In the first half of the course, I will discuss the basic ideas of linear algebra, review differential calculus, teach implicit function theorem, and explain how to apply these mathematical tools to formulate and analyze static economic models. In the second half of the course, I will discuss optimization. First, I will explain the basic ideas of optimization in the case of single variable optimization. Consumer utility maximization and producer profit maximization problems will be used to illustrate the procedure. Then more difficult cases (multi-variables, constraint optimization, nonlinear programming) will be discussed. Many mathematical concepts related economics (e.g., convexity) will be explained. The course ends with a brief introduction to general equilibrium and game theory.

每週進度及教學內容簡述

第一週：Static Economic Models and The Concept of Equilibrium
第二週：Matrix Algebra, Vector Space, and Linear Transformation
第三週：Determinant, Inverse Matrix, and Cramer’s Rule
第四週：Differential Calculus and Comparative Statics
第五週：Optimization
第六週：Optimization – Multivariate Case
第七週：Optimization-- Equality constraints and Nonlinear Programming
第八週：Optimization-- Equality constraints and Nonlinear Programming
第九週：Midterm
第十週：General Equilibrium and Game Theory
第十一週：Economic Dynamics and Integral Calculus
第十二週：Ordinary Differential Equation
第十三週：Difference Equation
第十四週：Diagonalization of a Matrix sand Jordan Theorem
第十五週：Simultaneous Difference Equation
第十六週：Simultaneous Differential Equation
第十七週：Dynamic Optimization – Discrete Time
第十八週：Final Exam