The resources below revisit complex Maths topics included your STEM course. Watch the videos and work through the exercises to boost your knowledge and understanding. If you need to 'dig deeper', please check the Higher section on the previous page or if you are looking for something more specific, use "Ctrl+F" for a faster search.
Enjoy your learning!
Vectors
Introduction to Vectors
Cartesian components of vectors
Lines and planes
Scalar product
Vector product
Matrices
Introduction to matrices
Addition and subtraction
Multiplication
- Video: Multiplying matrices by scalars
- Video: Matrix Multiplication
- HELM exercises on matrix multiplication
Determinants
- Video: Finding the Determinant of a 2x2 matrix
- HELM Exercise and Solution Booklet on matrix determinants
The inverse of a matrix
Eigenvectors and eigenvalues - Introduction
Applications of eigenvalues and eigenvectors
- Video: The applications of eigenvectors and eigenvalues
- HELM Exercises on Eigenvectors and eigenvalue applications
Repeated eigenvalues and symmetric matrices
- Video: Symmetric Matrices (Even with Repeated Eigenvalues) Have Orthogonal Eigenvectors
- HELM exercises on eigenvalues and symmetric matrices
Numerical determination of eigenvalues and eigenvectors
Solving Systems of Equations
Gaussian elimination
- Video: Gaussian elimination: Matrix Algebra for Engineers
- Video Gaussian Elimination and Row Echelon Form
- HELM Exercises Booklet on Gaussian elimination
Solution by Cramer's rule
- Video: Cramer's Rule - 3x3 Linear System (using matrices to solve Sims with 3 unknowns)
- HELM Exercise Booklet on using Cramer's rule to solve sims
Solution by inverse matrix method
- Video: Solving Linear Equations using the Inverse Matrix Method 2x2
- HELM BookletVideo Gaussian Elimination and Row Echelon Form
LU decomposition
- Video: Using lower diagonal and upper diagonal matrix decomposition
- HELM Exercises with worked solutions on LU matrix decomposition