University Course Planner The University of Adelaide Australia

PURE MTH 3019 - Complex Analysis III

Career: Undergraduate
Units: 3
Term: 4310
Campus: North Terrace
Contact: Up to 3 hours per week
Available for Study Abroad and Exchange: Yes
Available for Non-Award Study: Yes
Pre-Requisite: MATHS 2100 or MATHS 2101 or MATHS 2202 or ELEC ENG 2106
Assumed Knowledge: MATHS 2101
Assessment: Ongoing assessment, exam
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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Student Status

Domestic
International

What type of place are you studying in

Commonwealth supported
Full fee paying

Study Level

Undergraduate
Postgraduate Coursework
Non Award

Program of Study

Study Abroad student tuition fees are available here

Only some Postgraduate Coursework programs are available as Commonwealth Supported. Please check your program for specific fee information.

The fees displayed below for international students are for students commencing a program in 2024 only. International students who commenced a program in 2023 or prior can find their fee here.

Units
EFTSL
Amount
3
0.125
          
  


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
4310 Tue 14/03/2023 Thu 23/03/2023 Fri 05/05/2023 Fri 09/06/2023


Class Details

Enrolment Class: Workshop
Class Nbr Section Size Available Dates Days Time Location
10480 WR01 25 6 1 Mar - 5 Apr Wednesday 12pm - 1pm Engineering & Mathematics, EM218, Teaching Room
26 Apr - 31 May Wednesday 12pm - 1pm Engineering & Mathematics, EM218, Teaching Room
Related Class: Tutorial
Class Nbr Section Size Available Dates Days Time Location
11327 TU01 25 6 1 Mar - 5 Apr Wednesday 1pm - 2pm Engineering & Mathematics, EM218, Teaching Room
26 Apr - 31 May Wednesday 1pm - 2pm Engineering & Mathematics, EM218, Teaching Room
11330 TU02 0 FULL 2 Mar - 6 Apr Thursday 1pm - 2pm MyUni, OL, Online Class
27 Apr - 1 Jun Thursday 1pm - 2pm MyUni, OL, Online Class
Note: This class is for OFFSHORE students only. To request to enrol in this class please fill out this form: https://set.adelaide.edu.au/student-support/forms-policies/course-or-class-full-resolution-form. NOTE: You will need to provide evidence, or a statement, that you will be located offshore for the duration of the course when submitting this form.