MA206-5-AU-CO: Mathematical Methods
Note: This module is inactive. Visit the Module Directory to view modules and variants offered during the current academic year.
Department: Mathematical Sciences
Essex credit: 15
ECTS credit: 7.5
Available to Study Abroad / Exchange Students: Yes
Full Year Module Available to Study Abroad / Exchange Students for a Single Term: No
Outside Option: Yes
Dr Hadi Susanto
Dr Hadi Susanto, email firstname.lastname@example.org
Miss Claire Watts, Department Manager, Tel. 01206 873040, email email@example.com
|Module is taught during the following terms
The course gives an introduction to a range of core mathematical techniques, of broad applicability.
Sequences and series:
- Bounded, monotonic, convergent sequences of real numbers;
- Sums, products and quotients of sequences.
- 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.
- Taylor series, radius of convergence, term-by-term differentiation, exponential series
- Taylor series for a function of two variables;
- Lagrange multipliers: stationary points subject to constraints.
- 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 and Teaching Methods
This course runs at 3 hours per week in the Autumn term. There are 2 lectures in weeks 2-11 and one lecture in weeks 2-4,6 and 8 and one classes in weeks 5, 7, 9, 8 and 11
In the Summer term 3 revision lectures are given.
20 per cent Coursework Mark, 80 per cent Exam Mark
The coursework comprises one test worth 20%.
Information about coursework deadlines can be found in the "Coursework Information" section of the Current Students, Useful Information Maths web pages: Coursework and Test Information
Exam Duration and Period
2:00 during Summer Examination period.
Available to Socrates /IP students spending all relevant terms at Essex.
- Recommended Reading:
- G.B. Thomas & R.L. Finney, Calculus & Analytic Geometry, Addison-Wesley.
- E. Kreyszig, Advanced Engineering Maths. Wiley
- W.E. Boyce & R.C. Di Prima, Elementary Differential Equationsand Boundary Value Problems. Wiley
- E. Swokowski, M. Olinick & D.Pence, (1994) Calculus, 6th Edition, PWS Publishing Co.