homework
Homework #1 due Tue, Feb. 3
Section 1.1: 1d, 2, 5, 11b (assume 10), 17,
Section 1.2: 4,5
Section 1.3: 12,13
Homework #2 due Tue, Feb. 10
Section 2.1: 1,6,10,11,14,16 (use 15),18
Section 2.2: 2,3
Homework #3 due Tue, Feb. 17
Section 2.3: 8,9,10,11
Section 2.4: 1,2,3a,10,12
Homework #4 due Tue, Feb. 24
Section 3.1: 1,4,14
Section 3.2: 1,7
Section 3.3: 6
Section 3.4: 1, 5, 7
Homework #5 due Tue, March 3
Section 3.5: 1, 7c
Section 3.6: 2, 13
Section 3.7: 2, 8
Section 4.1: 4a, 5ab, 9
Section 4.2: 1, 2, 3
Homework #6 due Tue, March 10
Section 4.3: 5,19,20
Homework #7 due Tue, March 24
Section 4.4: 1
Section 6.1: 1,3,5
Section 6.2: 2,3,10,13
Homework #8 due Tue, March 31
Section 6.3: 4 (just show the left inequality -- for sup -- of each case);
also,
Problem X: is the upper integral of (f+g) always equal to
(upper integral of f) + (upper integral of g)?
Give a proof or counterexample.
Section 6.4: 1,3,7,9
Section 6.5: 1, 6
Section 6.6: 1bc,5,6
Homework #9 due Tuesday April 7
Section 6.6: 7,8,9
Section 7.3: 1,9,10
Section 6.4: 6
Section 6.2: 11,12 (Remark: it follows easily that a Lipschitz
function on [a,b] must be integrable.)
Homework #10 due Tuesday April 14
Section 8.1: 1,2,5
Section 8.2: 1,3,4,10
Section 8.3: 1a, 5 (Hint: show f satisfies (8.13).)
Section 8.4: 1,2
Section 8.5: 8
Homework #11 due Tuesday April 28
Section 9.1: 1adef (for 1a, say for which pairs (a,p) the series converges; for 1d,
find the sum),
3,7,8
Homework #12 due Tuesday May 5
Section 9.2: 1,6
Section 9.3: 2,3,4
Homework #13 due Tuesday May 12
Section 9.5: 2,3,6,13