Homework assignments

Homework 1, due Jan. 30

Ch. 7: 2, 4, 11, 6, 7, 8, 9, 15, 13b).
Prove 13b) for a compact subset of R.

Homework 2, due Feb. 13

Ch. 7: 16, 18, 19, 20, 21, 22, 24, 12
Ch. 8:
1. Prove that if a power series converges absolutely at a point x_0, then it converges uniformly on the closed interval [-a, a], where a=|x_0|.
2. Evaluate \sum_{n=1} n/ 2^n

Homework 3, due Feb. 27

1. Evalaute \sum_{n=1} (-1)^{n+1} 1/n.
2. Suppose \sum c_n converges. Show that \sum c_n x^n uniformly converges over [0,1].

Ch. 8: 12a), 12b),
Ch. 8: 4c), 5b), 5c), 6, 9, 24, 25.

Homework 4, due in ONE and Half week, March 9

Ch. 8: 3, 12c), 12 d), 12e), 14, 26, 29.

Homework 5, due March 26

Ch. 9: 5, 6, 7, 12, 14
Ch. 9: 16, 17, 23, 24, 27

Homework 6, due April 9. TEST 2 on March 30

Ch. 9: 28, 29
Ch. 11: (12), (13), (14), (15) on page 303
Ch: 11: 3, 14.

Homework 7, due April 23.

Ch. 11: 1, 2, 4, 15, Example 11. 6(b)
Ch: 11: 5, 6, Remark 11.23 (a-f).

Homework 8, due May 7-11. FINAL May 11, 8-10AM, VinH 206

Ch. 11: 8, 9,10, 17, 18
Ch: 11: 11, 12, 16