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Unit Summary

Unit type

UG Coursework Unit

Credit points

12

AQF level

7

Level of learning

Advanced

Former School/College

Former School of Education

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.

GA1: , GA2: , GA3: , GA4: , GA5: , GA6: , GA7:
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:

  1. demonstrate a sound knowledge and understanding of complex analysis
    • GA1:
    • GA4:
  2. demonstrate a proficiency in applying techniques from complex analysis
    • GA1:
    • GA4:
  3. use appropriate techniques from complex analysis to solve 'real world' problems
    • GA4:
    • GA6:
  4. communicate mathematical ideas, processes and results effectively at different levels of formality.
    • GA4:
    • GA6: