Preparing for an Engineering Degree

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:

  • Differentiation
  • Integration
  • Differential equations
  • Functions, such as trigonometric, logarithmic, exponential
  • Vectors
  • Matrices
  • Complex numbers
  • Mechanics
  • and Probability

Overview of Mathematics covered in first year Engineering Degrees

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
Taylor Series

Series expansions and limits

Introduction to partial differentiation
Integration methods, by parts, substitution, separation of variables

Volume of revolution, centroids

Numerical integration

Integration of rational functions

Improper integrals

Work done pumping water from a bore hole

Linear First Order ODEs

Linear Second Order ODEs

Particular solutions

Calculating Energy of an Oscillating Body
Functions Complex Numbers Matrices
Inverse Functions





Curve Sketching

Cartesian, Polar & Exponential Forms

Euler’s formula

De Moivre's theorem

Complex roots

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
Vectors Mechanics Probability
Vector Algebra

Scalar and vector products

Triple product

Differentiation and integration of vectors

Vector equations of lines and planes

Newton’s laws of motion

Conservation laws


Circular motion

Rigid body mechanics

Moments of inertia, rotation

Simple harmonic motion, damping, resonance

Random variables

Binomial distribution

Poisson distribution

Example Careers

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.

Useful links

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.