MTH4020 Complex analysis and integral transforms
Faculty of Science
MTH4020 Complex analysis and integral transforms is a level 4, 6-credit-point, undergraduate and postgraduate unit from the Faculty of Science, offered in 2026 in Semester 2 at Clayton. It has no prerequisites.
- Credit points
- 6
- Offered in 2026
- Semester 2
- Clayton
- Assessment
- Exam 50%
- and 1 other task
This is the 2026 handbook entry. See the 2027 entry.
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Requisites
Before MTH4020
No prerequisites or corequisites besides the enrolment rules below.
After MTH4020
No unit lists MTH4020 as a prerequisite in the 2026 handbook.
Enrolment rules
PROHIBITION: ENG2092, MTH3020
COREQUISITE: You must be enrolled in the Graduate Certificate in Mathematics or the Master of Mathematics
Equivalent units
The same content under another code. Only one of them counts.
Overview
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.
Offerings in 2026
| Teaching period | Campus | Mode |
|---|---|---|
| Second semester | Clayton | On campus |
Assessment
- Continuous assessmentDemonstration50%
- Final Assessment - Exam (3 hours and 10 minutes)Examination50%
Assessment details may change. Please refer to the assessment information in Moodle closer to the start of the teaching period.
Learning outcomes
When you finish this unit, you should be able to:
- 1
Demonstrate a deep understanding of complex numbers and functions
- 2
Compute and interpret line integrals in the complex plane using advanced techniques
- 3
Apply Cauchy’s integral theorem and its implications in various contexts
- 4
Develop and manipulate Laurent and Taylor series for complex functions
- 5
Master the method of Laplace transforms and proficiently evaluate inverse transforms.
- 6
Recognise the significance of complex analysis and its applications in physics and engineering and illustrate with real-world examples.
- 7
Utilise computer algebra systems to facilitate and enhance the application of complex analysis techniques.
Workload and teaching
- Applied sessions22 hours
- Seminars36 hours
- Teaching approachActive learning
- Three 1-hour seminars;
- One 2-hour applied class (in weeks 2-12) and
- 7 hours of independent study per week.
Active learning will occur in lectures and applied classes.
Learning resources
Required resources
A guide to writing homework solutions http://webpub.allegheny.edu/employee/r/rholmgre/Writing/writing.html
Principles of writing mathematics well http://www.saintjoe.edu/~karend/m441/m441writing.html
Recommended resources
Tips on writing in mathematics http://www.stolaf.edu/people/zorn/prooftips.pdf
Contacts
- Chief Examiners
- Dr Gregory Markowsky
- Unit Coordinators
- Dr Gregory Markowsky
Common questions
What are the prerequisites for MTH4020?
MTH4020 has no prerequisites, but enrolment rules apply.
When is MTH4020 offered?
In 2026, MTH4020 runs in Semester 2 at Clayton.
Does MTH4020 have an exam?
Yes. The exam is worth 50% of the final mark, alongside 1 other task.