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Module Specifications

Archived Version 2004 - 2005

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

Online Module Resources

Module Co-ordinatorDr David ReynoldsOffice NumberX138E
Level 2 Credit Rating 5
Pre-requisite MS101, MS102, MS103, MS104
Co-requisite None
Module Aims
1. To teach the Calculus of functions of several variables so that it can be applied in courses on mechanics, 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 value theorem and Taylor¿s theorem; determination of local maxima and minima; surfaces and Lagrange multipliers, statements of inverse and implicit function theorems. 2. Integral Calculus: Double integrals, Fubini¿s theorem, Jacobians and change of variables formula, 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.
Programme or List of Programmes
FMBSc in Financial & Actuarial Mathematics
MSBSc in Mathematical Sciences