I. Matrix algebra and matrix diagonalization

1.1. Matrices: Definitions and operations with matrices; determinant; rank of a matrix; inverse matrix

1.2. Diagonalization: Similar matrices; eigenvectors and eigenvalues; theorems on diagonalization; examples

II. Difference equations (discrete time)

2.1. Introduction: Definitions, classification

2.2. First order systems: Autonomous systems; fixed points; local and global stability; cycles

2.3. First order linear equation: General solution; stability; multiplier growth model; cobweb model

2.4. Second order linear equation: General solution; multiplier growth model (continued)

2.5. First order linear systems: General solution for diagonalizable systems; stability; variedad estable; Dynamic adjustment Cournot model

2.6. Non-linear first order equation: Local and global stability; phase diagram; periodicity and chaos; population models;

III. Differential equations (continuous time)

3.1. Introduction: Definitions, classification

3.2. integration methods: Primitives; separable equations, exact equations; integrating factor; linear equations; phase diagrams

3.3. Applications: Walrasian price adjustment; asset pricing model; population models of Malthus, Verhulst and with threshold; Solow's model of economic growth

3.4. Second order linear equations: General solution

3.5. Systems of two equations of first order: Fixed points and stability; linear systems, solution and stability; linearization; predator-prey models

RECITATION

Regular exercises will be assigned all throughout the course. It is recommended that you try to solve these exercises before they are solved in the class.

TEXTBOOKS

• Alpha C. Chiang and Kevin Wainwright. Fundamental Methods of Mathematical Economics. Mc Graw Hill, 2006
• Knut Sydsaeter and Peter J. Hammond. Mathematics for Economic Analysis. Prentice Hall, 1995

GRADING

The final grade is a weighted average of the final exam and the class grade. The final exam is the same for all the Mathematics for Economics groups and consists of practical exercises and theoretical questions. The class grade is obtained in the small groups and it is based on quizzes done in the classes.

Ordinary Exam

The final grade is the weighted average of the final exam (60%) and the class grade (40%).

Extraordinary Exam

The final grade is the maximum of the following grades:

a) A weighted average of the final exam (60%) and the class grade (40%).

b) 100% of the grade of the final exam.

---

Modified: September 2, 2021