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Year:

PMTH333 Complex Analysis

Updated: 15 January 2013
Credit Points 6
Offering
Responsible Campus Teaching Period Mode of Study
Armidale Trimester 1 Off Campus
Armidale Trimester 1 On Campus
Intensive School(s) None
Supervised Exam There is a UNE Supervised Examination held at the end of the teaching period in which you are enrolled.
Pre-requisites PMTH212 or PMTH212A or candidature in a postgraduate award in the School of Environmental and Rural Science or School of Science and Technology
Co-requisites None
Restrictions None
Notes None
Combined Units None
Coordinator(s) Adam Harris (aharris5@une.edu.au)
Unit Description

Topics covered 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.

Important Information

Where calculators are permitted in examinations, it must be selected from an approved list, which can be accessed from the Further Information link below.

Further information

Prescribed Material
Mandatory
Text(s):

Note: Students are expected to purchase prescribed material. Please note that textbook requirements may vary from one teaching period to the next.

Complex Variables and Applications
ISBN: 9780073051949
Brown, J.W. and Churchill, R.V., McGraw-Hill 8th ed. 2008
Text refers to: Trimester 1 , On and Off Campus
Referenced Material
Optional
Text(s):

Note: Reference material is held in the University Library - purchase is optional

Complex Analysis
ISBN: 9780070006577
Ahlfors, L., McGraw-Hill 3rd ed.
Note: Available from the Dixson Library, UNE
Text refers to: Trimester 1 , On and Off Campus
Theory of Complex Functions
ISBN: 9780387971957
Remmert, R., Springer-Verlag
Note: Available from the Dixson Library, UNE
Text refers to: Trimester 1 , On and Off Campus
Disclaimer Unit information may be subject to change prior to commencement of the teaching period.
Assessment
Title Exam Length Weight Mode No. Words
Assignment 1 30%
Assessment Notes
6 Problem-based assignments.
Relates to Learning Outcomes (LO) and Graduate Attributes (GA)
LO: 1, 2, 3, 4, 5 GA: 1, 2, 4, 6
Final Examination 2 hrs 70%
Relates to Learning Outcomes (LO) and Graduate Attributes (GA)
LO: 1, 2, 3, 4, 5 GA: 1, 2, 6

Learning Outcomes (LO) Upon completion of this unit, students will be able to:
  1. perform the basic arithmetic operations of complex numbers, including powers and extraction of multiple roots, using both cartesian and polar forms;
  2. relate concepts of continuity and differentiability of real functions of two variables to the properties of harmonic and analytic functions of one complex variable;
  3. locate singularities of a complex function and apply the formula of Cauchy (where needed) to evaluate path and contour integrals;
  4. compute complex power series as a tool for classification of isolated singularities of complex functions; and
  5. combine all of the above in the analysis and application of residues.

Graduate Attributes (GA)
Attribute Taught Assessed Practised
1 Knowledge of a Discipline
Knowledge gained by the student in lectures will be applied in collaboration with the lecturer to problems and examples in tutorials. The student will then map this experience onto further problem-solving tasks in assignments, where the identification of central concepts in the discipline, and the student's ability to articulate them, will be assessed.
True True True
2 Communication Skills
The student will be encouraged to participate actively in discussion during lectures and tutorials. Written communication skills, particularly with regard to construction and presentation of logical expositions and arguments, will be taught and assessed.
True True True
4 Information Literacy
The student will be guided in the use of online resources, library and internet access to recommended references, particularly in conjunction with assignment tasks.
True True True
5 Life-Long Learning
The student will discover the breadth of the discipline through this introductory unit and will become aware of its ongoing development as a field of higher degree research.
True True
6 Problem Solving
The student will encounter in this unit a field of knowledge that is intensely problem-based, and will acquire skill in connecting ideas within a network of logical relationships. A high emphasis will be placed on the development of analytical and deductive reasoning.
True True True
8 Team Work
The student will be encouraged to participate in interactive discussion with other students regarding ideas and problems addressed in the unit. Written assignment submissions must be the student's own work, but may be the outcome of group discussion.
True
   

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