Course Description:
The successful completion of this course would help students in achieving the following objectives:
• Model the problems arising in different areas of science and engineering in the form of differential equations
• Solve the linear 1st order differential equations that appear in circuit analysis, electronics, motion, electric machines etc.
• Solve second order differential equations using different techniques
• Apply 2nd order differential equations to the variety of theoretical problems
• Understand the meaning, use and applications of the partial differential equations

Course Learning Outcomes:
CLO:1 Use the knowledge of calculus to solve the ordinary differential equations by different techniques.
CLO:2 Apply the concepts of ordinary derivatives for the modeling of physical systems.
CLO:3 Illustrate the usage and application of partial differential equations.

Course Contents:

1. Introduction to Differential Equations – Four 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 – Six Lectures
• Variables separable forms,
• Homogenous equations,
• Non-homogenous equations,
• Exact equations,
• Linear equations,
• Solution by substitutions,
• Exercises

3. Applications of First Order DE’s – Five Lectures
• Modeling with the first order differential equations
• Orthogonal trajectories
• Population dynamics
• Applications of linear equations
• Applications of non-linear equations
• Exercises

4. Higher Order Linear Differential Equations – Six 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 engineering related problems

6. Introduction to Partial Differential Equations – Six Lectures
• Basic concepts,
• Vibrating string,
• Wave equation,
• Separation of variables,
• Heat equation solution by Fourier series.
• Exercises