Math 1260: Complex Analysis


Image of grid lines under sin(z).

Professor Richard Kenyon
Tel. 863-6406
rkenyon -at- math dot brown dot edu
office: Kassar 305
Office hours: Mondays 1:30-2:30pm

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.

Final Dec 16, 2:00pm BH153

PRactice final here

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


Homework:

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

Homework 1, due Thursday Sept. 11 in class:
Page 4: 1a,b,c,h,i,4,5,6,8

Homework 2, due Thursday Sept. 18 in class:
Page 10: 5,6
Page 14: 2,6
Page 21: 1,2
Page 27: 1,3
Page 31: 3,4,8

Homework 3, due Thursday Oct. 2 in class:
Page 39: 2,5,10
Page 46: 2,6
Page 50: 2, 3, 6
Page 53: 5, 7

Homework 4, due Thursday Oct. 9 in class:
page 57: 1c, 3, 4,6
Page 67: 1a,b,c, 8
Page 75: 1, 3

Homework 5, due Tuesday Oct. 21 in class:
Page 82: 1
Page 84: 1,4
Page 86: 1,3
Page 88: 2,3

Homework 6, due Tuesday Nov. 4 in class:
Page 106: 1,3, 8
Page 109: 2, 4
Page 111: 1, 3a, 6
Page 116: 1
Page 119: 1

Homework 7, due Tuesday Nov. 11 in class:
Page 133: 4
Page 137: 2
Page 143: 2, 7
Page 147: 2, 7, 12
Page 151: 1,2
Page 153: 3

Homework 8, due Tuesday Nov. 18 in class:
Page 157: 2, 8
Page 162: 1, 2
Page 170: 2, 5

Homework 9, due Tuesday Nov. 25 in class:
Page 176: 1, 2, 3
Page 179: 2, 4a
Page 181: 2
Page 185: 3

Homework 10, due Tuesday Dec 2 in class:
Page 198: 2, 3
Page 202: 2, 5, 8(The answer should be pi/e).
Page 205: 2, 5
Page 230: 1, 3

Homework 11, not to be turned in. Discussed in class Dec 9:
Page 261: 1, 7
Page 265: 3,7,8,9,10.
Page 272: 4, 13

Reading:
for Tuesday Sept 9: read Chapter I
for Tuesday Sept 16: read sections 2.1,2.2
for Tuesday Sept 23: read sections 2.3-2.6
for Tuesday Oct 7: read Chapter 3
for Tuesday Oct 14: read 4.1-4.4
for Tuesday Oct 28: read 5.1-5.7
for Tuesday Nov. 11: read 5.8-6.4
A 1-parameter family of Mobius transformations fixing two points.
preimage of some grid lines under exp(1/z).