Basic algebra
Mathematical notation and symbols
Indices
Simplification by collecting like terms
Removing brackets
Factorisation
Arithmetic of algebraic fractions
Formulae and transposition
Functions
Basic concepts of functions
The graph of a function
Composition of functions
Onetoone and inverse functions
Parametric form of a function
Characterising functions
The straight line
Some common engineering functions
Polynomials, inequalities and partial fractions
Solving linear equations
Solving quadratic equations
Solving polynomial equations
Solving simultaneous linear equations
Solving inequalities
Partial fractions
Sets and basic probability
Sets
Elementary probability
Addition and multiplication laws of probability
Discrete probability distributions
Discrete probability distributions
The Binomial distribution
The Poisson distribution
Logarithms and exponentials
The exponential function
The hyperbolic function
Logarithms
The logarithm function
Matrices
Introduction to matrices
Matrix multiplication
Determinants
The inverse of a matrix
Using matrices and determinants to solve equations
Cramer's rule for solving simultaneous equations
Solving simultaneous equations using the inverse matrix
Gauss elimination

Vectors
Basic concepts of vectors
Cartesian components of vectors
Direction ratios; direction cosines
The scalar product
The vector product
Lines and planes
Complex numbers
Complex arithmetic
Argand diagrams and polar form
Exponential form
De Moivre's theorem
Differentiation
Introducing differentiation
Using a table of derivatives
Higher derivatives
Techniques of differentiation
Differentiating products and quotients
The chain rule
Parametric differentiation
Applications of differentiation
Perpendicular lines
Maxima and minima
The NewtonRaphson method
Curvature
Integration
Basic concepts of integration
Definite integrals
The area bounded by a curve
Integration by parts
Integration by substitution and partial fractions
Integration of trigonometric functions
Applications of Integration
Integration as the limit of a sum
Volumes of revolution
Calculating centres of mass
Moment of inertia
Lengths of curves and surfaces of revolution
The mean value and rootmeansquare value of a function
Differentiation and integration of vectors
Sequences and series
Sequences and series
Infinite series
The binomial series
Power series
Maclaurin and Taylor series

Conic sections
Circle, ellipse, parabola, hyperbola
Polar coordinates
Parametric form
Functions of several variables
Functions of several variables
Partial derivatives
Stationary points
Errors and percentage change
Differential equations
Modelling with differential equations
Separation of variables
Exact equations
Integrating factor
Constant coefficient equations
Finding a particular integral
Applications of differential equations
The Laplace transform
Causal functions
The transform and its inverse
Further Laplace transforms
Solving differential equations
The delta function
The convolution theorem
Transfer functions
Continuous probability distributions
Continuous probability distributions
The standard normal distribution
The general normal distribution
