions/Switching gears to talk about quantum distributions — what makes bosons and fermions different, and why spin and the Pauli exclusion principle totally change the game!https://gdpark.blog/posts/microeconomics-49-chapter-7-practice-problems/Sun, 08 Jan 2017 00:00:00 +0000https://gdpark.blog/posts/microeconomics-49-chapter-7-practice-problems/Working through Chapter 7 cost-minimization problems with gradients and isoquants — turns out it&rsquo;s the exact same math as the utility-function stuff, just with different names.https://gdpark.blog/posts/thermal-statistical-49-the-stefan-boltzmann-law/Sat, 25 Jun 2016 00:00:00 +0000https://gdpark.blog/posts/thermal-statistical-49-the-stefan-boltzmann-law/Turns out everything — even you — emits electromagnetic waves, and the Stefan-Boltzmann law basically explains why Super Saiyans glow different colors lol.https://gdpark.blog/posts/thermal-statistical-50-the-stefan-boltzmann-constant/Sun, 26 Jun 2016 00:00:00 +0000https://gdpark.blog/posts/thermal-statistical-50-the-stefan-boltzmann-constant/We crack open the Stefan-Boltzmann constant σ using modern physics — photon energy, Bose-Einstein distributions, and density of states — to finally nail down that number!!!https://gdpark.blog/posts/thermal-statistical-51-black-body-radiation-energy-and-spectral-radiance/Mon, 27 Jun 2016 00:00:00 +0000https://gdpark.blog/posts/thermal-statistical-51-black-body-radiation-energy-and-spectral-radiance/Breaking down the blackbody energy formula to understand spectral radiance and why red-hot iron glows red while scorching-hot iron shifts to yellow.https://gdpark.blog/posts/thermal-statistical-52-the-bose-integral/Tue, 28 Jun 2016 00:00:00 +0000https://gdpark.blog/posts/thermal-statistical-52-the-bose-integral/Walking through the proof of the Bose integral — Taylor-expanding the tricky fraction, subbing variables, and tying it all together with the gamma function.https://gdpark.blog/posts/thermal-statistical-53-ultrarelativistic-gas/Wed, 29 Jun 2016 00:00:00 +0000https://gdpark.blog/posts/thermal-statistical-53-ultrarelativistic-gas/A casual walkthrough of relativistic effects — γ, momentum, energy — and how they reshape the math when gas particles scream close to the speed of light.https://gdpark.blog/posts/thermal-statistical-54-van-der-waals-gas-equation-of-state/Wed, 29 Jun 2016 00:00:00 +0000https://gdpark.blog/posts/thermal-statistical-54-van-der-waals-gas-equation-of-state/We crack open two ideal gas assumptions — molecular size and intermolecular forces — to build the Van der Waals equation of state from intuition up.https://gdpark.blog/posts/thermal-statistical-55-critical-temperature-volume-and-pressure-of-the-van-der-waal/Thu, 30 Jun 2016 00:00:00 +0000https://gdpark.blog/posts/thermal-statistical-55-critical-temperature-volume-and-pressure-of-the-van-der-waal/We figure out exactly when a van der Waals gas stops acting like an ideal gas and hunt down the critical temperature where that wild dented p-V curve first appears!https://gdpark.blog/posts/thermal-statistical-56-superheating-and-supercooling/Fri, 01 Jul 2016 00:00:00 +0000https://gdpark.blog/posts/thermal-statistical-56-superheating-and-supercooling/We dig into what actually happens below T_c — using Gibbs free energy to figure out which state a system really lands in when the P-V curve gets all weird and dented.https://gdpark.blog/posts/thermal-statistical-57-maxwell-s-construction/Sat, 02 Jul 2016 00:00:00 +0000https://gdpark.blog/posts/thermal-statistical-57-maxwell-s-construction/A quick look at Maxwell&rsquo;s construction — using ∫Vdp = 0 to pin down exactly where phase coexistence happens on the van der Waals curve.https://gdpark.blog/posts/thermal-statistical-58-joule-coefficient-and-joule-expansion-of-an-ideal-gas/Sun, 03 Jul 2016 00:00:00 +0000https://gdpark.blog/posts/thermal-statistical-58-joule-coefficient-and-joule-expansion-of-an-ideal-gas/Starting from the age-old puzzle of how to make things cold, we dig into Joule expansion to see why ideal