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# Module details

## MA206-5-AU: Mathematical Methods

Year: 2015/16
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

Staff
Supervisor: Dr Hadi Susanto, email: hsusanto@essex.ac.uk
Teaching Staff: Dr Hadi Susanto, email: hsusanto@essex.ac.uk
Contact details: Miss Claire Watts, Departmental Administrator, Tel. 01206 873040, email cmwatts (Non essex users should add @essex.ac.uk to create the full email address)

 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 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.

### 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 and Test 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 & 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.

## External Examiner Information

• Name: Dr Victoria Gould
• Institution: The University of York
• Academic Role: Professor

Should you have any queries about the Module Directory pages, please contact the Course Record Team, Systems Administration Office, Academic Section; email: crt (non Essex users should add @essex.ac.uk)