units

MTH3020

Faculty of Science

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Monash University Handbook 2011 Undergraduate - Unit

6 points, SCA Band 0 (NATIONAL PRIORITY), 0.125 EFTSL

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

LevelUndergraduate
FacultyFaculty of Science
OfferedClayton Second semester 2011 (Day)
Coordinator(s)Professor Paul Cally and Mr Mark Fisher

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.

Objectives

On completion of this unit, students will be able to: sketch the evolution of the solutions of the system on a phase-plane diagram; appreciate some applications of phase-plane analysis; be familiar with the basic properties of complex numbers and functions; have developed skills in the evaluation of line integrals; understand Cauchy's integral theorem and its consequences; be able to determine and work with Laurent and Taylor series; understand the method of Laplace transforms and be able to 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; have developed skills in using a computer algebra package.

Assessment

Examination (3 hours): 50%
Assignments and tests: 40%
Laboratory work: 10%

Chief examiner(s)

Professor Paul Cally

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, MTH2015 or MTH2111, or equivalent

Prohibitions

ENG2092