Handbook 1996 : Faculty of Science (Volume 4 page 209)
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618-202 Complex Analysis (Advanced)

Note: Credit cannot be gained for both 618-202 and 618-252.

Credit points: 12.0

Coordinator: Dr J J Koliha

Prerequisite: Mathematics 618-201 or by invitation of the head of the Department of Mathematics.

Contact: 39 lectures (three a week).

Timetable: Second semester

Objectives:

On completion of this subject, students should:

Comprehend:

• the concepts of an analytic function of a complex variable; complex derivative; power and Laurent series in complex variables;
• basic topological concepts in the complex plane
• Cauchy's theorem and its applications.

Have developed:

• skills in differentiating functions of a complex variable;
• skills in calculating contour integrals;
• the ability to work with analytic functions in the cut plane;
• the ability to apply Cauchy's integral formula and the residue theorem.

Appreciate:

• differences between functions of a real and a complex variable;
• the role of complex analytic methods in solving important problems in science and engineering.

Content:

Convergence: convergence of sequences and series, real and complex; ratio and n-th root tests; power series, circle of convergence. Functions of a complex variable: elementary functions of a complex variable, branches; differentiation, analytic functions, Cauchy-Riemann equations. Integration: Riemann integral for real and complex functions; line and contour integrals, Cauchy's integral theorem; Taylor and Laurent series; singularities, poles, Liouville's theorem; residue theorem, limiting contours, evaluation of integrals.

Assessment:

Up to 26 pages of written assignments and up to three hours of end-of-semester written examination.

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Handbook 1996 : Faculty of Science (Volume 4 page 209)

Status:          Official 1996
Date created:    Oct  9 1995
Last modified:   Oct  9 1995
Authorised by:   Academic Registrar
Email enquiries: Course_Information@registrar.unimelb.edu.au

Copyright © University of Melbourne 1995,1996.