# Ordinary Differential Equations 2

## Unit aims

The aim of this unit is to introduce the students to the basic theory of ordinary differential equations.

## Unit description

The subject of differential equations is a very important branch of applied mathematics. Many phenomena from physics, biology and engineering may be described using ordinary differential equations. In order to understand the underlying processes we have to find and interpret the solutions of these equations; this unit is an introduction to this endeavour.

## Relation to other units

This unit develops the ordinary differential equations material in Calculus 1. Partial differential equations are treated in a separate unit, Applied Partial Differential Equations 2. Together with Multivariable Calculus and Methods of Complex Functions, these courses provide essential tools for mathematical methods and applied mathematics units at Levels 3 and 4. Multivariable Calculus is recommended but not required as a co-requisite.

## Learning objectives

By the end of this unit students will be able to:

• recognize basic types of differential equations and understand the features of linear equations in particular.
• use phase plane analysis to investigate equations which are not easily solvable.
• apply the notions of equilibrium, linearization, stability and bifurcation to problems arising in physics, biology and engineering etc.

## Transferable skills

• Increased understanding of the relationship between mathematics and physical, biological, economic etc. systems.
• Development of problem-solving and analytical skills.

## Syllabus

1. What is dynamics? Simple examples from physics.
2. The geometric point of view. Flows in one and two dimensions.
3. Stability and linearization. Invariant sets and manifolds
4. Elementary bifurcation theory.

There may be minor changes to this syllabus, or to the order of presentation.

## Reading and References

Stephen Wiggins, Ordinary Differential Equations

Unit code: MATH20101
Level of study: I/5
Credit points: 20
Teaching block (weeks): 1 (1-12)
Lecturer: Dr Isaac Chenchiah

## Pre-requisites

Calculus 1 and Linear Algebra and Geometry

None

## Methods of teaching

Lectures supported by problem classes and problem and solution sheets.

## Methods of Assessment

The pass mark for this unit is 40.

The final mark is calculated as follows:

• 100% from a 2 hour 30 minute exam in January

NOTE: Calculators are NOT allowed in the examination.

For information resit arrangements, please see the re-sit page on the intranet.

Please use these links for further information on relative weighting and marking criteria.

Further exam information can be found on the Maths Intranet.