units

MTH3020

Faculty of Science

Undergraduate - Unit

This unit entry is for students who completed this unit in 2015 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.

print version

6 points, SCA Band 2, 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
Organisational UnitSchool of Mathematical Sciences
OfferedClayton Second semester 2015 (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:

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

  1. Evaluate line integrals in the complex plane;

  1. Understand Cauchy's integral theorem and its consequences;

  1. Determine and work with Laurent and Taylor series;

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

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

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

See also Unit timetable information

Chief examiner(s)

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

Prerequisites

MTH2010 or MTH2015, or equivalent

Prohibitions