London School of Economics and Political Science (LSE)

Modules

Advanced calculus [117] (half unit)

Note: this unit cannot be taken with 95 Further mathematics for economists.

Prerequisites (if taken as part of a BSc degree):
05a Mathematics 1 and 05b Mathematics 2.

This course unit follows on from Mathematics 1 and Mathematics 2, and continues further the study of calculus techniques and theory. The course unit will develop further the theory of functions, and will also include some new practical skills, such as how to evaluate multiple integrals, and how to use Laplace transforms to solve differential equations.

Topics included are: Functions of several variables, linear approximations and tangent planes, directional derivatives and the gradient, Edgeworth box and contract curves, concave and convex functions, inverse functions, local inverses and critical points, the Riemann integral, multiple integration, improper integrals, manipulation of integrals, introduction to the Laplace transform.