NMAC09	Theory of Analytic Functions, 15 ECTS-points /ANALYTISKA FUNKTIONER/ Advancement level: C
	Aim: To give the student a deeper understanding of the fundamental theorems of analysis as well as the theory of analytic functions. This theory is fundamental to continued studies in mathematics. Prerequisites: NMAA 11 Algebra, NMAA 12 Linear Algebra, NMAA 13 Calculus I and NMAB 13 Calculus II (at least 20 points obtained on these courses, or their equivalent). Course organization: Teaching is done in lectures and problem classes. Course content: Set-theoretic topology in metric spaces. Bolzano-Weierstraß' theorem in Rn. Theorems on continuous functions on compact sets. Functional sequences and functional series. Theorems on uniform convergence. Power series. Analytic functions. Complex integration. Cauchy's integral theorem and formula. Power series expansion of analytic functions. The maximum principle. Schwarz lemma. Analytic continuation. Laurent series. Isolated singular points. Calculus of residues. The argument principle. Course literature: Brink-Persson: Elementär teori för analytiska funktioner. Studentlitteratur. Gustavsson, S: Mängdtopologi i metriska rum (compendium).
TEN1	Oral examination
TEN2	Written examination

Course language is Swedish.