MTH328 Complex Analysis (8)

This subject allows you to appreciate how complex analysis extends the ideas of calculus to the complex plane, and throws light on real number problems. It generalises the concepts of calculus (limits, derivatives, Taylor series and integrals) to functions of complex variables. The subject culminates with residue theory and its applications to both complex and real integration. This subject enables you to be more familiar and comfortable with mathematical background, concepts and language necessary for the study of applicable mathematics.

Availability

Session 1 (30)
Online
Albury-Wodonga Campus

Continuing students should consult the SAL for current offering details: MTH328. Where differences exist between the Handbook and the SAL, the SAL should be taken as containing the correct subject offering details.

Subject Information

Grading System

HD/FL

Duration

One session

School

School of Computing and Mathematics

Prerequisites

MTH218

Learning Outcomes

Upon successful completion of this subject, students should:
  • be able to explain the nature of complex numbers, and their representation in the complex plane;
  • be able to explain the concept of function as applied to complex numbers, and the ideas of limit, continuity, and differentiation of complex functions;
  • be able to identify elementary functions defined in terms of complex numbers;
  • be able to apply the techniques of integration in the complex plane;
  • be able to write complex functions as Taylor and Laurent series and
  • be able to apply residue theory to evaluate closed contour integrals.

Syllabus

This subject will cover the following topics:
  • Complex numbers and their properties.
  • Complex functions, limits and continuity.
  • Derivatives, the Cauchy-Riemann equations, analytic functions.
  • Elementary functions.
  • Integration of complex functions.
  • Power series methods.
  • Residue theory.
  • Applications.

Indicative Assessment

The following table summarises the assessment tasks for the online offering of MTH328 in Session 1 2019. Please note this is a guide only. Assessment tasks are regularly updated and can also differ to suit the mode of study (online or on campus).

Item Number
Title
Value %
1
Complex numbers & complex functions
10
2
Elementary functions & complex integration
10
3
Complex series & residue theory
10
4
Final exam
70

The information contained in the CSU Handbook was accurate at the date of publication: July 2020. The University reserves the right to vary the information at any time without notice.

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