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)

Dr Gregory Markowsky

Unit Coordinator(s)

Dr Gregory Markowsky

Notes

This Level 4 unit and its Level 3 counterpart MTH3020 share the same core content and learning activities such as seminars and applied classes. However, studies at Level 4 are distinguished from those at Level 3 by a deeper understanding of mathematical theories and their applications, more challenging assessment tasks, higher levels of critical thinking, and greater autonomy in learning.

Learning outcomes

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

Demonstrate a deep understanding of complex numbers and functions

2.

Compute and interpret line integrals in the complex plane using advanced techniques

3.

Apply Cauchy’s integral theorem and its implications in various contexts

4.

Develop and manipulate Laurent and Taylor series for complex functions

5.

Master the method of Laplace transforms and proficiently evaluate inverse transforms.

6.

Recognise the significance of complex analysis and its applications in physics and engineering and illustrate with real-world examples.

7.

Utilise computer algebra systems to facilitate and enhance the application of complex analysis techniques.

Teaching approach

Active learning

Assessment

1 - Continuous assessment

2 - Final Assessment - Exam (3 hours and 10 minutes)

Scheduled and non-scheduled teaching activities

Applied sessions

Seminars

Workload requirements

Workload

Learning resources

Required resources

Recommended 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