## TMA4175 KOMPLEKS ANALYSE (COMPLEX ANALYSIS)

### 27.04, 4.5, 8.5 repetition of the syllabus.

 About the course "Complex analysis is a splendid realm within the world of mathematics, unmatched for its beauty and power. It has varifold elegant and oftentimes unexpected applications to virtually every part of mathematics. It is broadly applicable beyond mathematics, and in particular it provides powerful tools for the sciences and engineering." Book Elias Stein & Rami Shakarchi: Complex Analysis, Princeton. Lectures Tuesday 14–16, F4 Friday 12–14, F4 Exercises Monday 16–17, F3.   15.1. § 1. 4, ex. 1, 3, 7, 9, 10, 12, 13 22.1. § 1.4, ex. 14, 15, 16 a, b, c, d, 17, 19, 25 29.1  § 2.6, ex. 1, 2, 5, 7, 10. 5.2    § 2.6, ex. 8,11,14. § 3.8, ex. 1, 2, 3 ,4 12.2  § 3.8, ex. 6, 7, 9, 10, 11, 13. 19.2 § 3.8, ex. 12,15,16,17. § 3.9, ex. 3. 12.3 § 5.6, ex. 1, 2, 6, 7, 8, 9 19.3 § 5.6, ex. 10, 11, 13. Comments on midterm. 26.3 § 8.5, ex. 4,5,6,9,10. Study Figure 1, p. 213. Read §8.6, Problem 2. 16.4 § 8.5, ex. 11, 13b, 14, 20a. 23.4 § 6.3 ex. 2, 3, 5, 6, 7a. 30.4 § 7.3 ex. 1, 5, 10. § 8.5 ex. 12 7.5 § 1.4 ex.. 11, § 2.6 ex.. 3, § 3.8 ex.. 8, § 5.7 ex .1, § 8.5 ex.. 20b. Syllabus Chapters 1–3 and 5-8 from the book. The exercises. Examination Written examination 29.5.2007 (counts 80%) and midterm  13.03.2007(counts 20%). Teacher Peter Lindqvist, 1152 SB II, NTNU Other references L. V. Ahlfors: Complex Analysis can also be consulted.   Z. Nehari: Introduction to Complex Analysis. – This book is elementary with good exercises. R. Boas: Invitation to Complex Analysis. – A good exposition, easy to read. R. Nevanlinna & V. Paatero: Introduction to Complex Analysis " ("Einführung in die Funktionentheorie) – This is the best one!   Th. Gamelin: Complex Analysis.

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