Engineering degree courses all require good mathematical skills.
You will be taught the mathematics required for the course during your first year. The topics covered will be mostly content from A level Mathematics and Further Mathematics. These techniques and methods will be applied in engineering contexts and require you to pick up the skills and concepts quickly.
Consequently you are encouraged to do as much mathematics in the sixth-form as possible so that you have some familiarity with topics like:
The table below shows typical areas of mathematics that might be studied in the first year of an undergraduate engineering degree course.
The hyperlinked applications of A level Mathematics and Further Mathematics in red have been included in the overview to illustrate how these mathematical ideas are used in engineering contexts:
|Differential Calculus||Integral Calculus||Differential Equations|
|Differentiation – implicit and parametric
Finding stationary points
Numerical methods for finding roots
Series expansions and limits
Introduction to partial differentiation
|Integration methods, by parts, substitution, separation of variables
Volume of revolution, centroids
Integration of rational functions
Work done pumping water from a bore hole
|Linear First Order ODEs
Linear Second Order ODEs
Calculating Energy of an Oscillating Body
|Functions||Complex Numbers||Matrices||Inverse Functions
|Cartesian, Polar & Exponential Forms
De Moivre's theorem
Analysing AC current
Impedance can be complex
Inverse of a matrix
Solution of sets of linear equations
Eigenvalues and eigenvectors
Matrices as transformations
Calculating the current in a mesh
Motion of a coupled spring system
Scalar and vector products
Differentiation and integration of vectors
Vector equations of lines and planes
|Newton’s laws of motion
Rigid body mechanics
Moments of inertia, rotation
Simple harmonic motion, damping, resonance
The Tomorrow's Engineers website has information about routes into engineering and a large selection of career profiles.
Rebecca - a civil engineer describes her work and the pathway to her career as a civil engineer. This is one of many profiles on the Women's Engineering Society, WES website.
The following websites have useful information about the mathematical topics you will study during your first year of an engineering degree together with other resources to support your preparation for engineering at university.
MEI's Engineering Resources were developed for the Royal Academy of Engineering to support the teaching and learning of mathematics within engineering courses. These are free but schools need to register with MEI to access them. Here is a sample activity for Simple Gears and Transmission for students and for teachers.
EngNRICH - a section of the Nrich website with problems and articles specific to applications of mathematics in Engineering. It is for students aged 14 - 19 and is designed to complement and enhance the study of engineering. Some of the examples in the table above are from this website.
I want to study Engineering is a website with hundreds of problems based on A level questions to help students prepare for engineering at university
Isaac Physics - a bank of challenging questions for improving your mathematical problem solving skills for physics and engineering problems. The site includes notes and explanations of techniques and is designed and maintained by the University of Cambridge.
Tomorrow's Engineers Guide to Engineering at University gives an overview of different types of engineering courses.
The Maths Centre - this site was developed by a group from the Universities of Loughborough, Leeds and Coventry and has been set up to deliver mathematics support to students looking for post-16 mathematics help.