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Complex Analysis (MAST30021)
Undergraduate level 3Points: 12.5On Campus (Parkville)
For information about the University’s phased return to campus and in-person activity in Winter and Semester 2, please refer to the on-campus subjects page.
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
Please refer to the LMS for up-to-date subject information, including assessment and participation requirements, for subjects being offered in 2020.
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; holomorphic 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 holomorphic 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: 11 April 2024
Eligibility and requirements
Prerequisites
25 credit points of subjects, specifically inclusive of:
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
One of any other Level 2 subject from the Department of Mathematics and Statistics
Corequisites
None
Non-allowed subjects
None
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: 11 April 2024
Assessment
Due to the impact of COVID-19, assessment may differ from that published in the Handbook. Students are reminded to check the subject assessment requirements published in the subject outline on the LMS
Description | Timing | Percentage |
---|---|---|
Four written or online assignments amounting to a total of up to 50 pages; due at regular intervals
| During the teaching period | 20% |
Written examination
| During the examination period | 80% |
Last updated: 11 April 2024
Dates & times
- Semester 1
Principal coordinator Michael Wheeler 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 2 March 2020 to 7 June 2020 Last self-enrol date 13 March 2020 Census date 30 April 2020 Last date to withdraw without fail 5 June 2020 Assessment period ends 3 July 2020 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 3 August 2020 to 1 November 2020 Last self-enrol date 14 August 2020 Census date 21 September 2020 Last date to withdraw without fail 16 October 2020 Assessment period ends 27 November 2020 Semester 2 contact information
Email: thomas.quella@unimelb.edu.au
Time commitment details
Estimated total time commitment of 170 hours
Last updated: 11 April 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 Science-credited subjects - new generation B-SCI Informal specialisation Pure Mathematics Informal specialisation Selective subjects for B-BMED Major Pure Mathematics Informal specialisation Discrete Mathematics / Operations Research Informal specialisation Pure Mathematics Informal specialisation Applied Mathematics Informal specialisation Applied Mathematics Informal specialisation Discrete Mathematics / Operations Research Major Mathematical Physics Major Discrete Mathematics / Operations Research Major Applied Mathematics Informal specialisation Pure Mathematics specialisation Informal specialisation Operations Research / Discrete Mathematics specialisation Informal specialisation Applied Mathematics specialisation - Breadth options
This subject is available as breadth in the following courses:
- Bachelor of Arts
- Bachelor of Commerce
- Bachelor of Design
- Bachelor of Environments
- Bachelor of Fine Arts (Acting)
- Bachelor of Fine Arts (Animation)
- Bachelor of Fine Arts (Dance)
- Bachelor of Fine Arts (Film and Television)
- Bachelor of Fine Arts (Music Theatre)
- Bachelor of Fine Arts (Screenwriting)
- Bachelor of Fine Arts (Theatre)
- Bachelor of Fine Arts (Visual Art)
- Bachelor of Music
- 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.
- Available to Study Abroad and/or Study Exchange Students
This subject is available to students studying at the University from eligible overseas institutions on exchange and study abroad. Students are required to satisfy any listed requirements, such as pre- and co-requisites, for enrolment in the subject.
Last updated: 11 April 2024