MAS 381: Mathematics III (Electrical) Dr. I. Ballai

Semester: 1 Credits: 10
Prerequisites: MAS241
Corequisites: None

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, surface and volume integrals.

Objectives: At the end of the course the student should be able to

1. Have a working knowledge of complex functions
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

Outline Syllabus

1. Revision of complex 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, Divergence theorem

Module format:
Lectures 22 Tutorials/Problem Classes 11 Laboratory/Practicals 0

Recommended book:
E. Stein: Complex analysis, Princeton University Press, 2003
S. Lang: Complex analysis, London, Springer, 1999
E.B. Staff: Fundamentals of complex analysis with applications to engineering and
science, Prentice Hall, 2003
J.M. Howie: Complex Analysis, Soringer, 2003
E. Kreyszig: Advanced Engineering Mathematics, Wiley, 2006

Examination:
One two hour written examination
Exam format: 4 questions each worth 25 marks
One assessed Quiz in week 6-7