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.

Session 1 (30)

Online

Albury-Wodonga Campus

HD/FL

One session

School of Computing and Mathematics

MTH218

- 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.

- 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 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).

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: October 2020. The University reserves the right to vary the information at any time without notice.*