|
Module Title |
Calculus of Several Variables
|
|
Module Code |
MS205
|
|
School |
School of Mathematical Sciences
|
Online Module Resources
|
| Module Co-ordinator | Dr David Reynolds | Office Number | X138E |
|
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
|
|
|
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, 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.
|
| 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., Springer-Verlag, 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) |
| Archives: | |
