SECTION I: LINEAR ALGEBRA

Matrix algebra is often used in Economics to represent and solve linear systems of equations. An understanding of the basic operations and properties of matrix algebra is fundamental for the successful completion of many courses within the master program.

Part 1: Linear Algebra Basics

1. Definitions
2. Matrix Operations
3. Trace and Transpose
4. Determinant and Cofactors
5. Inverse

Part 2: Solving Linear Equations

1. Linear Dependence
2. Rank of a Matrix
3. Linear Equations
4. Cramer‘s Theorem

Part 3: Economic Applications of Linear Algebra

1. Linear Economic Models
- Structural and Reduced Form
- Comparative Statics

Section I: Course materials

Section II: Course Materials

SECTION II: BASIC ANALYSIS

Analysis is needed in any context of optimization: we often look for minima, optima and stable equilibriums in economics – we use limits, derivatives, and integral techniques therefore. Most courses of the master program will require a sound knowledge of these methods.

Part 1: Single Variable Functions

1. Compounding and Discounting Interest
- Nominal and Effective Interest
- Limits
2. Limits and Inverse
3. Composite Functions
4. Log-Functions
5. Derivatives
- Definition
- Basic Rules
- Elasticity
- Second Derivative
6. Optimization
- Production and Cost Functions
- Log functions
- Stationary Points

Part 2: Multi Variable Functions and Integrals

1. Introduction
- Examples
- Partial Derivatives
- Differentials
- Homogeneous Functions
2. Optimization of Multi Variable Functions
- Unconstraint optimization
- Constraint Optimization
3. Integration
- Definite and Indefinite Integrals
- Substitution and Integration by Parts

 

REFERENCES

Chiang, Alpha (2005).  Fundamental Methods of Mathematical Economics. McGraw-Hill Higher Education, New York.

Neftci, Salih N. (2000). An Introduction to the Mathematics of Financial Derivatives. Academic Press, New York.

Takayama, Akira (1974). Mathematical Economics.The Dryden Press, Hinsdale, Illinois.