MAI0063: Complex analysis, 8 hp - Ph.D. course, spring 2016

Course leader: Lars Alexandersson

Literature: Mats Andersson, Topics in Complex Analysis, Springer, chapter 1, 2.1-2.2, 3.1-3.4, 4, 5.1-5.2

Content: Integral representations of analytic functions; power series expansions and residues; global Cauchy theorems. Conformal mappings; the Riemann sphere and projective space. Approximation with rationals; Mittag-Leffler's theorem and the inhomogeneous Cauchy-Riemann equation; analytic continuation; simply connected domains. Harmonic functions; subharmonic functions. Weierstrass' theorem; zeros and growth

Organization: Lectures and problem sessions. Presentations

Examination: Active participation in problem sessions. Assigned problems. Presentation of a topic related to the course

Prerequisites: Graduate courses in integration theory and functional analysis (specific details). Some undergraduate course in complex analysis

Schedule: Hopn = Hopningspunkten, Komp = Kompakta rummet. Problem sessions are marked * and presentations +

Week 6

Tue 9/2 10-12, Hopn

Thu 11/2 10-12, Komp

Week 7

Tue 16/2 10-12, Hopn

* Fri 19/2 13-15, Åskådliga rummet (chapter 1)

The course is cancelled. Last time the entire course was given was in 2012.

Sidansvarig: Lars Alexandersson
Senast uppdaterad: 2019-11-29