The resources included below revisit topics needed in your STEM modules. Watch the videos and work through the exercises to boost your Maths confidence, knowledge and understanding.
If you need to 'dig deeper', please check the Foundations, Higher or Advanced sections on the previous pages or if you are looking for something more specific, use "Ctrl+F" for a faster search.
Enjoy your learning!
1. Basic Algebra
01.1 Mathematical Notation and Symbols
01.2 Indices
01.3 Simplification and Factorisation
01.4 Arithmetic of Algebraic Fractions
01.5 Formulae and Transposition
2. Basic Functions
02.1 Basic Concepts of Functions
02.2 Graphs of Functions and Parametric Form
02.3 One-to-One and Inverse Functions
02.4 Characterising Functions
02.5 The Straight Line
02.6 The Circle
02.7 Some Common Functions
3. Equations, Inequalities And Partial Fractions
03.1 Solving Linear Equations
03.2 Solving Quadratic Equations
03.3 Solving Polynomial Equations
03.4 Solving Simultaneous Linear Equations
03.5 Solving Inequalities
03.6 Partial Fractions
4. Trigonometry
04.1 Right-angled Triangles
04.2 Trigonometric Functions
04.3 Trigonometric Identities
04.4 Applications of Trigonometry to Triangles
04.5 Applications of Trigonometry to Waves
5. Functions and modelling
05.1 The Modelling Cycle and Functions
05.2 Quadratic Functions and Modelling
05.3 Oscillating Functions and Modelling
05.4 Inverse Square Law Modelling
6. Exponential and Logarithmic functions
06.1 The Exponential Function
06.2 The Hyperbolic Functions
06.3 Logarithms
06.4 The Logarithmic Function
06.5 Modelling Exercises
06.6 Log-linear Graphs
7. Matrices
07.1 Introduction to Matrices
07.2 Matrix Multiplication
07.3 Determinants
07.4 The Inverse of a Matrix
8. Matrix Solution of Equations
08.1 Solution by Cramer’s Rule
08.2 Solution by Inverse Matrix Method
08.3 Solution by Gauss Elimination
9. Vectors
09.1 Basic Concepts of Vectors
09.2 Cartesian Components of Vectors
09.3 The Scalar Product
09.4 The Vector Product
09.5 Lines and Planes
10. Complex Numbers
10.2 Argand Diagrams and the Polar Form
10.3 The Exponential Form of a Complex Number
10.4 De Moivre’s Theorem
11.Differentiation
11.1 Introducing Differentiation
11.2 Using a Table of Derivatives
11.3 Higher Derivatives
11.4 Differentiating Products and Quotients
11.5 The Chain Rule
11.6 Parametric Differentiation
11.7 Implicit Differentiation
12. Differentiation Applications
12.1 Tangents and Normals
12.2 Maxima and Minima
12.3 The Newton-Raphson Method
12.4 Curvature
12.5 Differentiation of Vectors
12.6 Case Study: Complex Impedance
13. Integrations
13.1 Basic Concepts of Integration
13.2 Definite Integrals
13.3 The Area Bounded by a Curve
13.4 Integration by Parts
13.5 Integration by Substitution and Using Partial Fractions
13.6 Integration of Trigonometric Functions
14. Integration Applications (1)
14.1 Integration as the Limit of a Sum
14.2 The Mean Value and the Root-Mean-Square Value
14.3 Volumes of Revolution
14.4 Lengths of Curves and Surfaces of Revolution
15. Integration Applications (2)
15.1 Integration of Vectors
15.2 Calculating Centres of Mass
15.3 Moment of Inertia
16. Sequences and Series
16.1 Sequences and Series
16.2 Infinite Series
16.3 The Binomial Series
16.4 Power Series
16.5 Maclaurin and Taylor Series
17. Conics and polar coordinates
17.1 Conic Sections
17.2 Polar Coordinates
17.3 Parametric Curves
18. Functions Of Several Variables
18.1 Functions of Several Variables
18.2 Partial Derivatives
18.3 Stationary Points
18.4 Errors and Percentage Change
19. Differential Equations
19.1 Modelling with Differential Equations
19.2 First Order Differential Equations
19.3 Second Order Differential Equations
19.4 Applications of Differential Equations
