MTH3020 - Complex analysis and integral transforms - 2019

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

Chief examiner(s)

Professor Paul Cally


Professor Paul Cally

Unit guides



  • Second semester 2019 (On-campus)


MTH2010, MTH2015 or ENG2005




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.


NOTE: From 1 July 2019, the duration of all exams is changing to combine reading and writing time. The new exam duration for this unit is 3 hours and 10 minutes.

End of semester examination (3 hours): 60% (Hurdle)

Continuous assessment: 40% (Hurdle)

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

Workload requirements

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

See also Unit timetable information

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