
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


Hours

Lectures 
36

Tutorials 
12

Laboratories 
0

Seminars 
0

Independent Learning Time 
27



Total 
75

Placements 

Assignments 


NOTE

Assume that a 5 credit module load represents approximately 75 hours' work, which includes all teaching, incourse 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.

Assessment  Continuous Assessment  25%  Examination Weight  75% 

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., SpringerVerlag, 1987.


Programme or List of Programmes

FM  BSc in Financial & Actuarial Mathematics 
MS  BSc in Mathematical Sciences 
Archives:  