Key facts
UNE unit code: PMTH433
*You are viewing the 2027 version of this unit which may be subject to change in future.
- Trimester 1 - On Campus
- Trimester 1 - Online
- Armidale Campus
- Yes
- No
- Yes
- 6
Unit information
Complex analysis is a fascinating and powerful branch of mathematics, with surprising practical applications. Unifying important principles from both pure and applied mathematics, it is used by mathematicians, electrical engineers and physicists as a tool for solving diverse physical problems.
This unit provides you with an introduction to complex analysis. Honing your skills in performing arithmetic operations of numbers, complex analysis offers you an opportunity to gain a new perspective on different branches of mathematics.
Integrating your prior knowledge of continuity and differentiability, you will learn about the concepts underpinning complex functions and variables. Topics include analytic functions, the Cauchy-Riemann Equations, transcendental functions, integration, Cauchy’s Theorem and applications, power series, Taylor series, Laurent series, theory of residues, and poles.
Offerings
For further information about UNE's teaching periods, please go to Principal Dates.
| Teaching period | Mode/location |
|---|---|
| Trimester 1 | On Campus, Armidale Campus |
| Trimester 1 | Online |
*Offering is subject to availability
Intensive schools
There are no intensive schools required for this unit.
Enrolment rules
Notes
Please refer to the student handbook for current details on this unit.
Unit coordinator(s)
Learning outcomes
Upon completion of this unit, students will be able to:
- exercise advanced skills in performing the arithmetic operations of complex numbers, including powers and extraction of multiple roots, using both Cartesian and polar forms;
- apply complex number notation in the study of Euclidean and non-Euclidean geometry;
- synthesise knowledge of continuity and differentiability of functions of two real variables with the concepts of harmonic and analytic functions of a complex variable;
- autonomously locate and analyse singularities of a complex function, and apply the formula of Cauchy (where appropriate) to evaluate path and contour integrals for a wide range of complex functions;
- use advanced knowledge to efficiently compute complex power series as a tool for analysis of isolated singularities of a complex function; and
- autonomously synthesise all of the above in the analysis and practical application of residues.
Assessment information
Assessments are subject to change up to 8 weeks prior to the start of the teaching period in which you are undertaking the unit.
| Title | Must Complete | Weight | Offerings | Assessment Notes |
|---|---|---|---|---|
| Assessment 1 | Yes | 3% | All offerings | Problem-based assignment. |
| Assessment 2 | Yes | 3% | All offerings | Problem-based assignment. |
| Assessment 3 | Yes | 3% | All offerings | Problem-based assignment. |
| Assessment 4 | Yes | 3% | All offerings | Problem-based assignment. |
| Assessment 5 | Yes | 3% | All offerings | Problem-based assignment. |
| Assessment 6 | Yes | 5% | All offerings | Advanced problem-based assignment. |
| Final Examination - Assurance Task | Yes | 80% | All offerings | It is mandatory to pass this examination in order to pass this unit. |
Learning resources
Textbooks are subject to change up to 8 weeks prior to the start of the teaching period in which you are undertaking the unit.
Note: Recommended material may be held in the University Library — purchase is optional.
Complex Variables and Applications
ISBN: 9780073383170
Brown, J.W. and Churchill, R.V., McGraw-Hill 9th ed. 2013
Text refers to: All offerings
Note: Referenced material may be held in the University Library — purchase is optional.
Complex Analysis
ISBN: 9780070006577
Ahlfors, L., McGraw-Hill 3rd ed. 1979
Text refers to: All offerings
Theory of Complex Functions
ISBN: 9780387971957
Remmert, R., Springer-Verlag
Text refers to: All offerings
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