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


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)


  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