MTH4020 · Complex analysis and integral transforms

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.

Areas of study: Applied mathematics Mathematical statistics 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 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

• Three 1-hour seminars; • One 2-hour applied class (in weeks 2-12) and • 7 hours of independent study per week.

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