One lecture session per week. Problem sets are due one week after the sessions they cover; see Assignments and Exams.
| Ses # | Topic | Main output |
|---|
| Part I · Single-variable analysis |
| 1 | Limits, Continuity, and the Logic of Analysis | Epsilon-delta proof |
| 2 | Sequences, Convergence, and Infinite Series | Convergence analysis |
| 3 | Differentiation, Mean Value Theorems, and Comparative Rates | Derivative derivations |
| 4 | Taylor Approximation, Convexity, and Single-Variable Optimization | Single-variable optimization |
| 5 | Integration, Riemann Sums, and the Fundamental Theorem | Integration assignment |
| Part II · Multivariable calculus |
| 6 | Multivariable Functions, Limits, and Continuity | Surface and level-set analysis |
| 7 | Partial Derivatives, Total Differentials, and the Chain Rule | Gradient/Jacobian exercises |
| 8 | Hessians and Unconstrained Multivariable Optimization | Midterm examination |
| Part III · Optimization and implicit functions |
| 9 | Equality Constraints and Lagrange Multipliers | Equality-constrained application |
| 10 | Inequality Constraints and Karush–Kuhn–Tucker Conditions | Inequality-constrained application |
| 11 | Implicit and Inverse Function Theorems | Comparative statics |
| Part IV · Multiple integration |
| 12 | Multiple Integrals, Change of Variables, and Probability | Probability integration |
| Part V · Dynamic systems |
| 13 | Differential Equations and Continuous-Time Dynamics | Continuous-time dynamics |
| 14 | Difference Equations and Discrete-Time Dynamics | Discrete-time stability project |