Mathematics Revision Materials#
Introduction#
Your course will assume you arrive with a certain amount of background in mathematics. Key topics that the programme will build on are Linear Algebra, Vector Calculus and Partial Differential Equations (the last is particularly needed for ACSE students). If you are unfamiliar with any of these topics, or if it has been a while since you last interacted with them, you may find the following resources useful to get up to speed before the course starts:
Imperial Metric is an online interactive Maths resource aimed at first-year undergraduates covering high school material, but it may be useful for brushing up on topics learned some time ago. The resource can be accessed here.
We particularly recommend reviewing any of the following topics that you do not feel confident with:
Linear algebra
Vectors
Matrices
Statistics and probability
Calculus
Differentiation
Integration
Partial differentiation & vector calculus
Differential equations
Numerical methods
A concise set of lecture notes introducing Vector Calculus and PDEs from the undergraduate maths courses in the Department of Earth Science and Engineering are available for download here
More general mathematics materials for all years of undergraduate tuition from the Earth Science and Engineering department at Imperial College are available here. Many of these notes also provide coding examples using the techniques in Python.
Practice Test#
A short practice test covering the above content is available here. It can be completed in under 15 minutes.
Other Learning Resources#
The Khan Academy series of online courses provide free, short video courses on a number of topics, including linear algebra and differential equations
Wolfram MathWorld has short articles on virtually any mathematical topic imaginable.