Complete written notes for each session. Every set of notes opens with learning objectives and closes with a problem set, a computational lab and readings. Use Print / save as PDF on any lecture page for an offline copy.
| Lec # | Topic and objectives | Length |
|---|---|---|
| Part I · Single-variable analysis | ||
| 1 | Limits, Continuity, and the Logic of Analysis Use epsilon-delta definitions; evaluate limits; distinguish pointwise values from limiting behavior; establish continuity; apply the intermediate and extreme value theorems. | 9 min read |
| 2 | Sequences, Convergence, and Infinite Series Define convergence rigorously; use monotone convergence and Cauchy criteria; test infinite series; distinguish absolute and conditional convergence; analyze power series. | 8 min read |
| 3 | Differentiation, Mean Value Theorems, and Comparative Rates Derive derivatives from first principles; apply differentiation rules; use mean value theorems; interpret marginal effects, elasticities, and comparative rates. | 8 min read |
| 4 | Taylor Approximation, Convexity, and Single-Variable Optimization Derive Taylor approximations; classify stationary points; use convexity; solve economic optimization problems and interpret first- and second-order conditions. | 7 min read |
| 5 | Integration, Riemann Sums, and the Fundamental Theorem Define the Riemann integral; connect antiderivatives and accumulated area; apply substitution and integration by parts; evaluate improper integrals and interpret economic accumulation. | 7 min read |
| Part II · Multivariable calculus | ||
| 6 | Multivariable Functions, Limits, and Continuity Analyze domains and level sets; define multivariate limits and continuity; distinguish pathwise behavior from genuine limits; interpret surfaces and economic production functions. | 8 min read |
| 7 | Partial Derivatives, Total Differentials, and the Chain Rule Compute partial derivatives; interpret gradients and directional derivatives; derive total differentials; apply multivariate chain rules and Jacobians. | 7 min read |
| 8 | Hessians and Unconstrained Multivariable Optimization Use Hessian matrices to classify curvature; derive multivariate first- and second-order conditions; apply optimization to utility, production, and likelihood functions. | 8 min read |
| Part III · Optimization and implicit functions | ||
| 9 | Equality Constraints and Lagrange Multipliers Derive Lagrange conditions; interpret multipliers as shadow values; solve constrained optimization problems; understand regularity and second-order conditions. | 8 min read |
| 10 | Inequality Constraints and Karush–Kuhn–Tucker Conditions State KKT conditions; identify active constraints; interpret complementary slackness; distinguish necessary and sufficient conditions; solve inequality-constrained economic problems. | 8 min read |
| 11 | Implicit and Inverse Function Theorems State local implicit and inverse function results; derive comparative statics; analyze equilibrium systems using Jacobians; distinguish local from global uniqueness. | 8 min read |
| Part IV · Multiple integration | ||
| 12 | Multiple Integrals, Change of Variables, and Probability Evaluate double and triple integrals; use Fubini's theorem; change coordinates with Jacobians; derive marginal densities and expectations. | 7 min read |
| Part V · Dynamic systems | ||
| 13 | Differential Equations and Continuous-Time Dynamics Solve first-order ODEs; analyze second-order linear equations; study systems using eigenvalues; interpret steady states and stability in economic dynamics. | 8 min read |
| 14 | Difference Equations and Discrete-Time Dynamics Solve first-order difference equations; analyze fixed points and local stability; study linear systems; apply discrete dynamics to economic adjustment and growth. | 7 min read |