On successful completion of this module, students will be able to:

Analyse the behaviour of functions of several variables, present the result graphically and efficiently calculate partial derivatives of functions of several variables (also for functions given implicitly);

Obtain equations for tangent lines to plane curves and tangent planes to space surfaces;

Apply derivative tests and the method of Lagrange multipliers to find maxima and minima of functions of several variables, local and global;

Effectively calculate multiple integrals, in Cartesian and polar coordinates, in particular, to find areas, volumes and centres of mass;

Module Content

These details may be varied somewhat in the current year.

Partial derivatives: definition, chain rule, gradients, maxima and minima (Chapter 13, Sections 13.1-13.9)

Multiple integrals: double and triple integrals, surface area (Chapter 14, Sections 14.1-14.8)

Module Prerequisite

MA1123 (Analysis on the real line I),
MA1111 (Linear Algebra I)

Assessment Detail

This module will be examined in a 2 hour examination in Trinity term. Continuous assessment will contribute 20% to the final grade for the module at the annual
examination session. Supplemental grade will consist of 100% examination.