## MAS381 Mathematics III (Electrical)

 Semester 1, 2017/18 10 Credits Lecturer: Dr Istvan Ballai uses MOLE 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, complex mapping 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 introduce the elements of conformal mapping. 4. To study complex differentiation, integration and the theory of residues 5. Introduce the concept of double operators and polar coordinates. 6. 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. Have a working knowledge of mappings in the complex plane 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