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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.