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Module MAU11202: Advanced Calculus
 Credit weighting (ECTS)

5 credits
 Semester/term taught

Hilary term 201920
 Contact Hours

11 weeks, 3 lectures including tutorials per week

 Lecturer
 Prof. Kirk Soodhalter
 Learning Outcomes
 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.
 Vectorvalued functions: parametric curves, calculus, change of parameter (Chapter 12, Sections 12.112.6)
 Partial derivatives: definition, chain rule, gradients, maxima and minima (Chapter 13, Sections 13.113.9)
 Multiple integrals: double and triple integrals, surface area (Chapter 14, Sections 14.114.8)
 Module Prerequisite
 MAU11201,
MAU11100
 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. Reassessments if required will consist of 100% exam.