Functions, limits and continuity; the derivative and differentation; behaviour of functions and their graphs-extreme function values and approximations; the definite integral and integration; logarithmic, exponential, inverse trigonometric and hyberbolic functions; additional applications of the definite integral; techniques of integration, indeterminate forms and improper integrals; polynomial approximations, sequences and the infinite series; parametric equations, plane curves and polar graphs; vectors and planes, lines and surfaces in space; vector-valued functions; differential calculus of more than one variable; multiple integration; introduction to the calculus of vector fields.
