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Unit of study_

MATH4079: Complex Analysis

The unit will begin with a revision of properties of complex numbers and complex functions. This will be followed by material on conformal mappings, Riemann surfaces, complex integration, entire and analytic functions, the Riemann mapping theorem, analytic continuation, and Gamma and Zeta functions. Finally, special topics chosen by the lecturer will be presented, which may include elliptic functions, normal families, Julia sets, functions of several complex variables, or complex manifolds.

Code MATH4079
Academic unit Mathematics and Statistics Academic Operations
Credit points 6
(A mark of 65 or above in 12cp of MATH2XXX) or (12cp of MATH3XXX)
MATH3979 or MATH3964
Assumed knowledge:
Good knowledge of analysis of functions of one real variable, working knowledge of complex numbers, including their topology, for example MATH2X23 or MATH2962 or MATH3068

At the completion of this unit, you should be able to:

  • LO1. demonstrate a conceptual understanding of limit, continuity, differentiation, and integration as well as a thorough background in variety of techniques and applications of complex analysis
  • LO2. assess problems in the framework of complex analysis, to choose among several potentially appropriate mathematical methods of solution, and persist in the face of difficulty
  • LO3. present complete and mathematically rigorous solutions for problems in complex analysis that include appropriate justification for their reasoning
  • LO4. recognise problems in mathematics, science, engineering and real life that are amenable to complex analysis, and to formulate models for such problems and apply the techniques of complex analysis in solving them