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 1

Course unit fact file
Unit code PHYS10071
Credit rating 10
Unit level Level 1
Teaching period(s) Semester 1
Available as a free choice unit? No

Overview

Mathematics 1

Aims

To allow students to develop their mathematical competence with functions, calculus, complex numbers, power series, linear algebra and differential equations to a level where they can cope with the demands of the first year of the physics course and beyond.

Learning outcomes

On completion successful students will be able to:

  1. describe the properties of different types of functions and be able to sketch them in both 2D cartesian and polar coordinates 
  2. integrate and differentiate functions of one variable using a range of techniques and be able to apply integration and differentiation to a range of physical problems. 
  3. show how smooth functions can be expressed in terms of power series.
  4. explain the properties of complex numbers and construct some basic complex functions.
  5. employ matrix notation, carry out matrix algebra and use matrices to solve systems of linear equations. 
  6. compute the properties of determinants, be able to evaluate them, and use them to test for unique solutions of linear equations. 
  7. solve first and second order ordinary differential equations using a range of techniques.

 

 

 

Syllabus

1.  Functions and 2D coordinates

Properties of functions. 2D and 3D coordinate systems. Index notation, Sketching functions, logarithmic functions.          

2.  Complex numbers

Definition, modulus and argument; addition, multiplication, division; roots of quadratic equations; complex numbers in polar form; De Moivre's theorem; Hyperbolic functions.

3.  Differential Calculus

Review of differentiation, the differential; differentiation of products, functions of functions; maxima, minima and inflexions; partial differentiation; examples and applications from physics.                                                              

4.  Power Series

Series, limits of series; binomial expansion; Taylor's and Maclaurin's series expansions.

5.  Integral Calculus

Review of integration; integration by parts, substitution, standard integrals, partial fractions and completing the square; simple line integrals; physical applications.   

6.  Linear Algebra

Matrix algebra, inverse matrix. Definition and properties of determinants, scalar triple product, test of unique solution to linear equations. Eigenvalues and eigenvectors, eigenanalysis.

7.  Ordinary Differential Equations

Physical motivation. 1st order separable. 1st order homogeneous. 1st order linear: integrating factors. 2nd order with constant coefficients. Physical applications.  

Assessment methods

Method Weight
Other 20%
Written exam 80%

* Other

10% Weekly online 

10% Tutorial Work/attendance 

 

Feedback methods

Online quizzes will also be incorporated into the weekly learning material to give students instant feedback on their understanding and ability to apply their knowledge and skills.

Recommended reading

Recommended texts:

Our recommended text is Mathematics for Physicists by Martin and Shaw (Manchester Physics Series). 

Supplementary texts.

Jordan, D. & Smith, P. Mathematical Techniques (OUP)

Tinker, M. & Lambourne, R. Further Mathematics for the Physical Sciences (Wiley) 

ASupplementary texts:

Lambourne, R. & Tinker, M. Basic Mathematics for the Physics Sciences (Wiley)

Study hours

Scheduled activity hours
Assessment written exam 1.5
Lectures 22
Tutorials 10
Independent study hours
Independent study 55.5

Teaching staff

Staff member Role
Robert Appleby Unit coordinator
Justin Evans Unit coordinator

Return to course details