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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
Paper code MATH302
Subject Mathematics
EFTS 0.15
Points 18 points
Teaching period Semester 2 (On campus)
Domestic Tuition Fees (NZD) $955.05
International Tuition Fees Tuition Fees for international students are elsewhere on this website.

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MATH 201
Schedule C
Arts and Music, Science
This paper is particularly relevant to Mathematics and Physics majors.

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.


Lecture notes are available from Uniprint in the Library.

Graduate Attributes Emphasised
Critical thinking.
View more information about Otago's graduate attributes.
Learning Outcomes

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

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Semester 2

Teaching method
This paper is taught On Campus
Learning management system


Stream Days Times Weeks
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


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