Module Details

MA206-5-AU-CO: Mathematical Methods

Year: 2016/17
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
Pre- or co-requisites: MA101

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, Department Manager, Tel. 01206 873040, email cmwatts@essex.ac.uk

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

Coursework

The coursework comprises one test worth 20%.

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 during Summer Examination period.

Other information

Available to Socrates /IP students spending all relevant terms at Essex.

Bibliography

  • 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.

Further information