PURE MTH 3019 - Complex Analysis III
Career: | Undergraduate |
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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
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.
EFTSL | |||
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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 |
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4310 | Tue 14/03/2023 | Thu 23/03/2023 | Fri 05/05/2023 | Fri 09/06/2023 |
Class Details
Enrolment Class: Workshop | |||||||
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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. |