Mathematical Economics I

Course Overview

This course is a core requirement for undergraduate students in economics. It has two main objectives:

1. To ensure that students develop a solid understanding of fundamental mathematical concepts.

2. To equip students with the ability to apply these concepts to various economic problems.

The course covers two major topics: Linear Algebra and Single-Variable Calculus.

Course Outline

Part 1: Linear Algebra

1. Systems of Linear Equations
   1.1 Definition and Representation of Linear Systems
   1.2 Solution Sets: Three Possibilities (Unique, Infinite, No Solution)
   1.3 Row Echelon Form and Reduced Row Echelon Form
   1.4 Gaussian & Gauss-Jordan Elimination Methods
   1.5 Rank of a Matrix and Its Implications for Solutions
   1.6 Homogeneous Systems and Their Properties
   
   

2. Matrices
   2.1 Definition, Notation, and Types of Matrices
   2.2 Matrix Algebra: Addition, Scalar Multiplication, and Multiplication
   2.3 Elementary Matrices, Inverse Matrices, and the Inversion Algorithm
   
   

3. Determinants
   3.1 Definition and Basic Properties of Determinants
   3.2 Determinants via Laplace Cofactor Expansion
   3.3 Applications: Cramer’s Rule and Matrix Invertibility

Part 2: Single-Variable Calculus

4. Limits and Continuity
   4.1 Definition of a Limit and Intuitive Understanding
   4.2 Techniques for Evaluating Limits (Algebraic, L’Hôpital’s Rule)
   4.3 One-Sided Limits and Limits at Infinity
   4.4 Definition of Continuity and Types of Discontinuities
   
   

5. Differentiation
   5.1 Definition of the Derivative and Its Interpretation
   5.2 Basic Differentiation Rules: Power Rule, Sum Rule, Product Rule, Quotient Rule
   5.3 Chain Rule and Its Applications
   5.4 Differentiation of Logarithmic, Exponential, and Trigonometric Functions
   5.5 Higher-Order Derivatives and Concavity
   
   

6. Integration
   6.1 Definition of an Integral and the Fundamental Theorem of Calculus
   6.2 Basic Integration Rules: Power Rule, Linearity, and Special Cases
   6.3 Advanced Techniques: Integration by Substitution and Integration by Parts
   6.4 Definite Integrals, Improper Integrals, and Applications in Area Calculations

Reading Materials

Prescribed Textbook:

(To be specified)

Recommended Readings:

Linear Algebra:

• Carl P. Simon & Lawrence Blume (1994). Mathematics for Economists. W.W. Norton, London. [Chapters 6–9]

• Howard Anton & Chris Rorres (2013). Elementary Linear Algebra. 11th Edition, Wiley.

Calculus:

• Carl P. Simon & Lawrence Blume (1994). Mathematics for Economists. W.W. Norton, London. [Chapters 2–5]

• Howard Anton, Irl Bivens & Stephen Davis (2020). Calculus: Early Transcendentals. 11th Edition, Wiley. (For rigorous treatment of limits, continuity, differentiation, and integration)