MA206-5-AU: Mathematical Methods
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 Pre-requisites: MA118
|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
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 hour exam 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.