Undergraduate - UnitMTH3020 - Complex analysis and integral transforms

This unit entry is for students who completed this unit in 2013 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.

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6 points, SCA Band 2, 0.125 EFTSL

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Level	Undergraduate
Faculty	Faculty of Science
Organisational Unit	School of Mathematical Sciences
Offered	Clayton Second semester 2013 (Day)
Coordinator(s)	Dr Greg Markowsky

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

Examination (3 hours): 60%
Assignments and quizzes: 40%

Chief examiner(s)

Dr Greg Markowsky

Contact hours

Three 1-hour lectures and an average of one 1-hour computer laboratory and one 1-hour support class per week

Prerequisites

MTH2010 or MTH2015, or equivalent

Prohibitions

ENG2092