Maths for Engineers

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

• 33.1 Two-point Boundary Value Problems
• 33.2 Elliptic PDEs

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

• 36.1 Describing Data
• 36.2 Exploring Data

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

• 42.1 Goodness of Fit
• 42.2 Contingency Tables

43. Regression and Correlation

• 43.1 Regression
• 43.2 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

46. Reliability and Quality Control

• 46.1 Reliability
• 46.2 Quality Control