MTH3025 · Complex analysis and integral transforms (Advanced)

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.

Areas of study: Applied mathematics Mathematics Pure mathematics

Offerings

Assessment

The Handbook lists an examination for this unit.

Assessment details may change. Please refer to the assessment information in Moodle closer to the start of the teaching period.

Requisites

The Handbook lists no prerequisite, corequisite or prohibition for this unit.

Learning outcomes

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

• Three hours of seminars; • Two hours of applied sessions and • Seven hours of independent study per week.

Student experience, not official rules. Nothing here changes what the Handbook says.