MTH328 Complex Analysis (8)

CSU Discipline Area: Mathematics and Statistics (MASTA)

Duration: One session

Abstract:

This subject generalises the concepts of calculus to functions of complex variables. Topics covered include: complex numbers and their properties; complex functions, limits, continuity; derivatives, the Cauchy-Riemann equations, analytic functions, elementary functions; integration of complex functions; power series methods; residue theory; conformal mappings; applications of complex analysis.

+ Subject Availability Modes and Locations

Session 1
Distance	Albury-Wodonga

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.

Prerequisite(s):

MTH218

Objectives:

Upon successful completion of this subject, students should:

Understand the nature of complex numbers, and their representation in the complex plane;
Understand the concept of function as applied to complex numbers, and the ideas of limit, continuity, and differentiation of complex functions;
Have a familiarity with the elementary functions defined in terms of complex numbers;
Understand and apply the techniques of integration in the complex plane;
Be able to write complex functions as Taylor and Laurent series;
Be able to apply residue theory to evaluate closed contour integrals;
Appreciate how complex analysis extends the ideas of calculus to the complex plane, and throws light on real number problems.

Syllabus:

The 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.

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