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|
|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.|
- 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
- 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.