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
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 - Continuous 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
Mathematical statistics
Mathematics
Pure mathematics