MTH3025 Complex analysis and integral transform (Advanced)
Faculty of Science
MTH3025 Complex analysis and integral transform (Advanced) is a level 3, 6-credit-point, undergraduate unit from the Faculty of Science, offered in 2024 in Semester 2 at Clayton. It has no prerequisites.
- Credit points
- 6
- Offered in 2024
- Semester 2
- Clayton
- Assessment
- Exam 50%
- and 1 other task
This is the 2024 handbook entry. See the 2027 entry.
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Requisites
Before MTH3025
No prerequisites or corequisites besides the enrolment rules below.
After MTH3025
No unit lists MTH3025 as a prerequisite in the 2024 handbook.
Enrolment rules
PROHIBITION: MTH3020
PREREQUISITE: A High Distinction in MTH2010, or a Distinction in MTH2015, or a High Distinction in ENG2005, or by approval of the Head of School of Mathematics.
You must enrol in this unit manually via the online Enrolment Amendment form
Overview
This unit provides an introduction to complex analysis and integral transform. Topics include: complex numbers and functions; domains and curves in the complex plane; complex differentiation; complex 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 2024
| Teaching period | Campus | Mode |
|---|---|---|
| Second semester | Clayton | On campus |
Assessment
- Continuos assessmentOther50%
- Examination (3 hours and 10 minutes)ExamThreshold hurdle50%
Learning outcomes
When you finish this unit, you should be able to:
- 1
Demonstrate an advanced understanding of the properties of complex numbers and functions, including differentiability;
- 2
Evaluate line integrals in the complex plane;
- 3
Apply Cauchy's integral theorem and its consequences;
- 4
Determine and work with Laurent and Taylor series;
- 5
Apply the method of Laplace transforms and evaluate the inverse transform;
- 6
Apply advanced complex analysis tools in applications to physics and engineering.
Workload and teaching
- Applied sessions22 hours
- Seminars36 hours
- Teaching approachProblem-based learning
- Three hours of seminars;
- Two hours of applied sessions and
- Seven hours of independent study per week.
In your standup applied classes you and your fellow students will work together in groups of 3-4, tackling mathematical problems while receiving guidance from your applied class leader. During these sessions, the focus will be on actively engaging with the problems and finding practical solutions. Additionally, in seminars more problem-based learning will complement lecture-style presentations.
Learning resources
Recommended resources
E.B. Saff and A.D. Snider, Fundamentals of Complex Analysis (International Editions), 3rd ed., Pearson/Prentice Hall, 2003.
Spiegel, Murray, Laplace transforms, 1965, Schaum Outline series, McGraw-Hill.
Where it fits
MTH3025 is part of 6 areas of study in the 2024 handbook.
- APPLMTH05Applied mathematics elective unitsApplied mathematicsNo reviews yet
- APPLMTH07Applied mathematics elective unitsApplied mathematicsNo reviews yet
- MATHS09Mathematics elective unitsMathematicsNo reviews yet
- MATHS11Mathematics elective unitsMathematicsNo reviews yet
- MATPURE09Pure mathematics elective unitsPure mathematicsNo reviews yet
- MATPURE11Pure mathematics elective unitsPure mathematicsNo reviews yet
Contacts
- Unit Coordinators
- Dr Gregory Markowsky
- Chief Examiners
- Dr Gregory Markowsky
Common questions
What are the prerequisites for MTH3025?
MTH3025 has no prerequisites, but enrolment rules apply.
When is MTH3025 offered?
In 2024, MTH3025 runs in Semester 2 at Clayton.
Does MTH3025 have an exam?
Yes. The exam is worth 50% of the final mark, alongside 1 other task.
Which majors and minors include MTH3025?
MTH3025 is part of Applied mathematics, Mathematics and Pure mathematics.