This unit entry is for students who completed this unit in 2016 only. For students planning to study the unit, please refer to the unit indexes in the the current edition of the Handbook. If you have any queries contact the managing faculty for your course or area of study.

MTH3020 - Complex analysis and integral transforms

6 points, SCA Band 2, 0.125 EFTSL

Undergraduate - Unit

Refer to the specific census and withdrawal dates for the semester(s) in which this unit is offered.

Faculty

Science

Organisational Unit

School of Mathematical Sciences

Coordinator(s)

Dr Greg Markowsky

Offered

Clayton

Second semester 2016 (Day)

Synopsis

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.

Outcomes

On completion of this unit students will be able to:

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

Evaluate line integrals in the complex plane;

Understand Cauchy's integral theorem and its consequences;

Determine and work with Laurent and Taylor series;

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

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

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

Assessment

Final examination (3 hours): 70%
Assignments and tests: 30%

Workload requirements

Three 1-hour lectures and one 2-hour support class per week

Chief examiner(s)

Dr Greg Markowsky

This unit applies to the following area(s) of study

Applied mathematics
Mathematical statistics
Mathematics
Pure mathematics

Prerequisites

MTH2010 or MTH2015, or equivalent

Prohibitions

ENG2092