## MAS381 Mathematics III (Electrical)

Note: Information for future academic years is provisional. Timetable information and teaching staff are especially likely to change, but other details may also be altered, some courses may not run at all, and other courses may be added.

 Semester 1, 2019/20 10 Credits Lecturer: Dr Istvan Ballai uses MOLE Timetable Reading List Aims Outcomes Assessment

Prerequisites: MAS241 (Mathematics II (Electrical))
No other modules have this module as a prerequisite.

## Outline syllabus

1. Revision of complex numbers and functions, analytic functions 2. Complex series 3. Poles, singularities, complex integration 4. More advanced vector calculus: double operators, polar coordinates 5. Line integrals, surface integrals, volume integrals 6. Stokes’ theorem, Gauss’ theorem

## Aims

1. To consolidate previous mathematical knowledge and to develop new mathematical techniques to electrical engineering at level 3 and 4. 2. To consolidate previous knowledge on complex numbers and introduce the concept of complex harmonic functions necessary to solve 2D Laplace equation 3. To study complex differentiation, integration and the theory of residues 4. Introduce the concept of double operators and polar coordinates. 5. To introduce the concepts of line integrals, Stoke’s theorem, and volume integrals.

## Learning outcomes

At the end of the course the student should be able to
1. Understand the fundamental concepts at the heart of complex analysis 2. Be able to manipulate complex series 3. Be able to solve problems involving the use of contour integrals 4. Be able to calculate line, surface and volume integrals, including applying Stokes’ and Gauss’ theorems

22 lectures, 11 tutorials

## Assessment

2 hour written examination 4 questions, each worth 25 marks. The exam mark counts as 95

## Reading list

Type Author(s) Title Library Blackwells Amazon
A E. B. Staff Fundamentals of complex analysis with applications to engineering and science,
A E. Stein Complex analysis

(A = essential, B = recommended, C = background.)

Most books on reading lists should also be available from the Blackwells shop at Jessop West.