### 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 12:30-1:30pm

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.

There will be homeworks collected weekly and one midterm. The final grade will be weighted as follows: Homework 35%, midterm 20%, final 45%.

## Review session: Thursday Dec 8, 9-10:20am, usual class location

### Homework:

Late homework will not be accepted. The lowest homework grade will be dropped.
It is expected that your homework should involve up to 10 hours of work per week. If you are spending considerably more time than this, let me know.

Homework 1 due Tuesday Sept 20 in class
Page 4: 1a,1b,1e,1i,4,6,11
Page 10: 5(in 5b, assume theta is nonzero), 6

Homework 2 due Tuesday Sept 27 in class
Page 19: 1a,1c,1e, 2a,2c,2e,
Page 21: 2c,2d
Page 24: 2a,2b,2c,4
Page 27: 1a,1b, 3, 6, 9

Homework 3 due Tuesday Oct 4 in class
Page 31: 4,8
Page 39: 2, 5, 7, 13, 14
Page 46: 5,6
Page 50: 2, 5, 6
hint

Homework 4 due Thursday Oct 13 in class
Page 53: 2,7,8,9
Page 57: 1f, 2,3,7
Page 62: 5,6

Homework 5 due Tuesday Oct 25 in class
Page 68: 1a, 5
Page 75: 1a,3,8

Homework 6 due Tuesday Nov 1 in class
Page 82: 1,3,5
Page 84: 1,2,4

Homework 7 due Tuesday Nov 8 in class
Page 89: 2,3,4
Page 106: 2,4,6,8
Page 109: 2,4

Homework 8 due Tuesday Nov 15 in class
Page 111: 1,6
Page 116: 1
Page 119: 1,4
Page 133: 4,5

Homework 9 due Tuesday Nov 22 in class
Page 137: 2, 5
Page 143: 2,4
Page 147: 1,3,7,9,12

Homework 10 due Tuesday Nov 29 in class
Page 153: 3
Page 157: 1a,b,c,d, 6,8
Page 170: 1a,5

Homework 11 due Tuesday Dec 6 in class
Page 176: 1a,d,e,h, 2a,b, 3,12

Homework 12 not to be turned in; discussed in review session
Page 179: 4
Page 181: 1
Page 198: 1,2,3
Page 202: 2,9
Page 208: 5

A 1-parameter family of Mobius transformations fixing two points.