MTH3020 · 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. 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

• 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.