# Partial Differential Equations in Engineering

Course code MATH2470
Available in 2016

## Description

Differential equations arise in all branches of science and engineering. In Chemical Engineering students encounter problems involving heat transfer, diffusion and vibration which involve functions of 2 variables and their derivatives. The resulting equations are partial differential equations. Usually the solutions must satisfy physical restrictions - the resulting equations are called boundary value problems. Students will apply their knowledge of calculus and ordinary differential equations, as well as learning new techniques. Theoretical methods such as Fourier series are covered in lectures and applied methods such as the finite difference method are studied using specialised computer software.

### Availability

#### Callaghan

• Semester 2 - 2016
• Semester 2 - 2017

### Learning Outcomes

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

1. Provide the necessary mathematical knowledge and skills in solving boundary-value problems related to the diffusion of heat, mass and momentum.

2. Provide the necessary numerical and computing skills for solving boundary-value problems arising in Chemical Engineering applications.

### Content

• Conduction of heat in solids and the heat equation.
• Types of boundary conditions.
• Steady-state temperature and Laplace's equation.
• Separation of variables.
• Fourier series.
• 1-dimensional heat transfer problems.
• Higher-dimensional problems in cartesian coordinates.
• Higher-dimensional problems in polar, spherical, and cylindrical coordinates.
• Numerical differentiation using finite differences.
• Discretisation of the steady state and transient heat equation.
• Discretisation of various types of boundary conditions.
• Numerical solutions of the steady state and transient heat equation.

### Assumed Knowledge

MATH1120 or MATH1220.

### Assessment Items

Tutorial / Laboratory Exercises: Laboratory Exercises

Formal Examination: Formal Examination

Written Assignment: Assignments

### Contact Hours

#### Callaghan

##### Computer Lab

Face to Face On Campus 2 hour(s) per Week for Full Term

##### Lecture

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