## Spring-2017. Math 185 (ccn 18272). Introduction to Complex Analysis

Instructor: Alexander Givental
Lectures: 8-9, 310 Hearst Mining
Office hours: Mo 2-3:30, Fr 9:30-11
GSI: Brandon Williams, Office hours: MWF 2-4:30, TT 12:30-2 in 961 Evans (starting 2nd week of classes)
Textbook: Complex Function Theory by D. Sarason, 2nd edition, AMS
Grading policies: Homework 40%, Midterm 20%, Final 40%
Midterm: Friday, February 24, in class, Chapters I-IV
Final: Monday, May 8, 8-11 am, 310 Hearst Mining, Chapters I-X
Homework: Due weekly on Wed. (assignments to be posted here).

#### NO LECTURES DURING THE RRR WEEK FINAL on Mon.. May 8, 8--11 AM in 310 Hearst Mining, CHAPTERS I-X Office hours during the RRR week: Mon. 2-3:30, Wed. 12-2, Fr. 9:30-11 Graded HW 12 can be picked during the office hours on Wed. or Fr. Sample Final And here are solutions to the actual final exam.

HW1, due by Wed., Jan. 25: Read Chapter 1.
Solve: I.4.3, I.7.4, I.10.1, I.11.5, I.14.1.

HW2, due by Wed., Feb. 1 Read Chapter 2.
Solve: II.8.1(b,d), II.8.2, II.16.4, II.16.7, II.16.8.

HW3, due by Wed., Feb. 8 Read Chapter 3.
Solve: III.5.2, III.6,3, III.9.2, III.9.5, III.9.7.

HW4, due by Wed., Feb. 15 Read Chapter 4.
Solve: IV.5.2, IV.9.2, IV.13.4, IV.16.1, IV.16.3.
Solutions

HW5, due by Wed., Mar. 1: Read Chapter 5.
Solve: V.6.2, V.7.2, V.14.1(b), V.16.2, V.18.1.

HW6, due by Wed., Mar. 8: Read Chapter 6.
Solve: VI.7.2, VI.8.1, VI.8.4, VI.12.2, and
give an example of two convergent series whose product diverges.

HW7, due by Wed., Mar. 15: Read Chapter VII, pages 75-82.
State and prove directly, i.e. not using Cauchy's theorem for triangles, the analogue of this theorem for rectangles.
Solve: VII.4,1, VII.4.2, VII.5.1, VII.6.1.

HW8, due by Wed., Mar. 22: Read Chapter VII to the end.
Solve: VII.8.1, VII.11.3, VII.13.1, VII.14.1, VII.16.1.

HW9: due by Wed., Apr. 5: Read Chapter VIII.
Solve: VII.17.1, VII.18.2, VIII.1.1, VIII.2.1, VIII.4.1.

HW10: due by Wed., Apr. 12: Read Chapter IX.
Solve: VIII.7.4, VIII.8.1, VIII.8.2, VIII.12.2, VIII.12.3.

HW11: due by Wed., Apr. 19: Read Chapter X up to page 130.
Solve: IX.5.2, IX.5.3, IX.10.2, IX.17.2, IX.17.3.

HW12: due by Wed., Apr. 26: Read: Chapter X.
Solve: X.8.4, X.10.2, X.10.5, X.12.2, X.12.5.

HW13: I didn't see much excitement today about having one more homework. Maybe indeed you can use your time more efficiently in the RRR week by preparing for the finals rather than submitting one more assigment to grade. So, let's assume that no hw 13 is due. However, I still recommend doing as many exercisesfrom the book as you can, and if you are curious to know what I would assign as hw 13, it could be: X.15.1, X.16.1, X.16.5, X.19.1, X.19.4.