Chapter 3: # 1, 2, 5, 17, 18, 21, 23, 34, 39, 40
Chapter 4, # 2, 4, 11, 12, 14, 15, 20, 21, 24, 41, 43
Chapter 5, # 7, 8, 11, 20, 25, 27, 28 [Hint: Cauchy-Schwartz], 36 [Hint: use problem 20!].
Chapter 7, # 13, 16, 18, 17 [use any one of the equivalent metrics for the product space in #46 on p. 48], and: Let M=(0,∞), with d(x,y) = | 1/x – 1/y |. Is M complete? Justify your answer.
Chapter 8, #4 (and do A∩B also), 6, 9, 15, 44, 51, 53, 55
Chapter 10, # 7, 9(bef), 13, 15
Chapter 10, #19, 20, 26, 27, 29, 32
Chap 11: practice problems on C(X) and Weierstrass approx:prac_Weierstrass
Chap 11: Equicontinuity and Arzelà-Ascoli: # 50, 57 (you need an extra condition on the family!), 58 (need #20), 62, 63, 64.
Chap 15: #1, 2, 7, math4a3_fourier
Chap 16: 4, 13, 22
Chap 17: 4, 7
Chap 18: 10, 11, 27 (think Weierstrass!), 36, 38, 47bd, for (d) only do the case a>0.