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;
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)
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. Supplementals if required will consist of 100% exam.