COURSE OBJECTIVES

This course provides an introduction to the theory, solution, and application of ordinary differential equations. Topics discussed in the course include methods of solving first-order differential equations, existence and uniqueness theorems, second-order linear equations, power series solutions, higher-order linear equations, and their applications.

COURSE LEARNING OUTCOMES (CLO)

CLO-1: Use their knowledge of calculus to solve the 1st order ordinary differential equations.
CLO-2: Use various techniques to solve higher order ordinary differential.
CLO-3: Model the problems arising in different areas of science and engineering in the form of ordinary differential equations.
CLO-3: Understand the meaning, use and applications of the partial differential equations

COURSE CONTENTS

  1. Introduction to Differential Equations – Five Lectures                
  • Introduction,
  • Definitions and terminology
  • Formulations
  • Order
  • Degree and the linearity of differential equation
  • Initial-Value problems
  • DE’s in Mathematical Models

2. First Order Differential Equations – Five Lectures                                

  • Variables Separable Forms
  • Homogenous Equations
  • Non-homogenous equations
  • Exact Equations
  • Linear Equations
  • Solution by Substitutions

3. Applications of First Order DE’s – Six Lectures                          

  • Modeling with the First Order Differential Equations
  • Orthogonal Trajectories
  • Population Dynamics
  • Applications of Linear Equations
  • Applications of Non-linear Equations

4. Higher Order Linear Differential Equations – Five Lectures                              

  • Introduction and Preliminary Theory
  • Initial-value and Boundary-value Problems
  • Homogenous and Non-Homogenous Equations
  • Method of Undetermined Coefficients
  • Method of Variation of Parameters
  • Power Series Solution

5. Applications of the Second Order Differential Equations – Five Lectures                                  

  • Spring Mass Problems
  • Electrical Circuit Problem

6. Partial Differential Equations – Six Lectures                                                                             

  • Basic Concepts
  • Vibrating String
  • Wave Equation
  • Separation of Variables
  • Heat Equation Solution by Separation of variables