- UCAS course code
- F305
- UCAS institution code
- M20
Master of Physics (MPhys)
MPhys Physics
Join a physics Department of international renown that offers great choice and flexibility, leading to master's qualification.
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Duration: 4 years
Year of entry: 2025
UCAS course code: F305 / Institution code: M20
- Key features:
Scholarships available
Accredited course
- Typical A-level offer: A*A*A including specific subjects
- Typical contextual A-level offer: A*AA including specific subjects
- Refugee/care-experienced offer: AAA including specific subjects
- Typical International Baccalaureate offer: 38 points overall with 7,7,6 at HL, including specific requirements
Fees and funding
Fees
Tuition fees for home students commencing their studies in September 2025 will be £9,535 per annum (subject to Parliamentary approval). Tuition fees for international students will be £36,500 per annum. For general information please see the undergraduate finance pages.
Policy on additional costs
All students should normally be able to complete their programme of study without incurring additional study costs over and above the tuition fee for that programme. Any unavoidable additional compulsory costs totalling more than 1% of the annual home undergraduate fee per annum, regardless of whether the programme in question is undergraduate or postgraduate taught, will be made clear to you at the point of application. Further information can be found in the University's Policy on additional costs incurred by students on undergraduate and postgraduate taught programmes (PDF document, 91KB).
Scholarships/sponsorships
The University of Manchester is committed to attracting and supporting the very best students. We have a focus on nurturing talent and ability and we want to make sure that you have the opportunity to study here, regardless of your financial circumstances.
For information about scholarships and bursaries please visit our undergraduate student finance pages and our Department funding pages .
Course unit details:
Mathematics of Waves and Fields
| Unit code | PHYS20171 |
|---|---|
| Credit rating | 10 |
| Unit level | Level 2 |
| Teaching period(s) | Semester 1 |
| Available as a free choice unit? | No |
Overview
Mathematics of Waves and Fields
Pre/co-requisites
| Unit title | Unit code | Requirement type | Description |
|---|---|---|---|
| Mathematics 1 | PHYS10071 | Pre-Requisite | Compulsory |
| Vibrations & Waves | PHYS10302 | Pre-Requisite | Compulsory |
| Mathematics 2 | PHYS10372 | Pre-Requisite | Compulsory |
Aims
To introduce and develop the mathematical skills and knowledge needed to understand classical fields and quantum mechanics.
Learning outcomes
On completion successful students will be able to:
1. Solve partial differential equations using the method of separation of variables.
2. Define the term “orthogonality” as applied to functions, and recognise sets of orthogonal functions which are important in physics (e.g. trigonometric functions and complex exponentials on appropriate intervals, Legendre polynomials, and spherical harmonics).
3. Represent a given function as a linear superposition of orthogonal basis functions (e.g. a Fourier series) using orthogonality to determine the coefficients,
4. State how a Fourier transform differs from a Fourier series, and calculate Fourier transforms of simple functions.
5. Solve eigenvalue problems (differential equations subject to boundary conditions) either in terms of standard functions or as power series.
6. Use partial differential equations to model wave, heat flow and related phenomena.
7. Make basic use of Dirac notation.
Syllabus
1. Wave problems in one dimension
Separation of variables
Normal modes of a string: eigenfunctions and eigenvalues
General motion of a string
2. Fourier series
Orthogonality and completeness of sines and cosines
Complex exponential form of Fourier series
3. Other PDE’s
Laplace’s equation
The heat-flow equation
4. Integral transforms
Fourier transform
Convolutions
Wave packets and dispersion
5. Special functions
Orthogonal sets of eigenfunctions
Series solution of differential equations
Legendre polynomials and related functions
Bessel functions
6. Problems in two and three dimensions
Normal modes of a square membrane; degeneracy
Wave guide
Normal modes of circular and spherical systems
Heat flow in circular and spherical systems
Laplace’s equation: examples in cartesian and polar coordinates
7. Dirac notation
Vector spaces
Ket notation
Inner products and Bras
Hilbert spaces
Assessment methods
| Method | Weight |
|---|---|
| Other | 10% |
| Written exam | 90% |
* Other 10% Tutorial Work/attendance
Feedback methods
Students will receive feedback on their work and performance in this module as a component of their weekly tutorial meeting with their academic tutor.
Recommended reading
Boas, M.L. Mathematical Methods for Physical Sciences, 3rd edn. (Wiley, 2006)
Martin, B.R. & Shaw, G, Mathematics for Physicists. (Wiley 2015)
Riley, K.F. Hobson, M.P. & Bence, S.J. Mathematical Methods for Physics and Engineering, 3rd edn (Cambridge 2006) [Chapters 12 to 19]
Stephenson, G. Partial differential equations for scientists and engineers (Imperial College 1996)
Study hours
| Scheduled activity hours | |
|---|---|
| Assessment written exam | 1.5 |
| Lectures | 22 |
| Tutorials | 4 |
| Independent study hours | |
|---|---|
| Independent study | 72.5 |
Teaching staff
| Staff member | Role |
|---|---|
| Roger Jones | Unit coordinator |