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Module MA1132: Advanced Calculus

Credit weighting (ECTS)
5 credits
Semester/term taught
Hilary term 2015-16
Contact Hours
11 weeks, 3 lectures including tutorials per week
Prof. Sergey Frolov
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.
  • Vector-valued functions: parametric curves, calculus, change of parameter (Chapter 12, Sections 12.1-12.6)
  • 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.