MTH3020 Complex analysis and integral transforms
Faculty of Science
MTH3020 Complex analysis and integral transforms is a level 3, 6-credit-point, undergraduate unit from the Faculty of Science, offered in 2027 in Semester 2 at Clayton. It has no prerequisites.
- Credit points
- 6
- Offered in 2027
- Semester 2
- Clayton
- Assessment
- Exam 50%
- and 1 other task
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Requisites
Before MTH3020
No prerequisites or corequisites besides the enrolment rules below.
After MTH3020
No unit lists MTH3020 as a prerequisite in the 2027 handbook.
Enrolment rules
PROHIBITION: ENG2092
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 2027
| 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
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.
Workload and teaching
- Seminars36 hours
- Applied sessions22 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
Spiegel, Murray, Laplace transforms, 1965, Schaum Outline series, McGraw-Hill.
Tips on writing in mathematics http://www.stolaf.edu/people/zorn/prooftips.pdf
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
Contacts
- Chief Examiners
- Dr Gregory Markowsky
- Unit Coordinators
- Dr Gregory Markowsky
Common questions
What are the prerequisites for MTH3020?
MTH3020 has no prerequisites, but enrolment rules apply.
When is MTH3020 offered?
In 2027, MTH3020 runs in Semester 2 at Clayton.
Does MTH3020 have an exam?
Yes. The exam is worth 50% of the final mark, alongside 1 other task.