## 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