
MAST 30021
Complex Analysis

Lecturer: Craig Westerland, 168 Richard Berry, phone: 8344 9712,
email: C.Westerland@ms.unimelb.edu.au
Lectures:
 Tuesday 2:15pm  3:15pm, MSLELower Theatre.
 Thursday 2:15pm  3:15pm, Richard BerryRussell Love Theatre.
 Friday 11:00am  12:00pm, Richard BerryRussell Love Theatre.
Practice class: Monday 4:15pm  5:15pm, Richard BerryRussell Love Theatre.
Consultation hours: Thursday 12 and 3:155.
Subject Outline
Complex analysis is a core subject in pure and applied mathematics, as well as the physical and engineering sciences.
While it is true that physical phenomena are given in terms of real numbers and real variables, it is often too
difficult and sometimes not possible, to solve the algebraic and differential equations used to model these phenomena
without introducing complex numbers and complex variables and applying the powerful techniques of complex analysis.
Here is the booklet for the course.
Main Topics
The material covered will be drawn from the following:
 the topology of the complex plane
 convergence of complex sequences and series
 analytic functions
 the CauchyRiemann equations
 harmonic functions and applications
 contour integrals and the Cauchy Integral Theorem
 singularities
 Laurent series
 the Residue Theorem
 evaluation of integrals using contour integration
 conformal mapping
 aspects of the gamma function
References
 J. E. Marsden and M. J. Hoffman, Basic Complex Analysis Freeman (Third Edition) 1998 (Preferred textbook).
 A. David Wunsch, Complex Variables with Applications, Second Edition (AddisonWesley).
 E. B. Saff and A. D. Snider, Fundamentals of Complex Analysis for Mathematics, Science and
Engineering (Prentice Hall).
 Stephen D. Fisher, Complex Variables, Second Edition (Wadsworth and Brooks/Cole).
 Murray R. Spiegel, Theory and Problems of Complex Variables, Schaum's Outline Series (McGrawHill).
Here are the
slides for the course. They may be updated as the subject
progresses.
Assessment
Three written assignments due at regular intervals during
semester (20%), and a 3hour
written examination in the examination period (80%).
Homework assignments: Here are the
problem sheets. The assignments are:
 First problem set, due Friday 7 September at 5pm: Sheets 1 and 2, Problems 3, 4, 6, 7, 8, 10, 12, 14, 16, 19, 20,
21, 23, 24,
27, 28, 29, 35, 36, 38, 40, 42, 45, 49.
 Second problem set, due Monday 8 October at 9am: Sheets 3 and 4, Problems 57, 60, 64,
65, 70, 73, 77, 78.
 Third problem set, due Friday 26 October at 5pm: Sheets 5 and 6, Problems 82, 87, 88, 91, 95,
96, 100, 102.
Practice problems: Here are the
problem sheets. The solutions are here:
 30 July, Prac 1.
 6 August, Prac 2.
 13 August, Prac 3.
 20 August, Prac 4.
 27 August, Prac 5.
 3 September, Prac 6.
 10 September, Prac 7.
 1 October, Prac 8.
 8 October, Prac 9.
 15 October, Prac 10.
 22 October, Prac 11.