MTH3020 - Complex analysis and integral transforms - 2017

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.



Organisational Unit

School of Mathematical Sciences


Dr Greg Markowsky

Professor Paul Cally

Unit guides



  • Second semester 2017 (Day)


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.


On completion of this unit students will be able to:

  1. Understand the basic properties of complex numbers and functions, including differentiability;
  2. Evaluate line integrals in the complex plane;
  3. Understand Cauchy's integral theorem and its consequences;
  4. Determine and work with Laurent and Taylor series;
  5. Understand the method of Laplace transforms and evaluate the inverse transform;
  6. Appreciate the importance of complex analysis for other mathematical units, as well as for physics and engineering, through seeing applications of the theory;
  7. Use a computer algebra package to assist in the application of complex analysis.


Examination (3 hours): 60% (Hurdle)

Continuous assessment: 40%

Hurdle requirement: To pass this unit a student must achieve at least 50% overall and at least 40% for the end-of-semester exam.

Workload requirements

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

See also Unit timetable information

Chief examiner(s)

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