CODE NO: MATH281 :                    TITLE: COMPLEX FUNCTIONS

 YEAR: 2                               SEMESTER: 1

 7.5 CREDITS                           DIVISION: Applied Mathematics

 STUDENT CONTACT: 24 hours (max)       DELIVERY: 18 lectures and 6 tutorials

 PRE-REQUISITES: MATH101-3             CO-REQUISITES: None

 BARRED COMBINATIONS: None             FOLLOW-UP MODULES: Any Honours
                                       module on Complex Analysis or
                                       Complex Dynamics.Certain Physics
                                       modules.

 PRELIMINARY READING: Revision of any
 previous work on complex numbers,
 with emphasis on the role of the
 module circle.

AIMS:

To introduce the student to a surprising, very beautiful theory having
intimate connections with other areas of mathematics and physical sciences,
for instance ordinary and partial differential equations and potential
theory.

LEARNING OUTCOMES:

After completing this module students should:

   * appreciate the central role of complex numbers in mathematics;
   * be competent at computing contour integrals and Green theorem.
   * be able to compute Taylor and Laurent series of such functions;
   * understand the content and relevance of the various Cauchy formulae and
     theorems;
   * be familiar with the reduction of real definite integrals to contour
     integrals.

OUTLINE SYLLABUS:

Reminder of complex arithmetic.

Cauchy-Riemann equations.  Green theorems.

Contour integration and Cauchys Theorem.

Taylor and Laurent Series

Poles and essential singularities.

The Residue Theorem.

Evaluation of real integrals by means of contour integration.

RECOMMENDED TEXTS: (under review)

-- E Kreyszig, Advanced Engineering Mathematics, Wiley.
-- R V Churchill, Complex variables and applications,  McGraw-Hill.

ASSESSMENT WEIGHTINGS:

80% Examination; 20% Continuous Assessment (4 sets)