Basic algebra (factorisation, partial fractions), geometry, trigonometry.
Exponential and logarithmic functions and their properties. Odd, even and periodic functions. Concept of a function and inverse functions, inverse trigonometric functions, hyperbolic functions and their inverses, solution of trigonometric and hyperbolic equations.
Real and imaginary parts, polar form, Argand diagram, exp(jx), De Moivre’s theorem and applications.
Concept of derivative and rules of differentiation for a function of one variable. Applications to gradients, tangents and normals, extreme points and curve sketching.
Series and Limits:
Arithmetic and geometric progressions, Maclaurin and Taylor series, use of series in approximations, Newton Raphson method, various techniques for the evaluation of limits.
Concept of indefinite integration as the inverse of differentiation and standard methods for integration such as substitution, integration by parts and integration of rational functions. Definite integration, area under curves, use of recurrence relationships, numerical integration. Applications of integration to curve lengths, surfaces and volumes of revolution.
Probability and statistics:
Descriptive statistics: numerical (mean, mode, median, variance etc) and graphical summaries. Basic Probability: elementary laws, random variables, mean and variance.