Module Title 
Calculus of Several Variables

Module Code 
MS205

School 
School of Mathematical Sciences

Online Module Resources

Module Coordinator  Dr David Reynolds  Office Number  X138E 
Level 
2

Credit Rating 
5

Prerequisite 
None

Corequisite 
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


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 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.

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

BQF  BSc in Quantitative Finance 
BSSA  Study Abroad (DCU Business School) 
BSSAO  Study Abroad (DCU Business School) 
ECSA  Study Abroad (Engineering & Computing) 
ECSAO  Study Abroad (Engineering & Computing) 
FM  BSc in Financial & Actuarial Mathematics 
HMSA  Study Abroad (Humanities & Soc Science) 
HMSAO  Study Abroad (Humanities & Soc Science) 
MS  BSc in Mathematical Sciences 
SHSA  Study Abroad (Science & Health) 
SHSAO  Study Abroad (Science & Health) 
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