Mathematical Methods for Economics-II

Module No.

Module Name

Introduction to Differential Equations

Differential Equation of First Order and First Degree

Homogenous Equations

Non-homogeneous Equations of First Degree in x and y

Linear Differential Equations

Exact Differential Equations

Economic Applications of Differential Equations

Vectors: An Introduction and Properties

Vectors: Scalar Products, Norms and Orthogonality

Linear Transformations: Properties and Matrix Representations

Properties of Matrices

Addition and Multiplication of Matrices

Determinants: Characterization and Properties

Crammer's Rule and Linear Equations

Adjoint and Inverse of Matrix

Economic Applications of Matrix and Determinants

Functions of Several Real Variables: An Introduction

Geometric Representations: Graphs and Level Curves

Economic Applications of Differentiable Functions

Derivatives of Standard Functions

Differentiation of the Products and the Quotients, Chain Rule

Differentiation of Implicit Functions and Parametric Functions

Differentiation of Logarithmic and Exponential Functions

Second Order Derivatives: Properties and Applications

Application of Differentiation to Comparative Static Problem

Homogeneous Functions and Euler Theorem

Applications of Homogenous Functions

Monotonic Transformation of Homogenous Functions

Homothetic Functions: Theorem and Applications

Convex Sets and Their Properties

Convex Functions: Differentiability and Convexity

Properties and Applications of Convex Functions

Quasi Convex Functions: Characterization and Properties

Applications of Quasi-Convex Functions

Unconstrained Optimization: Geometric Characterization and Properties

Optimization of Simple Unconstrained Functions

Optimization of Simple Unconstrained Functions with Two and More Variables

Calculus and Unconstrained Optimization

Economic Applications of Optimization of Unconstrained functions

Constraint Optimization: An Overview, Characteristics and Properties

Constraint Optimization- The Geometric Characterization

Constraint Optimization with Equality Constraints

Use of Partial Derivatives- Constrained Optimization

Constraint Optimization- Lagrange’s method

Constrained Optimization- Economic Applications

Value Functions: Introduction and Properties

Envelope Theorem and
Constrained Optimization: An Introduction

Linear Programming – An Introduction

Linear Programming – Graphic Method

Economic Models