Advanced Complex Analysis

Subject MAST90056 (2010)

Note: This is an archived Handbook entry from 2010.

Credit Points: 12.50
Level: 9 (Graduate/Postgraduate)
Dates & Locations:

This subject has the following teaching availabilities in 2010:

Semester 2, Parkville - Taught on campus.
Pre-teaching Period Start not applicable
Teaching Period not applicable
Assessment Period End not applicable
Last date to Self-Enrol not applicable
Census Date not applicable
Last date to Withdraw without fail not applicable


Timetable can be viewed here. For information about these dates, click here.
Time Commitment: Contact Hours: 2 x one hour lectures + 1 x one hour practical class per week
Total Time Commitment: 120 hours
Prerequisites: None
Corequisites: None
Recommended Background Knowledge: It is recommended that students have completed a sound subject in real and complex analysis (equivalent to 620-221 [2008] Real and Complex Analysis).
Non Allowed Subjects: None
Core Participation Requirements:

For the purposes of considering requests for Reasonable Adjustments under the Disability Standards for Education (Cwth 2005), and Students Experiencing Academic Disadvantage Policy, academic requirements for this subject are articulated in the Subject Description, Subject Objectives, Generic Skills and Assessment Requirements for this entry.

The University is dedicated to provide support to those with special requirements. Further details on the disability support scheme can be found at the Disability Liaison Unit website: http://www.services.unimelb.edu.au/disability/

Coordinator

Dr Paul Norbury

Contact

Email: norbury@unimelb.edu.au
Subject Overview: This course is a second course in complex analysis. Complex analysis is a powerful tool that can be applied in many problems form pure and applied mathematics and in numerical problems. Some applications will be discussed in the last few lectures of the course. Applications are listed below and will be chosen according to the tastes of the students. The syllabus of this subject include: holomorphic functions, Cauchy’s theorem maximum principle and Schwarz’s lemma residue theorem and argument principle limits of analytic functions, power series, special functions, normal families Riemann mapping theorem applications. The applications of this subject include: heat flow, random walks, fluid flow, and electrostatics.
Objectives:

After completing this subject, students will gain:

  • an understanding of complex analytic functions, Cauchy-Riemann equations;
  • an understanding of Cauchy's theorem, residue theorem and an ability to apply this to real integrals;
  • an understanding of limits of analytic functions and power series;
  • an understanding of Riemann mapping theorem and its proof;
  • familiarisation with special functions that arise in many fields;
  • an ability to apply techniques from this subject via asymptotic analysis; and
  • the ability to pursue further studies in this and related areas.
Assessment:
  • Up to 60 pages of written assignments (60%: three assignments worth 20% each, due early, mid and late in semester), and
  • a 2 hour written examination (40%, in the examination period).
Prescribed Texts: TBC
Recommended Texts: TBC
Breadth Options:

This subject is not available as a breadth subject.
Fees Information: Subject EFTSL, Level, Discipline & Census Date
Generic Skills:

At the completion of this subject, students should gain:

  • Problem-solving skills (especially through exercises and assignments) including engaging with unfamiliar problems and identifying relevant strategies;
  • Analytical skills including the ability to construct and express logical arguments and to work in abstract or general terms to increase the clarity and efficiency of the analysis.
Related Course(s): Master of Science (Mathematics and Statistics)

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