Math 1260: Complex Analysis

Professor Richard Kenyon
Tel. 863-6406
rkenyon -at- math dot brown dot edu
office: Kassar 305
Office hours: Mondays 1-3pm

Text: T. Gamelin, Complex Analysis (isbn 978-0-387-95069-3)

Course outline: Topics include the complex numbers, trigonometric functions and exponentials, derivatives and analyticity, contour integration and Cauchy's theorem, series, singularities and residues. We will cover most of the material in chapters 1-7, and some material of chapters 8-11.

There will be homeworks collected weekly and one midterm. The final grade will be weighted as follows: Homework 35%, midterm 25%, final 40%.


FINAL: Dec 18, 2pm-5pm, BH 141. No notes, books, calculators will be allowed.


Homework:

Late homework will not be accepted. The lowest homework grade will be dropped.

Homework 1, due Thursday Sept. 13 in class:
page 4: #1a,1b,1c,1h,3,5,8
Solution to problem 8

Homework 2, due Thursday Sept. 20 in class:
page 9: #1e,1f,6
page 21: 2
page 24: 2a,2b,4
Page 27: 3
Page 31: 3,4

Homework 3, due Tuesday Oct. 2 in class:
Page 40: 11
Page 46: 1g,2,5
Page 50: 2,6,7
Page 53: 6,7,8,9
Page 57: 1d,1f,2,3

Homework 4, due Tuesday Oct. 9 in class:
Page 62: 6,9
Page 67: 1a,1c,5,11,12

Homework 5, due Tuesday Oct. 16 in class:
Page 75: 1,4
Page 82: 1,3
Page 84: 1c,4,5

Homework 6, due Tuesday Oct. 23 in class:
Page 89: 2,3
Page 106: 1,2,5,8
Page 109: 2,4
Page 111: 1

Homework 7 due Nov 6.
Page 116: 1,3
Page 119: 1,2,4
Page 132: 2,5
Page 137: 1,5,6,8

Homework 8 due Nov 13.
Page 143: 1,2,3,4,6,7

Homework 9 due Nov 20.
Page 147: 1c,1e,1f,2,4,7,8,9,12
Page 151: 1d, 2
Page 153: 4
Page 157: 1f, 3, 6

Homework 10 due Dec. 4.
Page 162: 2
Page 170: 1,3,4,5
Page 176: 1,2,3,8
Page 179: 4

Homework 11 not to be turned in (discussion Tuesday Dec. 11).
Page 181: 1,2a
Page 185: 3
Page 198: 1d,h,i, 2,3e,3f
Page 202: 2,6,8
Page 205: 4,5

Reading:
for Tuesday Sept 11: read Chapter I
for Tuesday Sept 18: read Chapter 2, sections 1-6
for Tuesday Sept 25: finish Chapter 2, and Chapter 3, section 1-3.
for Tuesday Oct 23: Chapter 4, sections 1-6.
for Tuesday Nov. 6: Chapter 5, sections 1-6.
for Tuesday Nov. 20: Chapter 6, sections 1-4.
for Tuesday Dec. 3: Chapter 7, sections 1-5.
A 1-parameter family of Mobius transformations fixing two points.
Image of grid lines under sin(z).