Differential Equations

Module code: MA2021

This is a branch of mathematics that forms as a foundation for all parts of pure and applied mathematician, scientist or engineer. This module provides a comprehensive overview on differential equations, from their analytical and geometric interpretations to the differences between classes of differential equations, such as:

Autonomous
Non-autonomous
Linear and non-linear
Homogeneous, inhomogeneous

By widening your understanding of differential equations, this module will demonstrate how to analyse initial value problems in order to determine whether or not they have unique solutions. We will then outline the fundamental theorems that are used to prove basic existence and uniqueness results. During this module you will develop your computing and analytical skills by writing programs for finding numerical solutions of ordinary differential equations (involving both explicit and implicit procedures).

Topics covered

Solutions of general ODEs of the first-order in normal form
Peano existence theorem
Osgood’s uniqueness theorem
Picard’s theorem