Complex Analysis

Subject MAST30021 (2015)

Note: This is an archived Handbook entry from 2015.

Credit Points: 12.5
Level: 3 (Undergraduate)
Dates & Locations:

This subject has the following teaching availabilities in 2015:

Semester 1, Parkville - Taught on campus.
Pre-teaching Period Start not applicable
Teaching Period 02-Mar-2015 to 31-May-2015
Assessment Period End 26-Jun-2015
Last date to Self-Enrol 13-Mar-2015
Census Date 31-Mar-2015
Last date to Withdraw without fail 08-May-2015

Semester 2, Parkville - Taught on campus.
Pre-teaching Period Start not applicable
Teaching Period 27-Jul-2015 to 25-Oct-2015
Assessment Period End 20-Nov-2015
Last date to Self-Enrol 07-Aug-2015
Census Date 31-Aug-2015
Last date to Withdraw without fail 25-Sep-2015

Timetable can be viewed here. For information about these dates, click here.
Time Commitment: Contact Hours: 3 x one hour lectures per week, 1 x one hour practice class per week
Total Time Commitment:

Estimated total time commitment of 170 hours


One of

Study Period Commencement:
Credit Points:
Semester 1, Semester 2

And any other second year level subject from the Department of Mathematics and Statistics.

Corequisites: None
Recommended Background Knowledge: None
Non Allowed Subjects:

Core Participation Requirements:

For the purposes of considering request for Reasonable Adjustments under the Disability Standards for Education (Cwth 2005), and Student Support and Engagement Policy, academic requirements for this subject are articulated in the Subject Overview, Learning Outcomes, Assessment and Generic Skills sections of this entry.

It is University policy to take all reasonable steps to minimise the impact of disability upon academic study, and reasonable adjustments will be made to enhance a student's participation in the University's programs. Students who feel their disability may impact on meeting the requirements of this subject are encouraged to discuss this matter with a Faculty Student Adviser and Student Equity and Disability Support:


Dr Anita Ponsaing, Prof Peter Forrester


Subject Overview:

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.

Topics include:the topology of the complex plane; convergence of complex sequences and series; analytic functions, the Cauchy-Riemann 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; and aspects of the gamma function.

Learning Outcomes:

At the completion of this subject, students should understand the concepts of analytic function and contour integral and should be able to:

  • apply the Cauchy-Riemann equations
  • use the complex exponential and logarithm
  • apply Cauchy’s theorems concerning contour integrals
  • apply the residue theorem in a variety of contexts
  • understand theoretical implications of Cauchy’s theorems such as the maximum modulus principle, Liouville’s Theorem and the fundamental theorem of algebra

Three or four written assignments due at regular intervals during semester amounting to a total of up to 50 pages (20%), and a 3-hour written examination in the examination period (80%).

Prescribed Texts: None
Recommended Texts:

Spiegel, Lipschutz, Schiller and Spellman, Schaum's Outline of Complex Variables, 2nd edition, McGraw-Hill, 2009

Breadth Options:

This subject potentially can be taken as a breadth subject component for the following courses:

You should visit learn more about breadth subjects and read the breadth requirements for your degree, and should discuss your choice with your student adviser, before deciding on your subjects.

Fees Information: Subject EFTSL, Level, Discipline & Census Date
Generic Skills:

In addition to learning specific skills that will assist students in their future careers in science, they will have the opportunity to develop generic skills that will assist them in any future career path. These include:

  • problem-solving skills: the ability to engage with unfamiliar problems and identify relevant solution strategies;
  • analytical skills: the ability to construct and express logical arguments and to work in abstract or general terms to increase the clarity and efficiency of analysis;
  • collaborative skills: the ability to work in a team;
  • time-management skills: the ability to meet regular deadlines while balancing competing commitments.

This subject is available for science credit to students enrolled in the BSc (both pre-2008 and new degrees), BASc or a combined BSc course.

Related Majors/Minors/Specialisations: Applied Mathematics
Applied Mathematics
Applied Mathematics
Applied Mathematics
Applied Mathematics (specialisation of Mathematics and Statistics major)
Discrete Mathematics / Operations Research
Discrete Mathematics / Operations Research
Discrete Mathematics / Operations Research
Discrete Mathematics / Operations Research
Discrete Mathematics and Operations Research (specialisation of Mathematics and Statistics major)
Mathematical Physics
Pure Mathematics
Pure Mathematics
Pure Mathematics
Pure Mathematics
Pure Mathematics (specialisation of Mathematics and Statistics major)
Science-credited subjects - new generation B-SCI and B-ENG.
Selective subjects for B-BMED

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