The Department of Mathematics and Statistics

Differentiation: Functions of a single real variable, polynomials, exponentials and basic trigonometric functions. Product, quotient and 'function of a function' rules. Implicit differentiation. Finding and classifying stationary points. Basic curve sketching for quadratic, polynomial, exponential and logarithmic functions. Application to velocity, acceleration, deceleration, distance travelled. Calculating rates of change. Basic rules for partial differentiation for functions of more than one real variable. Taylor series for a function of a single real variable.

Limits: Concept of a limit. Evaluation of basic limits.

Errors: precision of calculations, round-off errors.

Integration: Definition as reverse of differentiation. Definite integrals and areas under curves. Integration by substitution (u=f(x)), integration by parts, integration by partial fractions. Calculation of work done.

Differential Equations (Topic to be motivated by models of physical systems): First order separable and linear equations. Second order linear with constant coefficients - complementary functions and particular integrals