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Module MA1132: Advanced calculus

Credit weighting (ECTS)
5 credits
Semester/term taught
Hilary term 2013-14
Contact Hours
11 weeks, 3 lectures including tutorials per week
Prof. Stephen Britton
Learning Outcomes
On successful completion of this module, students will be able to:
  • apply the basic theory of convergence of sequences and series to a range of examples;
  • calculate partial derivatives involving algebraic and transcendental functions (including trigonometric functions, exponential, logarithm, hyperbolic functions and inverses);
  • apply the standard results and concepts concerning differentiation in a number of appropriate contexts (such as graphical or geometric interpretations of tangents, critical points, linear approximation, solving simple linear differential equations);
  • compute double and triple integrals by application of Fubini's theorem or use change of variables;
  • use integrals to find quantities defined via integration in a number of context (such as average, area, volume, mass).
Module Content
These details may be varied somewhat in the current year.
  • Sequences (definition and basic results on convergence).
  • Series (definition of the sum, seriese of positive terms, absolute convergence, tests for convergence).
  • Power series and (use of) Taylor's theorem.
  • Differentiation of curves, tangent lines in 2 or 3 dimensions.
  • Graphical representation of functions of 2 or 3 variables.
  • Patrial derivatives, gradients, direction derivatives, tangent planes to graphs and level surfaces.
  • Linear approximation for functions of 2 or 3 variables, chain rule.
  • Linear and exact differential equations.
  • Double and triple integrals, computation via iterated integrals (Fubini theorem).
  • Double integrals in polar coordinates.
Module Prerequisite
MA1123 (Analysis on the real line I), MA1111 (Linear Algebra I)
Assessment Detail
Regular assignments and tutorial work. In class exams twice in the term (at dates to be advised). No annual examination. For those requiring a supplemental examination, this will consist of 100% exam.