Overview

Complex numbers and functions; domains and curves in the complex plane; differentiation; integration; Cauchy's integral theorem and its consequences; Taylor and Laurent series; Laplace and Fourier transforms; complex inversion formula; branch points and branch cuts; applications to initial value problems.

Offerings

S2-01-CLAYTON-ON-CAMPUS

Rules

Enrolment Rule

Contacts

Chief Examiner(s)

Associate Professor Zihua Guo

Unit Coordinator(s)

Associate Professor Zihua Guo

Notes

IMPORTANT NOTICE:
Scheduled teaching activities and/or workload information are subject to change in response to COVID-19, please check your Unit timetable and Unit Moodle site for more details.

Learning outcomes

On successful completion of this unit, you should be able to:
1.

Understand the basic properties of complex numbers and functions, including differentiability;

2.

Evaluate line integrals in the complex plane;

3.

Understand Cauchy's integral theorem and its consequences;

4.

Determine and work with Laurent and Taylor series;

5.

Understand the method of Laplace transforms and evaluate the inverse transform;

6.

Appreciate the importance of complex analysis for other mathematical units, as well as for physics and engineering, through seeing applications of the theory;

7.

Use a computer algebra package to assist in the application of complex analysis.

Teaching approach

Active learning

Assessment

1 - In-semester assessment
2 - Examination (3 hours and 10 minutes)

Scheduled and non-scheduled teaching activities

Applied sessions
Lectures

Workload requirements

Workload

Learning resources

Required resources

Other unit costs

Costs are indicative and subject to change.
Miscellaneous items required (unit course reader, printing, stationery) - $120.

Availability in areas of study

Applied mathematics
Mathematical statistics
Mathematics
Pure mathematics