This course covers topics in linear algebra, multi-variable calculus and their applications. In Linear Algebra students learn about normal forms of operators, in particular, Jordan normal form, diagonalisation of Hermitian operators, polynomial and Fourier approximations and quadratic forms. In Calculus, students learn partial derivatives and the gradient, methods of optimisation of functions of several variables, double, triple and line integrals, conservative vector fields, and, finally, an all-important Green's theorem. The course shows unity and inseparability of Algebra and Calculus. It lays a foundation for a large number of stage 3 and graduate courses in pure and applied mathematics, statistics, and also for many advanced courses in physics and various other applied sciences. It is a core mathematics course for the BSc(Hons), BAdvSci and PGDipSci.