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Unit Summary
Unit type
UG Coursework Unit
Credit points
12
AQF level
Level of learning
Advanced
Former School/College
Pre-requisites
Unit aim
Extends the concepts developed in Calculus to functions of a complex variable. Topics from complex analysis include derivatives, Cauchy-Riemann equations, integration, power series methods, residues and poles as well as applications of residues, mapping of elementary functions and applications of conformal mapping.
Unit content
Topic 1: Complex Numbers
Topic 2: Complex Functions
Topic 3: Elementary Functions
Topic 4: Integration
Topic 5: Series
Topic 6: Residues
Topic 7: Applications of Residues 1
Topic 8: Applications of Residues 2
Topic 9: Conformal Mapping
Topic 10: Applications of Conformal Mapping and Poisson Integral Formula
Topic 11: Applications of Conformal Mapping and Schwarz-Christoffel Transformation
Learning outcomes
Unit Learning Outcomes express learning achievement in terms of what a student should know, understand and be able to do on completion of a unit. These outcomes are aligned with the graduate attributes. The unit learning outcomes and graduate attributes are also the basis of evaluating prior learning.
| On completion of this unit, students should be able to: | GA1 | GA2 | GA3 | GA4 | GA5 | GA6 | GA7 | |
|---|---|---|---|---|---|---|---|---|
| 1 | demonstrate a sound knowledge and understanding of complex analysis | |||||||
| 2 | demonstrate a proficiency in applying techniques from complex analysis | |||||||
| 3 | use appropriate techniques from complex analysis to solve 'real world' problems | |||||||
| 4 | communicate mathematical ideas, processes and results effectively at different levels of formality. | |||||||
On completion of this unit, students should be able to:
-
demonstrate a sound knowledge and understanding of complex analysis
- GA1:
- GA4:
-
demonstrate a proficiency in applying techniques from complex analysis
- GA1:
- GA4:
-
use appropriate techniques from complex analysis to solve 'real world' problems
- GA4:
- GA6:
-
communicate mathematical ideas, processes and results effectively at different levels of formality.
- GA4:
- GA6:
Prescribed texts
- This text is for Complex Analysis: Wunsch, D, 2005, Complex Variables with Applications, 3rd edn, Pearson, Boston, MA. ISBN: ISBN-13: 978-0201756098 ISBN-10: 0201756099.