# MATH302 Complex Analysis

Develops the differential and integral calculus of functions of a complex variable, and its applications.

This paper provides an introduction to the mathematics and analysis of complex numbers, which are a central topic of pure and applied mathematics.

Paper title Complex Analysis MATH302 Mathematics 0.15 18 points Semester 2 (On campus) \$955.05 Tuition Fees for international students are elsewhere on this website.
Prerequisite
MATH 201
Schedule C
Arts and Music, Science
Eligibility
This paper is particularly relevant to Mathematics and Physics majors.
Contact

robert.vangorder@otago.ac.nz

Teaching staff

Dr. Robert A. Van Gorder

Paper Structure

Main topics:

• Complex numbers (modulus, argument, etc; inequalities, powers, roots, geometry and topology of the complex plane)
• Analytic functions (Cauchy-Riemann equations, harmonic functions, polynomials, power series, exponential, trigonometric and logarithmic functions)
• Complex integration (curves, rectifiability, curve integrals, domains, starlikeness, homotopy, simple-connectedness, Cauchy's theorem via Goursat's lemma, Cauchy's integral formulae, Cauchy's inequalities, Liouville's theorem, mean value theorem (for harmonic functions), fundamental theorem of algebra, maximum modulus principle, Morera's theorem, isolated singularities, Weierstrass's theorem, residue theorem, real integrals, Rouche's theorem, Schwarz's lemma)
Teaching Arrangements

Three lectures per week.

One Tutorial per week.

Textbooks

Lecture notes are available from Uniprint in the Library.

Critical thinking.
Learning Outcomes

Students who successfully complete this paper will demonstrate in-depth knowledge of basic concepts of complex analysis and mathematical proof.

## Timetable

### Semester 2

Location
Dunedin
Teaching method
This paper is taught On Campus
Learning management system
Other

#### Lecture

Stream Days Times Weeks
Attend
A1 Monday 14:00-14:50 28-34, 36-41
Wednesday 14:00-14:50 28-34, 36-41
Friday 14:00-14:50 29-34, 36-41

#### Tutorial

Stream Days Times Weeks
Attend
A1 Thursday 14:00-14:50 29-34, 36-41