Mathematical Methods for Physics module (PH31008)

Physics is built on mathematics. The deeper you go into understanding the physical world, the more you need powerful mathematical tools to describe it. This module equips you with exactly that: the essential maths used by physicists to solve real-world problems and make sense of complex systems. 

You'll build a toolkit of mathematical techniques, including vector calculus, matrix algebra, and methods for solving differential equations. These are the mathematical tools needed to understand electromagnetism, fluid dynamics, quantum mechanics, and many other areas of physics. 

You’ll learn how to work with curvilinear coordinates, calculate gradients and fluxes, and apply Gauss’s and Stokes’ theorems. You’ll explore Fourier transforms, the delta function, and how to solve the wave and heat equations. 

This module gives you the mathematical confidence to tackle advanced topics.  

What you will learn

In this module, you will: 

• explore vector calculus and apply Gauss’s, Green’s, and Stokes’ theorems 
• solve differential equations using series methods and special functions 
• use Fourier transforms and delta functions in physical problems 
• learn linear algebra techniques including eigenvalues, eigenvectors, and matrix methods 

By the end of this module, you will be able to: 

• apply advanced mathematical techniques to physics problems 
• solve equations in curvilinear coordinates and interpret physical meaning 
• confidently handle mathematical tools required for higher-level physics courses 

Assignments / assessment

• Coursework (20%) 
• Final exam, two hours (80%) 

Teaching methods / timetable

You will learn through lectures and interactive problem-solving workshops.