Develops the differential and integral calculus of functions of a complex variable, and its applications.
This paper provides an introduction to the mathematics and analyis of complex numbers, which are a central topic of pure and applied mathematics.
|Paper title||Complex Analysis|
|Teaching period||Second Semester|
|Domestic Tuition Fees (NZD)||$868.95|
|International Tuition Fees (NZD)||$3,656.70|
- MATH 201
- Schedule C
- Arts and Music, Science
- This paper is particularly relevant to Mathematics and Physics majors.
- More information link
- View more information about MATH 302
- Teaching staff
- Dr Melissa Tacy
- 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
- Five lectures each fortnight
One tutorial per week
- We will follow the book Complex Analysis, 3rd edition, by J. Bak and D.J. Newman,
Springer (2010), XII, 328pp, available online from the Resources page.
Lecture notes are also available online free of charge.
- Course outline
- View course outline for MATH 302
- Graduate Attributes Emphasised
- Critical thinking.
View more information about Otago's graduate attributes.
- Learning Outcomes
- Demonstrate in-depth knowledge of basic concepts of complex analysis and mathematical proof.