PMAT 22282: Ordinary Differential Equations

Course Code        : PMAT 22282

Title                     : Ordinary Differential Equations

Pre-requisites          : PMAT 12253

 Learning Outcomes:

At the end of this course, the student should be able to

1. classify the differential equations with respect to their order and linearity
2. find a particular solution of a differential equation using initial conditions
3. solve first-order and higher-order linear ordinary differential equations
4. examine the existence and uniqueness of a solution of an initial value problem
5. solve linear differential equations using Laplace transform method
6. solve differential equations involving real-life applications.

 Course Contents:

Introduction: 

• Differential Equations, Ordinary Differential Equations (ODE), Order, Degree, classification of linear and non-linear ODEs, solution of a differential equation, Family of curves.

First-Order ODEs: 

• Separable ODEs., Homogeneous equations, Exact ODEs., Integrating Factors, Linear ODEs, Bernoulli Equation. Orthogonal Trajectories, Existence and Uniqueness of Solutions for Initial Value Problems, applications of first order ODEs.

Second/Higher Order Linear ODEs: 

• Homogeneous Linear ODEs with Constant Coefficients, Homogeneous Linear ODEs of Second Order, method of order reduction, Existence and Uniqueness of Solutions, Wronskian, Differential Operators, Euler–Cauchy Equations, Nonhomogeneous ODEs, Solution by Variation of Parameters,
  Method of undetermined coefficients, applications of higher order ODEs.

The Laplace Transform: 

• Definition of Laplace transforms, Basic properties, Inverse Laplace transform, Convolution theorem, Solve Linear Differential Equations with constant coefficients using Laplace transform

Teaching/Learning methods : A combination of lectures and tutorial discussions.

 Assessment : Based on tutorials, tests and end of course examination.

 Recommended Reading:

1. Kreyszig, E. (2018). Advanced Engineering Mathematics, Wiley.
2. Shepley, L.R, (1989). Introduction to Ordinary Differential Equations, John Wiley and Sons.
3. Nagle R.K., Saff, E.B. & Snider A.D. (2011) Fundamentals of Differential Equations, Pearson.
4. Krantz, S.G. (2014). Differential equations: theory, technique and practice (Vol. 17). CRC Press.
5. Tenenbaum, M. & Pollard, H. (1985). Ordinary Differential Equations, Dover Publications.
6. Murray, R., Murray, R., & Spiegal. (1974). Theory and problems of Laplace transforms. Shaum's
Outline Series.