Mathematical Methods for Economics-II

The objective of this sequence is to transmit the body of basic mathematics that enables the study of economic theory at the undergraduate level. In this course, particular economic models are not the ends, but the means for illustrating the method of applying mathematical techniques to economic theory in general. This sequence will continue to acquaint the students with basic and advanced mathematical tools used in economic analysis.

Module No.

Module Name

1

Introduction to Differential Equations

2

Differential Equation of First Order and First Degree

3

Homogenous Equations

4

Non-homogeneous Equations of First Degree in x and y

5

Linear Differential Equations

6

Exact Differential Equations

7

Economic Applications of Differential Equations

8

Vectors: An Introduction and Properties

9

Vectors: Scalar Products, Norms and Orthogonality

10

Linear Transformations: Properties and Matrix Representations

11

Properties of Matrices

12

Addition and Multiplication of Matrices

13

Determinants: Characterization and Properties

14

Crammer's Rule and Linear Equations

15

Adjoint and Inverse of Matrix

16

Economic Applications of Matrix and Determinants

17

Functions of Several Real Variables: An Introduction

18

Geometric Representations: Graphs and Level Curves

19

Economic Applications of Differentiable Functions

20

Derivatives of Standard Functions

21

Differentiation of the Products and the Quotients, Chain Rule

22

Differentiation of Implicit Functions and Parametric Functions

23

Differentiation of Logarithmic and Exponential Functions

24

Second Order Derivatives: Properties and Applications

25

Application of Differentiation to Comparative Static Problem

26

Homogeneous Functions and Euler Theorem

27

Applications of Homogenous Functions

28

Monotonic Transformation of Homogenous Functions

29

Homothetic Functions: Theorem and Applications

30

Convex Sets and Their Properties

31

Convex Functions: Differentiability and Convexity

32

Properties and Applications of Convex Functions

33

Quasi Convex Functions: Characterization and Properties

34

Applications of Quasi-Convex Functions

35

Unconstrained Optimization: Geometric Characterization and Properties

36

Optimization of Simple Unconstrained Functions

37

Optimization of Simple Unconstrained Functions with Two and More Variables

38

Calculus and Unconstrained Optimization

39

Economic Applications of Optimization of Unconstrained functions

40

Constraint Optimization: An Overview, Characteristics and Properties

41

Constraint Optimization- The Geometric Characterization

42

Constraint Optimization with Equality Constraints

43

Use of Partial Derivatives- Constrained Optimization

44

Constraint Optimization- Lagrange’s method

45

Constrained Optimization- Economic Applications

46

Value Functions: Introduction and Properties

47

Envelope Theorem and
Constrained Optimization: An Introduction

48

Linear Programming – An Introduction

49

Linear Programming – Graphic Method

50

Economic Models