gases don&rsquo;t cool down — but real gases do!https://gdpark.blog/posts/thermal-statistical-59-joule-kelvin-expansion-and-the-inversion-curve/Mon, 04 Jul 2016 00:00:00 +0000https://gdpark.blog/posts/thermal-statistical-59-joule-kelvin-expansion-and-the-inversion-curve/A casual walkthrough of Joule-Kelvin (Joule-Thomson) expansion and the throttling process — the much simpler way to cool a gas that won&rsquo;t give you cancer hehe.https://gdpark.blog/posts/thermal-statistical-60-trouton-s-rule/Tue, 05 Jul 2016 00:00:00 +0000https://gdpark.blog/posts/thermal-statistical-60-trouton-s-rule/A casual dive into Trouton&rsquo;s Rule, unpacking why phase transitions happen and how latent heat ties into entropy — because stability is literally everything.https://gdpark.blog/posts/thermal-statistical-61-the-clausius-clapeyron-equation/Wed, 06 Jul 2016 00:00:00 +0000https://gdpark.blog/posts/thermal-statistical-61-the-clausius-clapeyron-equation/We revisit phase transitions using Gibbs free energy and chemical potential to derive the phase coexistence condition and work toward the Clausius-Clapeyron equation hehehe.https://gdpark.blog/posts/thermal-statistical-62-temperature-dependence-of-latent-heat-for-an-ideal-gas/Thu, 07 Jul 2016 00:00:00 +0000https://gdpark.blog/posts/thermal-statistical-62-temperature-dependence-of-latent-heat-for-an-ideal-gas/We derive the liquid-gas phase boundary with the Clausius-Clapeyron equation, then dig into why latent heat L actually depends on temperature.https://gdpark.blog/posts/thermal-statistical-63-phase-coexistence-curves-of-water/Fri, 08 Jul 2016 00:00:00 +0000https://gdpark.blog/posts/thermal-statistical-63-phase-coexistence-curves-of-water/We draw out phase coexistence curves using the Clausius-Clapeyron equation and figure out why water&rsquo;s solid-liquid line has a negative slope — spoiler: hydrogen bonding!!https://gdpark.blog/posts/thermal-statistical-64-kelvin-s-formula-and-why-water-boils/Sat, 09 Jul 2016 00:00:00 +0000https://gdpark.blog/posts/thermal-statistical-64-kelvin-s-formula-and-why-water-boils/We dig into why water boils by layering surface tension on top of phase-transition theory, then crank through the math to land on Kelvin&rsquo;s formula.https://gdpark.blog/posts/thermal-statistical-65-gibbs-free-energy-of-a-water-droplet-and-bubble-nucleation/Sun, 10 Jul 2016 00:00:00 +0000https://gdpark.blog/posts/thermal-statistical-65-gibbs-free-energy-of-a-water-droplet-and-bubble-nucleation/Walk through calculating the Gibbs free energy of a liquid droplet in vapor equilibrium, factoring in surface tension to set up the physics behind bubble nucleation.https://gdpark.blog/posts/thermal-statistical-66-ebullioscopic-and-cryoscopic-constants/Mon, 11 Jul 2016 00:00:00 +0000https://gdpark.blog/posts/thermal-statistical-66-ebullioscopic-and-cryoscopic-constants/Let&rsquo;s derive the boiling point elevation and freezing point depression constants from scratch using chemical potential and Raoult&rsquo;s law.https://gdpark.blog/posts/thermal-statistical-67-symmetry-breaking/Tue, 12 Jul 2016 00:00:00 +0000https://gdpark.blog/posts/thermal-statistical-67-symmetry-breaking/Turns out not all phase transitions are the same — Ehrenfest classified them by order, and second-order ones like superconductivity behave totally differently!https://gdpark.blog/posts/thermal-statistical-68-ising-model-monte-carlo-method-and-the-metropolis-algorithm/Wed, 13 Jul 2016 00:00:00 +0000https://gdpark.blog/posts/thermal-statistical-68-ising-model-monte-carlo-method-and-the-metropolis-algorithm/A breezy intro to the Ising model, Monte Carlo method, and Metropolis algorithm — just enough to say you&rsquo;ve heard of them once.https://gdpark.blog/posts/thermal-statistical-69-fourier-series-and-fourier-transform-a-brief-introduction/Wed, 13 Jul 2016 00:00:00 +0000https://gdpark.blog/posts/thermal-statistical-69-fourier-series-and-fourier-transform-a-brief-introduction/A casual walkthrough of how Fourier&rsquo;s trick uses the orthogonality of