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Complex Analysis (MAST30021)
Undergraduate level 3Points: 12.5On Campus (Parkville)
About this subject
- Overview
- Eligibility and requirements
- Assessment
- Dates and times
- Further information
- Timetable(opens in new window)
Contact information
Semester 1
Semester 2
Email: thomas.quella@unimelb.edu.au
Overview
Availability | Semester 1 Semester 2 |
---|---|
Fees | Look up fees |
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.
Intended 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
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.
Last updated: 22 March 2024
Eligibility and requirements
Prerequisites
One of
Code | Name | Teaching period | Credit Points |
---|---|---|---|
MAST20026 | Real Analysis |
Semester 2 (On Campus - Parkville)
Semester 1 (On Campus - Parkville)
|
12.5 |
MAST10009 | Accelerated Mathematics 2 | Semester 2 (On Campus - Parkville) |
12.5 |
And any other second year level subject from the Department of Mathematics and Statistics.
Corequisites
None
Non-allowed subjects
Inherent requirements (core participation requirements)
The University of Melbourne is committed to providing students with reasonable adjustments to assessment and participation under the Disability Standards for Education (2005), and the Assessment and Results Policy (MPF1326). Students are expected to meet the core participation requirements for their course. These can be viewed under Entry and Participation Requirements for the course outlines in the Handbook.
Further details on how to seek academic adjustments can be found on the Student Equity and Disability Support website: http://services.unimelb.edu.au/student-equity/home
Last updated: 22 March 2024
Assessment
Additional details
- Four written or online assignments amounting to a total of up to 50 pages; due at regular intervals during semester (20%)
- 3-hour written examination, held in the examination period (80%)
Last updated: 22 March 2024
Dates & times
- Semester 1
Principal coordinator Barry Hughes Mode of delivery On Campus (Parkville) Contact hours 3 x one hour lectures per week, 1 x one hour practice class per week Total time commitment 170 hours Teaching period 27 February 2017 to 28 May 2017 Last self-enrol date 10 March 2017 Census date 31 March 2017 Last date to withdraw without fail 5 May 2017 Assessment period ends 23 June 2017 Semester 1 contact information
- Semester 2
Principal coordinator Thomas Quella Mode of delivery On Campus (Parkville) Contact hours 3 x one hour lectures per week, 1 x one hour practice class per week Total time commitment 170 hours Teaching period 24 July 2017 to 22 October 2017 Last self-enrol date 4 August 2017 Census date 31 August 2017 Last date to withdraw without fail 22 September 2017 Assessment period ends 17 November 2017 Semester 2 contact information
Email: thomas.quella@unimelb.edu.au
Time commitment details
Estimated total time commitment of 170 hours
Last updated: 22 March 2024
Further information
- Texts
Prescribed texts
There are no specifically prescribed or recommended texts for this subject.
- Subject notes
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 Handbook entries
This subject contributes to the following:
Type Name Informal specialisation Applied Mathematics Informal specialisation Pure Mathematics Informal specialisation Discrete Mathematics / Operations Research Informal specialisation Pure Mathematics Informal specialisation Applied Mathematics Informal specialisation Science-credited subjects - new generation B-SCI and B-ENG. Major Mathematical Physics Informal specialisation Discrete Mathematics / Operations Research Informal specialisation Selective subjects for B-BMED Informal specialisation Pure Mathematics Major Pure Mathematics Informal specialisation Applied Mathematics Informal specialisation Operations Research / Discrete Mathematics Major Applied Mathematics Major Discrete Mathematics / Operations Research - Breadth options
This subject is available as breadth in the following courses:
- Available through the Community Access Program
About the Community Access Program (CAP)
This subject is available through the Community Access Program (also called Single Subject Studies) which allows you to enrol in single subjects offered by the University of Melbourne, without the commitment required to complete a whole degree.
Entry requirements including prerequisites may apply. Please refer to the CAP applications page for further information.
Last updated: 22 March 2024