# Partial Differential Equations

## Course summary

Course code: MATH1151
Level: 6
Credits: 15
School: Architecture, Computing and Hums
Department: Mathematical Sciences
Course Coordinator(s): Yvonne Fryer

## Specification

### Pre and co requisites

Linear Algebra and Applications, Numerical Mathematics and Computer Algorithms

### Aims

This course aims to provide students with a balanced introduction to partial differential equations by covering modern analytical and numerical solution techniques, including a discussion of restrictions and problems associated with various solution approaches. Students will also be exposed to some of the many real-world applications of partial differential equations.

### Learning outcomes

On successful completion of this course a student will be able to:

1. Apply a selection of standard solution techniques such as separation of variables and integral transform methods to the solution of partial differential equations

2. Identify appropriate solution procedures for a given partial differential equation

3. Derive and implement finite difference schemes for partial differential equations

4. Develop an awareness of alternative numerical approaches to solving partial differential equation problems, such as the finite volume method and the finite element method.

5. Appreciate the potential sources of error in numerical methods for partial differential equations

### Indicative content

Introduction and Classification of PDEs: elliptic, parabolic and hyperbolic equations;
Separation of Variables;
Similarity Solutions;
Laplace Transforms;
Fourier Transforms;
Finite difference schemes: derivation and implementation for all classes of PDEs;
Overview of finite volume and finite element methods;
Accuracy, stability and error control;
Applications of PDEs.

### Teaching and learning activity

Concepts and methods will be introduced and demonstrated in lectures. Tutorials will provide students with an opportunity to solve partial differential equations and apply a variety of theoretical tools to examine them. Students will also derive, implement, and analyse numerical schemes in tutorial work.

### Assessment

Summative assessment: Coursework - 50%
LO - 1-5
Coursework covering the learning outcomes, which may include selected tutorial work.

Summative assessment: Exam - 50%
LO - 1-5
Examination of 3 hours in duration covering learning outcomes.

Formative assessment: Weekly tutorial exercises reinforcing the lecture material.