Mathematical skills for Masters-level short courses in engineering

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

Matrices

• 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

Determinants

• 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

• Rates of change form the basis of much of mechanics and the dynamics of engineering systems.
• HELM sections 11 and 12
• HELM section 18.2

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.