Pre-requisite: 64612/75612
The unit introduces the basic techniques of multi-variable calculus with particular emphasis on functions of two or three variables. Differential calculus is extended to cover gradients and directional derivatives, the determination of extrema and the divergence and curl of vector fields. Integral calculus is extended to double and triple integrals, line integrals and Green's theorem. Single variable calculus is developed to cover series approximations and differentiation of integrals. Vector spaces are introduced with discussions of linear independence, bases, the Gram-Schmidt process, the eigenvalue problem and the theory of equations.