### Math 1130: Functions of Several Variables

Professor Richard Kenyon
Tel. 863-6406
rkenyon -at- math dot brown dot edu
office: Kassar 305
Office hours: Wednesdays 12:30-1:30pm
TA Session: Mondays 5:00-6:00pm, Kassar 105

Text: A. Browder, Mathematical Analysis, an Introduction (isbn 978-1-4612-6879-6)

Course outline: After a review of real analysis and the Riemann integral, we discuss point-set topology, function spaces, measures and integration. We will cover most of the material in chapters 5-10.

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

## Final exam: Mon, Dec 18, 2017 2:00-5:00pm Salomon Ctr 003

### 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 Thursday Sept 21 in class
Page 25: 8,15,18
Page 51-52: 11, 17, 21
Page 70: 4, 10, 12, 15.

Homework 2: due Thursday Sept 28 in class
Page 95: 16,17
Page 118: 1,2,3,4,5,6

Homework 3: due Thursday Oct 5 in class
Page 120: 8, 15, 18, 19, 20, 21

Homework 4: due Thursday Oct 12 in class
Page 150: 1, 2, 5 (assume for this problem X=Reals with usual topology), 7, 10

Homework 5: due Thursday Oct 26 in class
Page 150: 4, 9, 12 (for the topology of example 6.4, include -infinity in all sets except the empty set), 22

Homework 6: due Thursday Nov 2 in class
Page 151: 16, 20, 24

Homework 7: due Thursday Nov 9 in class
Page 171: 1,4(in this problem, show that the distance in the uniform metric between p(z) and zbar is always at least 1. In the hint given, the value of the integral is 2pi),5,6

Homework 8: due Thursday Nov 16 in class
Page 172: 9, 11, 13, 14, 18

Homework 9: due Thursday Nov 30 in class
Page 219: 1, 3, 6, 10, 11, 12, 14

Homework 10: due Thursday Dec 7 in class
Page 247: 1, 2, 3, 4, 5