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 304
Office hours: Mondays 12:30-1:30 or by appointment

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

Another text with a slightly different viewpoint is Steven Krantz, "Complex Variables: A Physical Approach" (freely available online)

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%.

Final: Dec 17, 9:00am-12:00pm, BH 141

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 18
Page 4: 1e,1f,1h,1j, 5, 6, 7
Page 9-10: 1a,1c, 1d, 3

Homework 2: due Tuesday Sept 25
Page 18: 1,2a,2b,4c
Page 21: 2, 4
Page 24: 2,3
Page 28: 6,8
Page 31: 4

Homework 3: due Tuesday Oct 2
Page 39-40: 4, 10, 11, 19
Page 46: 2, 5, 6(I won't require you to show continuity of the derivative)

Homework 4: due Tuesday Oct 9
Page 50: 2, 6,
Page 53: 2, 5, 7, 8
Page 57: 1a,1b,1c, 3,
Page 62: 4, 5, 6

Homework 5: due Tuesday Oct 23
Page 75: 3,5
Page 82: 1, 6
Page 84: 1a, 1b, 4

Homework 6: due Tuesday Oct 30
Page 87: 3
Page 89: 2, 3, 9
Page 106: 1, 4, 8

Homework 7: due Tuesday Nov 6
Page 109: 1, 2, 4
Page 111: 1
Page 116: 1

Homework 8: due Tuesday Nov 13
Page 119: 1, 2, 4
Page 133: 4, 5
Page 137: 2, 3, 5, 9

Homework 9: due Tuesday Nov 20
Page 143: 1d,1f,1h, 2, 5, 7
Page 147: 1, 4, 6, 7, 10, 13


Check out this video about sqrt(z)