Available in 2021
Course code

MATH2800

Units

10 units

Level

2000 level

## Course handbook

### Description

Differential equations provide one of the most powerful mathematical tools for understanding the natural world. Since rates of change are commonly expressed using derivatives, differential equations arise whenever some continuously varying quantities and their rates of change in space or time are known or postulated. Whether seeking to understand biological or physical processes, behaviours of solids or liquids, ecological or mechanical systems, differential equations provide essential insights. If only one independent variable is involved, which is often time, these equations are called ordinary differential equations.

This course introduces students to the world of ordinary differential equations. The main focus of the course will be to investigate analytical and numerical solution techniques, qualitative behaviour of the solutions and mathematical modelling to explore a wide breadth of application areas.

### Availability2021 Course Timetables

#### Callaghan

• Semester 1 - 2021

### Learning outcomes

On successful completion of the course students will be able to:

1. Formulate differential equation models arising from the mathematical modelling of real-life problems, interpret solutions and assess their implications for answering questions of practical importance.

2. Solve important classes of differential equations analytically and numerically.

3. Analyse important classes of numerical methods to approximate solutions of differential equations.

4. Use qualitative analysis of important classes of differential equations to investigate properties of their solutions.

### Content

Topics will include:

• Differential equations and mathematical modelling
• Analytical solution techniques of ordinary differential equations including systems
• Numerical solution techniques: Taylor series and Runge-Kutta methods, error analysis, step-size control and stability
• Existence, uniqueness and continuous dependence on the data
• Stability of solutions
• Lyapunov techniques
• The phase plane

MATH1120

### Assessment items

Written Assignment: Assignments 1

Formal Examination: Examination

Written Assignment: Assignment 2

Quiz: Online Quizzes

In Term Test: Mid Semester Test

### Contact hours

#### Callaghan

##### Lecture

Face to Face On Campus 3 hour(s) per Week for Full Term

##### Tutorial

Face to Face On Campus 1 hour(s) per Week for Full Term

The tutorial may be held in a computer lab when needed.

The University of Newcastle acknowledges the traditional custodians of the lands within our footprint areas: Awabakal, Darkinjung, Biripai, Worimi, Wonnarua, and Eora Nations. We also pay respect to the wisdom of our Elders past and present.