20. The Laplace Transform
20.1 Causal Functions
20.2 The Transform and its Inverse
20.3 Further Laplace Transforms
20.4 Solving Differential Equations
20.5 The Convolution Theorem
20.6 Transfer Functions
21. The Z transform
21.1 The z-Transform
21.2 Basics of z-Transform Theory
21.3 z-Transforms and Difference Equations
21.4 Engineering Applications of z-Transforms
21.5 Sampled Functions
22. Eigenvalues and Eigenvectors
22.1 Eigenvalues and Eigenvectors
22.2 Applications of Eigenvalues and Eigenvectors
22.3 Repeated Eigenvalues and Symmetric Matrices
22.4 Numerical Determination of Eigenvalues and Eigenvectors
23. Fourier series
23.1 Periodic Functions
23.2 Representing Periodic Functions by Fourier Series
23.3 Even and Odd Functions
23.4 Convergence
23.5 Half-Range Series
23.6 The Complex Form
23.7 An Application of Fourier Series
24. Fourier transforms
24.1 The Fourier transform
24.2 Properties of the Fourier Transform
24.3 Some Special Fourier transform Pairs
25. Partial Differential Equations
25.1 Partial Differential Equations
25.2 Applications of PDEs
25.3 Solution Using Separation of Variables
25.4 Solution Using Fourier Series
26. Functions of a Complex Variable
26.1 Complex Functions
26.2 Cauchy-Riemann Equations and Conformal Mapping
26.3 Standard Complex Functions
26.4 Basic Complex Integration
26.5 Cauchy’s Theorem
26.6 Singularities and Residues
27. Multiple Integration
27.1 Introduction to Surface Integrals
27.2 Multiple Integrals over Non-rectangular Regions
27.3 Volume Integrals
27.4 Changing Coordinates
28. Differential Vector Calculus
28.1 Background to Vector Calculus
28.2 Differential Vector Calculus
28.3 Orthogonal Curvilinear Coordinates
29. Integral Vector Calculus
29.1 Line Integrals Involving Vectors
29.2 Surface and Volume Integrals
29.3 Integral Vector Theorems
30. Introduction to Numerical Methods
30.1 Rounding Error and Conditioning
30.2 Gaussian Elimination
30.3 LU Decomposition
30.4 Matrix Norms
30.5 Iterative Methods for Systems of Equations
31. Numerical Methods of Approximation
31.1 Polynomial Approximations
31.2 Numerical Integration
31.3 Numerical Differentiation
31.4 Nonlinear Equations
32. Numerical Initial Value Problems
32.1 Initial Value Problems
32.2 Linear Multistep Methods
32.3 Predictor-Corrector Methods
32.4 Parabolic PDEs
32.5 Hyperbolic PDEs
33. Numerical Boundary Value Problems
34. Modelling Motion
34.1 Projectiles
34.2 Forces in More Than One Dimension
34.3 Resisted Motion
35. Sets and Probability
35.1 Sets
35.2 Elementary Probability
35.3 Addition and Multiplication Laws of Probability
35.4 Total Probability and Bayes’ Theorem
36. Descriptive Statistics
37. Discrete Probability Distributions
37.1 Discrete Probability Distributions
37.2 The Binomial Distribution
37.3 The Poisson Distribution
37.4 The Hypergeometric Distribution
38. Continuous Probability Distributions
38.1 Continuous Probability Distributions
38.2 The Uniform Distribution
38.3 The Exponential Distribution
39. The Normal Distribution
39.1 The Normal Distribution
39.2 The Normal Approximation to the Binomial Distribution
39.3 Sums and Differences of Random Variables
40. Sampling Distributions and Estimation
40.1 Sampling Distributions and Estimation
40.2 Interval Estimation for the Variance
41. Hypothesis Testing
41.1 Statistical Testing
41.2 Tests Concerning a Single Sample
41.3 Tests Concerning Two Samples
42. Goodness of Fit and Contingency Tables
43. Regression and Correlation
44. Analysis of Variance
44.1 One-Way Analysis of Variance
44.2 Two-Way Analysis of Variance
44.3 Experimental Design
45. Non-parametric Statistics
45.1 Non-parametric Tests for a Single Sample
45.2 Non-parametric Tests for Two Samples