University Course Planner The University of Adelaide Australia

PURE MTH 4119 - Complex Analysis - Honours

Career: Undergraduate
Units: 3
Term: 4210
Campus: North Terrace
Contact: Up to 3 hours per week
Restriction: Honours students only
Available for Study Abroad and Exchange: Yes
Available for Non-Award Study: No
Pre-Requisite: MATHS 2100 or MATHS 2101 or MATHS 2202 or ELEC ENG 2106
Assumed Knowledge: MATHS 2101
Incompatible: PURE MTH 3019
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

To display course fees, please select your status and program below:

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
4210 Tue 15/03/2022 Thu 24/03/2022 Fri 06/05/2022 Fri 10/06/2022


Class Details

Enrolment Class: Workshop
Class Nbr Section Size Available Dates Days Time Location
10607 WR01 5 5 2 Mar - 6 Apr Wednesday 11am - 12pm Ingkarni Wardli, B18, Teaching Room
27 Apr - 1 Jun Wednesday 11am - 12pm Ingkarni Wardli, B18, Teaching Room
Note: This class will be delivered both online and face to face. Please refer to MyUni for details once enrolled.
Related Class: Tutorial
Class Nbr Section Size Available Dates Days Time Location
11496 TU01 5 5 3 Mar - 7 Apr Thursday 9am - 10am Engineering & Mathematics, EMG07, Teaching Room
28 Apr - 2 Jun Thursday 9am - 10am Engineering & Mathematics, EMG07, Teaching Room
Note: This class is only available for face-to-face (on-campus) students.
11499 TU02 5 5 2 Mar - 6 Apr Wednesday 12pm - 1pm MyUni, OL, Online Class
27 Apr - 1 Jun Wednesday 12pm - 1pm MyUni, OL, Online Class
Note: This class is for offshore / interstate students only. Where this requirement is not met, students risk being removed from this class. Please refer to MyUni for details once enrolled.
Related Class: Lecture
Class Nbr Section Size Available Dates Days Time Location
19393 LEC0 5 5 This class does not have any timetabled face-to-face sessions. Please check MyUni or contact your Course Coordinator for details.