PURE MTH 3019 - Complex Analysis III
Career: | Undergraduate |
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Units: | 3 |
Term: | 3810 |
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 |
Assumed Knowledge: | MATHS 2101 or MATHS 2202 |
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
Course fees are displayed for the Program: select program
Study Abroad student tuition fees available here
Only some Postgraduate Coursework programs are available as Commonwealth Supported. Please check your program for specific fee information
Commonwealth Supported Student Contribution | |||||||
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Units | EFTSL | Pre-2010 | 2010 Onwards | Domestic | International | ||
3 | 0.125 | Band 2 | $1,169 | Band 2 | $1,169 | select program | select program |
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Course Outline
A Course Outline which includes Learning Outcomes, Learning Resources, Learning & Teaching for this course may be accessed here
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Critical Dates
Term | Last Day to Add Online | Census Date | Last Day to WNF | Last Day to WF |
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3810 | Mon 12/03/2018 | Sat 31/03/2018 | Fri 04/05/2018 | Fri 08/06/2018 |
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Class Details
Enrolment Class: Lecture | |||||||
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Class Nbr | Section | Size | Available | Dates | Days | Time | Location |
12617 | LE01 | 30 | 5 | 28 Feb - 28 Mar | Wednesday | 1pm - 2pm | Napier, 208, Lecture Theatre |
1 Mar - 29 Mar | Thursday | 12pm - 1pm | Lower Napier, LG28, Lecture Theatre | ||||
2 Mar - 30 Mar | Friday | 10am - 11am | Marjoribanks, 126, SANTOS Lecture Theatre | ||||
18 Apr - 6 Jun | Wednesday | 1pm - 2pm | Napier, 208, Lecture Theatre | ||||
19 Apr - 7 Jun | Thursday | 12pm - 1pm | Lower Napier, LG28, Lecture Theatre | ||||
20 Apr - 8 Jun | Friday | 10am - 11am | Marjoribanks, 126, SANTOS Lecture Theatre |
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