University Course Planner The University of Adelaide Australia

PURE MTH 3019 - Complex Analysis III

Career: Undergraduate
Units: 3
Term: Semester 1
Campus: North Terrace
Contact: Up to 3 hours per week
Available for Non-Award Study: Yes
Pre-Requisite: MATHS 2100 or MATHS 2101 or MATHS 2202
Assumed Knowledge: MATHS 2101 or MATHS 2202
Assessment: ongoing assessment 30%, exam 70%
Syllabus:

When the real numbers are replaced by the complex numbers in the definition of the derivative of a function, the resulting (complex-)differentiable functions turn out to have many remarkable properties not enjoyed by their real analogues. These functions, usually known as holomorphic functions, have numerous applications in areas such as engineering, physics, differential equations and number theory, to name just a few. The focus of this course is on the study of holomorphic functions and their most important basic properties. Topics covered are: Complex numbers and functions; complex limits and differentiability; elementary examples; analytic functions; complex line integrals; Cauchy's theorem and the Cauchy integral formula; Taylor's theorem; zeros of holomorphic functions; Rouche's Theorem; the Open Mapping theorem and Inverse Function theorem; Schwarz' Lemma; automorphisms of the ball, the plane and the Riemann sphere; isolated singularities and their classification; Laurent series; the Residue Theorem; calculation of definite integrals and evaluation of infinite series using residues; Montel's Theorem and the Riemann Mapping Theorem.

Course Fees

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  Commonwealth Supported Student Contribution
Tuition Fees
Units EFTSL Pre-2010 2010 Onwards Domestic International
3 0.125 Band 2 $1,131 Band 2 $1,131 select program select program


Course Outline

A Course Outline which includes Learning Outcomes, Learning Resources, Learning & Teaching for this course may be accessed here


Critical Dates

Term Last Day to Add Online Census Date Last Day to WNF Last Day to WF
Semester 1 Mon 13/03/2017 Fri 31/03/2017 Fri 05/05/2017 Fri 09/06/2017


Class Details

Enrolment Class: Lecture
Class Nbr Section Size Available Dates Days Time Location
12715 LE01 35 8 28 Feb - 4 Apr Tuesday 12pm - 1pm Napier, 208, Lecture Theatre
2 Mar - 6 Apr Thursday 4pm - 5pm Napier, 209, Lecture Theatre
3 Mar - 7 Apr Friday 4pm - 5pm Napier, 209, Lecture Theatre
25 Apr - 6 Jun Tuesday 12pm - 1pm Napier, 208, Lecture Theatre
27 Apr - 8 Jun Thursday 4pm - 5pm Napier, 209, Lecture Theatre
28 Apr - 9 Jun Friday 4pm - 5pm Napier, 209, Lecture Theatre