MAU11202 Advanced calculus

Vector-valued functions: parametric curves, calculus, change of parameter.
Partial derivatives: definition, chain rule, gradients, maxima and minima.
Multiple integrals: double and triple integrals, surface area.

Module Code	MAU11202
Module Title	Advanced calculus
Semester taught	Semester 2
ECTS Credits	5
Module Lecturer	Dr. Mariam Al-Hawaj
Module Prerequisites	MAU11201 Single-variable calculus

This module is examined in a 2-hour examination at the end of Semester 2.
Continuous assessment contributes 20% towards the overall mark.
The module is passed if the overall mark for the module is 40% or more. If the overall mark for the module is less than 40% and there is no possibility of compensation, the module will be reassessed as follows:
1) A failed exam in combination with passed continuous assessment will be reassessed by an exam in the supplemental session;
2) The combination of a failed exam and failed continuous assessment is reassessed by the supplemental exam;
3) A failed continuous assessment in combination with a passed exam will be reassessed by one or more summer assignments in advance of the supplemental session.

11 weeks of teaching with 3 lectures and 1 tutorial per week.

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

Analyse the behaviour of functions of several variables, present the result graphically, and calculate partial derivatives of functions of several variables including those which are defined implicitly.
Obtain equations for tangent lines to plane curves and tangent planes to surfaces.
Apply derivative tests and the method of Lagrange multipliers to find maxima and minima of functions of several variables, both local and global.
Compute multiple integrals, in both Cartesian and polar coordinates, and thus compute areas, volumes and centres of mass.