MAT 102 – Ordinary Differential Equations

Mathematical Modelling, Change, Growth & Dynamic Systems

Course Description

This course introduces ordinary differential equations arising from physical, biological and engineering systems. Students learn analytical methods for solving first and second order equations, Laplace transforms, and qualitative analysis of solutions.

5 Topics

Core ODE modules

Applications

Science, Engineering & Population Models

Assessment

Test + Assignment + Final Exam

Skills

Modelling and analytical solution methods

Learning Outcomes

Concepts

Understand order, linearity and classification of ODEs.

Methods

Solve first and second order differential equations.

Transforms

Apply Laplace transforms to differential equations.

Interpretation

Use solutions in applied real-world contexts.

Search Topics

Course Topics

Topic I

Introduction to Differential Equations

Topic I Tutorial

Practice Questions

Topic II

First Order Differential Equations

Topic II Tutorial

Practice Questions

Topic III

Second Order Linear Differential Equations

Topic III Tutorial

Practice Questions

Topic IV

Laplace Transforms

Module

Topic V

Qualitative Theory of Differential Equations

Module

Assessment

Test – 20%
Assignment – 20%
Final Examination – 60%

Mode of Delivery

Lectures, seminars, tutorials and case studies.

References

Ross – Introduction to Ordinary Differential Equations
Massawe & Manja – Elementary Ordinary Differential Equations
Boyce & DiPrima – Differential Equations and Boundary Value Problems
Derrick & Grossman – Introduction to Differential Equations
Kreyszig – Advanced Engineering Mathematics