sines and cosines to pin down the coefficients for representing any periodic function.https://gdpark.blog/posts/thermal-statistical-70-brownian-motion-and-the-langevin-equation/Wed, 13 Jul 2016 00:00:00 +0000https://gdpark.blog/posts/thermal-statistical-70-brownian-motion-and-the-langevin-equation/A casual romp through the wild history of Brownian motion — from Robert Brown&rsquo;s baffled pollen experiments all the way to Einstein&rsquo;s miracle-year paper and beyond.https://gdpark.blog/posts/thermal-statistical-71-diffusion-equation-and-diffusion-constant-via-brownian-motio/Thu, 14 Jul 2016 00:00:00 +0000https://gdpark.blog/posts/thermal-statistical-71-diffusion-equation-and-diffusion-constant-via-brownian-motio/We piece together Fick&rsquo;s law and the diffusion equation step by step — from number density gradients to flux — and nail down what the diffusion constant D actually means.https://gdpark.blog/posts/thermal-statistical-72-brownian-motion-and-the-correlation-function/Fri, 15 Jul 2016 00:00:00 +0000https://gdpark.blog/posts/thermal-statistical-72-brownian-motion-and-the-correlation-function/Deriving the velocity correlation function ⟨v(0)v(t)⟩ from the Langevin equation — basically asking whether your current state still remembers where it started, gold-spoon style.https://gdpark.blog/posts/thermal-statistical-73-fluctuations/Sat, 16 Jul 2016 00:00:00 +0000https://gdpark.blog/posts/thermal-statistical-73-fluctuations/Can wild, chaotic fluctuations actually be tamed by state functions like S, T, and V? Turns out entropy and probability density are more buddy-buddy than you&rsquo;d think.https://gdpark.blog/posts/thermal-statistical-74-practice-problems-chapter-19/Fri, 23 Dec 2016 00:00:00 +0000https://gdpark.blog/posts/thermal-statistical-74-practice-problems-chapter-19/Working through Chapter 19 practice problems on average energy, the equipartition theorem, and potential wells — plus one I got stuck on and would love feedback on!https://gdpark.blog/posts/thermal-statistical-75-practice-problems-chapter-20/Fri, 23 Dec 2016 00:00:00 +0000https://gdpark.blog/posts/thermal-statistical-75-practice-problems-chapter-20/Work through Chapter 20 practice problems on high-temperature partition functions, thermodynamic quantities, and rotational energy levels for harmonic oscillators and diatomic molecules.https://gdpark.blog/posts/thermal-statistical-76-practice-problems-chapter-21/Tue, 27 Dec 2016 00:00:00 +0000https://gdpark.blog/posts/thermal-statistical-76-practice-problems-chapter-21/A collection of practice problems from Chapter 21 to help you study and test your understanding of the material.https://gdpark.blog/posts/thermal-statistical-77-practice-problems-chapter-29/Wed, 28 Dec 2016 00:00:00 +0000https://gdpark.blog/posts/thermal-statistical-77-practice-problems-chapter-29/Sharing my worked solutions for Chapter 29 practice problems on Fermi-Dirac &amp; Bose-Einstein distributions — not all problems covered, so take it as a reference and feel free to correct me!https://gdpark.blog/posts/thermal-statistical-78-practice-problems-chapter-23/Fri, 30 Dec 2016 00:00:00 +0000https://gdpark.blog/posts/thermal-statistical-78-practice-problems-chapter-23/A set of practice problems from Chapter 23, compiled as image-based problem sets for study and review.https://gdpark.blog/posts/thermal-statistical-79-practice-problems-chapter-25/Fri, 30 Dec 2016 00:00:00 +0000https://gdpark.blog/posts/thermal-statistical-79-practice-problems-chapter-25/A set of practice problems for Chapter 25 — work through these to test your understanding before the next exam.https://gdpark.blog/posts/thermal-statistical-80-practice-problems-chapters-26-27/Sun, 01 Jan 2017 00:00:00 +0000https://gdpark.blog/posts/thermal-statistical-80-practice-problems-chapters-26-27/Working through practice problems from Chapters 26 &amp; 27 on van der Waals gases, isothermal compressibility, and isobaric expansivity near the critical point — 27.2 was already covered, so we&rsquo;re skipping ahead~