Readings are listed by session. Core textbooks for the whole course are listed at the end.
Lecture 1: Limits, Continuity, and the Logic of Analysis
Apostol, Calculus, Vol. 1; Spivak, Calculus; Rudin, Principles of Mathematical Analysis.
Lecture 2: Sequences, Convergence, and Infinite Series
Apostol, Calculus, Vol. 1; Spivak, Calculus; Rudin, Principles of Mathematical Analysis.
Lecture 3: Differentiation, Mean Value Theorems, and Comparative Rates
Apostol, Calculus, Vol. 1; Chiang and Wainwright, Fundamental Methods of Mathematical Economics; Simon and Blume, Mathematics for Economists.
Lecture 4: Taylor Approximation, Convexity, and Single-Variable Optimization
Apostol, Calculus, Vol. 1; Chiang and Wainwright, Fundamental Methods of Mathematical Economics; Simon and Blume, Mathematics for Economists.
Lecture 5: Integration, Riemann Sums, and the Fundamental Theorem
Apostol, Calculus, Vol. 1; Spivak, Calculus; Chiang and Wainwright, Fundamental Methods of Mathematical Economics.
Lecture 6: Multivariable Functions, Limits, and Continuity
Apostol, Calculus, Vol. 2; Simon and Blume, Mathematics for Economists; Chiang and Wainwright, Fundamental Methods of Mathematical Economics.
Lecture 7: Partial Derivatives, Total Differentials, and the Chain Rule
Apostol, Calculus, Vol. 2; Simon and Blume, Mathematics for Economists; Chiang and Wainwright, Fundamental Methods of Mathematical Economics.
Lecture 8: Hessians and Unconstrained Multivariable Optimization
Simon and Blume, Mathematics for Economists; Sundaram, A First Course in Optimization Theory; Apostol, Calculus, Vol. 2.
Lecture 9: Equality Constraints and Lagrange Multipliers
Sundaram, A First Course in Optimization Theory; Chiang and Wainwright, Fundamental Methods of Mathematical Economics; Simon and Blume, Mathematics for Economists.
Lecture 10: Inequality Constraints and Karush–Kuhn–Tucker Conditions
Sundaram, A First Course in Optimization Theory; Nocedal and Wright, Numerical Optimization; Chiang and Wainwright, Fundamental Methods of Mathematical Economics.
Lecture 11: Implicit and Inverse Function Theorems
Simon and Blume, Mathematics for Economists; Chiang and Wainwright, Fundamental Methods of Mathematical Economics; Apostol, Calculus, Vol. 2.
Lecture 12: Multiple Integrals, Change of Variables, and Probability
Apostol, Calculus, Vol. 2; Casella and Berger, Statistical Inference; Simon and Blume, Mathematics for Economists.
Lecture 13: Differential Equations and Continuous-Time Dynamics
Boyce, DiPrima, and Meade, Elementary Differential Equations; Chiang and Wainwright, Fundamental Methods of Mathematical Economics; Strogatz, Nonlinear Dynamics and Chaos.
Lecture 14: Difference Equations and Discrete-Time Dynamics
Chiang and Wainwright, Fundamental Methods of Mathematical Economics; Simon and Blume, Mathematics for Economists; Strogatz, Nonlinear Dynamics and Chaos.
Core textbooks
- Apostol, Calculus, Volumes 1 and 2.
- Spivak, Calculus.
- Simon and Blume, Mathematics for Economists.
- Chiang and Wainwright, Fundamental Methods of Mathematical Economics.
- Rudin, Principles of Mathematical Analysis (selected advanced topics).