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.

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

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