Master of Physics (MPhys)

MPhys Physics

Join a physics Department of international renown that offers great choice and flexibility, leading to master's qualification.

  • Duration: 4 years
  • Year of entry: 2025
  • UCAS course code: F305 / Institution code: M20
  • Key features:
  • Scholarships available
  • Accredited course

Full entry requirementsHow to apply

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 2

Course unit fact file
Unit code PHYS10372
Credit rating 10
Unit level Level 1
Teaching period(s) Semester 2
Available as a free choice unit? No

Overview

Mathematics 2

Pre/co-requisites

Unit title Unit code Requirement type Description
Mathematics 1 PHYS10071 Pre-Requisite Compulsory

Aims

To acquire the skills in vector calculus needed to understand Electromagnetism, Fluid and Quantum Mechanics. To acquire an introductory understanding of Fourier Series and their use in physics.

Learning outcomes

On completion successful students will be able to:

1. Explain the concepts of scalar and vector fields.

2. Describe the properties of div, grad and curl and be able to calculate the divergence and curl of vector fields in various coordinate systems.

3. Calculate surface and volume integrals in various coordinate systems.

4. Calculate flux integrals and relate them to the divergence and the Divergence Theorem.

5. Calculate line integrals and relate them to the curl and to Stokes' Theorem.

6. Apply the methods of vector calculus to physical problems.

7. Calculate the Fourier series associated with simple functions and apply them to selected physical problems.

Syllabus

1.  Differentiation and integration with multiple variables                                                                         (6 lectures)

Partial and total derivatives. Taylor’s theorem for multivariable functions. Multiple integration over areas and volume; volumes, masses and moments of inertia. Use of limits in integrals. Methods of evaluation of multiple integrals. Cylindrical and spherical polar coordinates.  Jacobian Determinant.

2.  Vector operators: div, grad and curl                                                                                                          (6 lectures)

Scalar and vector fields. Definition and uses of the gradient operator. The method of Lagrange multipliers. Definitions of divergence and curl. Combinations of div, grad and curl; theorems. The Laplacian. Vector operators in cylindrical and spherical polar co-ordinates.

3.  The Divergence Theorem, Stokes Theorem, conservative forces                                                         (7 lectures)

Line integrals of scalar and vector fields. Surface integrals and flux of vector fields. Integral expression for divergence. Divergence theorem and its uses. Conservation laws; continuity equation. Integral expression for curl. Stokes' theorem and its uses. Definition of conservative field. Relation to potentials.

4. Introduction to Fourier Series                                                                                                                   (3 lectures)

Rationale for using Fourier series. The Dirichlet conditions. Orthogonality of functions. The Fourier coefficients, symmetry considerations. Examples of Fourier series. Complex representation of Fourier Series.

 

Assessment methods

Method Weight
Other 10%
Written exam 90%

* Other

10% Weekly online 

10% Tutorial Work/attendance 

Feedback methods

Feedback will be offered by tutors on students’ written solutions to weekly examples sheets, and model answers will be issued. Interactive feedback will be offered during the Workshop sessions.

Recommended reading

Martin, B. R. and Shaw, G. Mathematics for Physicists (Manchester Physics Series, Wiley). 

Rile, K.F., Hobson, M.P. and Bence, S.J. Mathematical Methods for Physics and Engineering

Schey, H. M. Div. Grad, Curl and All that, 2nd ed. (Norton)

M. Boas, Mathematical Methods in the Physical Sciences (3rd Edition, Wiley) 

 

Study hours

Scheduled activity hours
Assessment written exam 1.5
Lectures 24
Practical classes & workshops 12
Tutorials 6
Independent study hours
Independent study 56.5

Teaching staff

Staff member Role
Mark Lancaster Unit coordinator

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