## PHYS2380 Maths 4- Transforms and Partial Differential Equations

### 10 creditsClass Size: 250

Module manager: Dr Chris Nixon
Email: C.J.Nixon@leeds.ac.uk

Taught: Semester 2 (Jan to Jun) View Timetable

Year running 2023/24

Module replaces

PHYS2170

This module is not approved as a discovery module

### Objectives

On completion of this module, students will be able to:
- use the method of separation of variables to solve the wave, Laplace, Poisson and diffusion equations with appropriate boundary conditions;
- determine the Fourier series for a given function;
- use Fourier series and Fourier transform methods to solve partial differential equations with several independent variables.

Learning outcomes
Students will be able to demonstrate knowledge, understanding and application of:
1. appropriate partial differential equations and boundary conditions to model the behaviour of physical systems
2. the method of separation of variables to solve partial differential equations
3. Fourier series and Fourier transform methods to solve partial differential equations

Skills outcomes
Basic mathematical methods needed in all branches of science.

### Syllabus

- Wave, Laplace, Poisson, diffusion and SchrÃ¶dinger equations in relevant physical contexts;
- Formulation of boundary-value problems involving each of the above PDEs;
- Solution of boundary-value problems by separation of variables;
- Fourier series and transforms with their applications to PDEs;
- Dirac Delta function and the convolution theorem;
- Solutions of PDEs involving Bessel functions and Legendre polynomials (including orthogonality properties);

### Teaching methods

 Delivery type Number Length hours Student hours Lecture 33 1.00 33.00 Private study hours 67.00 Total Contact hours 33.00 Total hours (100hr per 10 credits) 100.00

### Opportunities for Formative Feedback

Homework assignments.

### Methods of assessment

Coursework
 Assessment type Notes % of formal assessment In-course Assessment Regular Homeworks 20.00 Total percentage (Assessment Coursework) 20.00

Resits will be in standard exam format.

Exams
 Exam type Exam duration % of formal assessment Standard exam (closed essays, MCQs etc) 2 hr 30 mins 80.00 Total percentage (Assessment Exams) 80.00

Students will have to complete an in-person exam at the end of the module. This will take place during the examinations period at the end of the semester and will be time bound.