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Module Specifications

Archived Version 2009 - 2010

Module Title Calculus of Several Variables
Module Code MS205
School School of Mathematical Sciences

Online Module Resources

Level 2 Credit Rating 5
Pre-requisite None
Co-requisite None
Module Aims
1. To teach the Calculus of functions of several variables so that it can be applied in courses onmechanics, economic, numerical analysis and probability.2. To present this theory rigorously and elegantly.

Learning Outcomes
1. That students be able to apply the theory to examples.2. That students understand the basic concepts and theorems.

Indicative Time Allowances
Lectures 36
Tutorials 12
Laboratories 0
Seminars 0
Independent Learning Time 27

Total 75
Assume that a 5 credit module load represents approximately 75 hours' work, which includes all teaching, in-course assignments, laboratory work or other specialised training and an estimated private learning time associated with the module.

Indicative Syllabus
1. Differential Calculus: Limits and Continuity, directional derivatives and partial derivatives;affine approximation and definition of derivative; chain rule; higher derivatives, mean valuetheorem and Taylor''s theorem; determination of local maxima and minima; surfaces andLagrange multipliers, statements of inverse and implicit function theorems.2. Integral Calculus: Double integrals, Fubini''s theorem, Jacobians and change of variablesformula, triple integrals.
Continuous Assessment25% Examination Weight75%
Indicative Reading List
Essential:Marsden, J. and A. Tromba, Vector Calculus, 4 th ed., Freeman, 1996.Supplementary:Lang, S., Calculus of Several Variables, 3rd ed., Springer-Verlag, 1987.
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