Mathematical skills for Masters-level short courses in engineering

What level of maths skills will you need?

The short course you’re reviewing uses mathematical skills that are typically learned during undergraduate engineering mathematics modules.

This page is a guide to the level of maths skills you’ll require for this short course.

Use our free online reference guide

Engineering departments across the UK have developed a set of free online resources called Helping Engineers Learn Mathematics (HELM).

You can use HELM to assess your own preparedness for this short course.

View free HELM resource

Maths topics you’ll cover

Here are the maths topics that may be used during this short course.

We’ve included a brief description of each topic, and the relevant sections of HELM that cover these:

Foundation Mathematics

  • Arithmetic; algebra; equations; graphs; linear equations and simultaneous linear equations; polynomial equations; partial fractions; trigonometry; binomial series; differentiation; integration; functions.
  • HELM sections 1-6 and 11-16

Complex Numbers

  • Uses of the number j = √-1, particularly in the description of random functions and hyperbolic functions. Applied in dynamics and control theory problems.
  • HELM section 10


  • More advanced solution methods for groups of simultaneous equations. Used in reliability theory; solid mechanics; finite element methods; control theory.
  • HELM sections 7 and 8


  • Solution methods for simultaneous equations. Used for aspects of solid mechanics, structural engineering and control.
  • HELM section 7.3

Scalars, Vectors and Tensors

  • Description of physical quantities in engineering systems. Required for numerical subjects; Tensors required for aspects of solid mechanics.
  • HELM section 9

Differentiation and Partial Differentiation

Integration - Direct and Approximate Solutions

  • Application of integration to engineering problems including area under a function; mean values of functions; RMS values of functions; surfaces of revolution; volumes of revolution; locating centroids; moments of inertia; second moments of area.
  • HELM section 13 for the theory of integration
  • HELM sections 14 and 15 for applications of integration
  • HELM section 31.2 for approximate numerical integration methods

Multiple Integrals

  • Multiple integrals used to describe multi-dimensional systems including structural analysis; reliability theory.
  • HELM section 27

Polar Co-ordinates

  • Use of polar co-ordinate system to describe behaviour of engineering systems.
  • HELM section 17.2

Differential equations and Laplace transforms

  • Used for the description of dynamic behaviours of engineering systems. Laplace Transforms used as a solution method for certain types of differential equations.
  • HELM section 19 for differential equations
  • HELM section 20 for Laplace transforms

Fourier transforms

  • Mapping of time domain functions into frequency domain using Fourier pairs. Use of both real and imaginary components for signals analysis; random functions and dynamics.
  • HELM section 24

Probability theory and statistics

  • Probability calculus used to describe physical and knowledge-based uncertainties in engineering systems. Used in reliability theory. Statistics used in failure data analysis and collection of data from engineering systems.
  • HELM section 35 for basic probability
  • HELM section 36 for basic statistics
  • HELM section 37-39 for probability density functions

The above list should not be taken as definitive, but as a guide to prospective applicants in understanding the level of maths skills required in some of the Masters-level courses delivered by our School of Engineering.

You should be prepared to have this knowledge assessed if you have not done so already through an undergraduate-level course. In this case, the above list of topics should be used as a guide for self-study; a task for which the HELM resources are well designed.