MA206-5-AU: MATHEMATICAL METHODS
Year: 2013/14
Department: Mathematical Sciences
Essex credit: 15
ECTS credit: 7.5
Available to Study Abroad / Exchange Students: Yes Pre-requisites: MA118
| Module is taught during the following terms |
| Autumn |  | Spring |  | Summer | |
Module Description
The course gives an introduction to a range of core mathematical techniques, of broad applicability.
Syllabus
Sequences and series:
- Bounded, monotonic, convergent sequences of real numbers;
- Sums, products and quotients of sequences.
Series:
- Summable and absolutely summable series of real numbers;
- Finite and infinite geometric series;
- harmonic series; harmonic series with alternating signs.
- Ratio and comparison tests for summability.
Power series:
- Taylor series, radius of convergence, term-by-term differentiation, exponential series
Partial differentiation:
- Taylor series for a function of two variables;
- Lagrange multipliers: stationary points subject to constraints.
Double integrals:
- change in order of integration;
- change of variable to polar co-ordinates.
On completion of the course students should be able to:
- recognise and manipulate simple sequences and series;
- distinguish summable series from others;
- calculate Taylor series expansions;
- calculate radii of convergence of power series;
- find the stationary points of quadratic functions subject to linear constraints;
- change order of integration in repeated integrals.
Learning & Teaching Methods
This course runs at 3 hours per week in the Autumn term. There are 5 lectures and one class in every fortnight.
In the Summer term 3 revision lectures are given.
Assessment
20 per cent Coursework Mark, 80 per cent Exam Mark
Other details:
Information about coursework deadlines can be found in the "Coursework Information" section of the Current Students, Useful Information Maths web pages: Coursework Information
Exam Duration and Period
2:00 hour exam during Summer Examination period.
Other information
Available to Socrates /IP students spending all relevant terms at Essex.
Bibliography
- G.B. Thomas & R.L. Finney, "Calculus and Analytic Geometry", Addison-Wesley
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Supplementary Texts:
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E. Kreyszig, "Advanced Engineering Mathematics", Wiley
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Boyce & Di Prima, "Elementary Differential Equations and Boundary Value Problems", Wiley.
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E. Swokowski, M. Olinick & D.Pence, (1994) "Calculus", 6th Edition, PWS Publishing Co.
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