COURSE OBJECTIVES

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)


    CLO: 1. Use the knowledge of calculus to solve the ordinary differential equations by different techniques. (Level: C3)
    CLO: 2. Apply the concepts of ordinary derivatives for the modeling of physical systems. (Level: C3)
    CLO: 3. Understand the meaning, use and applications of the partial differential equations. (Level: C2)

    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