Handbook

This is a core second-year higher mathematics course for students from all disciplines. The course extends the theory of one-variable calculus to functions or mappings with several variables. It forms the foundation for various courses in pure and applied mathematics, as well as in physics, economics and others. Topics covered include functions of several variables, limits and continuity, differentiability, gradients, surfaces, maxima and minima, Taylor series, Lagrange multipliers, chain rules, inverse function theorem, Jacobian derivatives, double and triple integrals, iterated integrals, Riemann sums, cylindrical and spherical coordinates, change of variables, centre of mass, curves in space, line integrals, parametrised surfaces, surface integrals, divergence and curl, Stokes' theorem, Green's theorem in the plane, applications of integral theorems, Fourier series, convergence of Fourier series, applications of Fourier series. The material will be covered in lectures, problem sheets will be discussed in tutorials.