Harvard University,FAS
Fall 2001

Mathematics 1b
Fall 2001

Calculus, Series
and differential equations

Course Head: Robin Gottlieb

Office: SciCtr 429
Email: gottlieb@math

Head CA: Jonathan Yang
Email: jyang@fas
Math1b applied: a Biological system
Tues, Thurs Homework                      Main page

Homework
Monday, Wednesday, and Friday Sections

HW # Assignment Due Solutions
Primer Problem Set 0 Monday, September 17 Solution 0
1 Problem Set 1 Wednesday, September 19 Solution 1
2 Problem Set 2 Friday, September 21 Solution 2
3 Problem Set 3 Monday, September 24 Solution 3
4 Read Section 8.4
Do: Section 8.3 #5, 9
Section 8.4 #2, 12, 13, 19 (for 19, explain your reasoning clearly. There are several different lines of reasoning that can be used.)
Plus: Problem 1 from Handout A
Wednesday, September 26 Solution 4
5 Read Section 8.5
Do: Section 8.4 #20, 22, 31, 33 plus: Look back at #33. Which grows faster, exponentials or factorials? Tie your answer in with #33.
Section 8.5 #2, 4, 6, 14. Do 16 but don't worry about the endpoints of the interval.
Plus: Problem 2 from Handout A
Friday, September 28 Solution 5
6 Read Section 8.6
Do: Section 8.5 #20abc, 22, 23ab, 28
Section 8.6 #6, 12, 16, 28
Plus: Problems 3 and 4 from Handout A
Monday, October 1 Solution 6
7 Read the Series handout
Do (from the handout, pg. 931): #1, 2, 4, 9, 12, 13
Plus: All of Handout B
Wednesday, October 3 Solution 7
8 Read Section 8.7
Do: Section 8.7 #12, 14, 18, 20, 23, 27, 29, 36
Friday, October 5 Solution 8
9 Read Section 8.8
Do: Section 8.7 #25, 34, 38
Section 8.8 #1, 4, 9, 16a (b and c are extra credit)
Wednesday, October 10 Solution 9
10 Read Section 8.9
Do: Section 8.9 #3, 19, 20, 22, page 641 #40
Plus: Problems 1 and 2 from Handout C.
Friday, October 12 Solution 10
11 Do: Section 8.9 #23, 25 (Read the notes on Handout C for guidance)
As a start to your exam review, do the Concept Check: pg. 640 #3, 4, 10, 11a-d, and the true/false quiz #1-7 and 11.
Plus: Problem 3 from Handout C.
See Note Below Solution 11
12 Good Luck on the Exam!! - -
13 Do: Section 5.5 #4, 5, 8, 10, 14, 16, 20, 24, 27, 28, 32
Plus: Looking at Integration from a Graphical Perspective (due October 24)
Friday, October 19  
14 Do: Section 5.5 #57, 60
Section 5.6 #4, 5, 8, 14, 22, 28
Plus: pg. 438 #5 (as review from first semester calculus)
Extra credit: Section 5.6 #34
Monday, October 22  
15 Do: Section 5.6 #6, 18
Section 5.7 #18, 20, 24, 27, 29
Plus: Problem 1 from Handout D
Wednesday, October 24 Solution 15
16 Do: Section 5.7 #1, 2, 3, 8 (From sin^2 t + cos^2 t = 1 you can derive the identity tan^2 t + 1 = sec^2 t.)
Plus: Problems 2-5 from Handout D
Friday, October 26 Solution 16
17 Do: Section 5.9 #2, 13, 23, 24
Extra credit: pg. 441 #72 OR Problem 7 on Handout D
Plus: Problem 6 from Handout D
Monday, October 29 Solution 17
18 Do: Section 5.10 #2, 6, 12, 13, 20, 24, 26. Note that one of these requires no work. Look before you roll up your sleeves to compute!
Extra credit: Section 5.10 #50 Plus: Problem 1 from Handout E
Wednesday, October 31 Solution 18
19 Do: Section 5.10 #53
Plus: Problems 2-6 from Handout E
Friday, November 2 Solution 19
20 Do: Section 6.1 #1, 4, 16 (to integrate |x| you must split the integral up into pieces on which x doesn't change sign), 22, 23, 24, 25
Extra Credit: #27
Monday, November 5 Solution 20
21 Do: Section 6.2 #3, but change the instructions from ``a typical disk or ``washer"" to ``a typical slice." To #3, add parts (b),(c), and (d) below. For each of these, set up the integral or integrals but do not evaluate:
(b) rotate the same region about the horizontal line y = 4.
(c) rotate the same region about the horizontal line y = 5.
(d) rotate the same region about the vertical line x = -1.
Do: Section 6.2 #10 (same change in instructions as above), 23, 31, 35, 46
Extra Credit: #48
Wednesday, November 7 Solution 21
22 Do: Section 6.3 #1, 4, 21
Section 6.4 #2, 5, 11
Section 6.5 #1
Extra Credit: Section 6.4 #16 (due Wednesday, November 12)
Friday, November 9
(Extra Credit due Wednesday as noted)
Solution 22
23 Do: Section 6.5 #4, 7, 10, 12, 19, 22
Extra Credit: Section 6.5 # 17, 18
Wednesday, November 14 Solution 23
24 Do: Section 6.7 # 2, 3, 4, 6, 8, and Chapter 6 Review #29 (pg. 501)
Extra Credit: Section 6.7 # 13
Friday, November 16 Solution 24
25 Read: Text Section 7.1, Supplementary Materials packet p. 1-4 (working through the worksheet), and Handout p. 983 - 992
Do: Section 7.1 # 1, 3, 4, 6
Handout p.990 # 1, 2, 4
Plus: Problem 1 from Handout F
Monday, November 19 Solution 25
26 Read: Section 7.2 in the text and p. 5-9 in the Supplement Do: Section 7.1 #9, 11, 12, 14
Section 7.2 #1
Plus: Problems 2 and 3 from Handout F
Wednesday, November 21 Solution 26
27 Happy Thanksgiving! - -
28 Read: p. 10-14 in the Supplement
Do: Supplement p. 14-15 #1 (you might want to draw the family of solutions and then, using another color, highlight solutions corresponding to the initial conditions given), 2, 3, 4
Handout p. 997 #3
Text Section 7.2 #3, 4, 5, 6, 9
Extra Credit: p. 1000 #17
Wednesday, November 28 Solution 28
29 Read: Text Section 7.3 Do: Section 7.2 #28ab
Section 7.3 #3, 4, 5, 6, 9, 16, 28, 33
(Section 7.2 #28c can be done for extra credit)
Friday, November 30 Solution 29
30 Do: Section 7.4 #13
Section 7.5 #8,9
Stewart's p. 557, do the true/false quiz in the center of the page
Plus: Problems 1-3 from Handout G
Monday, December 3 Solution 30
(Please use to study for the exam)
31 Read: Section 8.10
Do: Section 8.10 #3 (express as a familiar function), 5 (which cannot be expressed as a familiar function)
Wednesday, December 5 Solution 31
32 Read the supplement pp. 16-40
In the text, do Section 7.6 #1,2
Plus: Problem 4 from Handout G
ADDITION: The problems listed after Problem 1 in Handout H
Friday, December 7 Solution 32
33 Read: (text) Section 7.6 and the supplement pp. 41-45
In the text, do chapter review problems #20 and 21 on p. 559
The next part of the homework is in preparation for next week's classes. We will use the results:
Do: Handout p.1002 #28 (typo: it's e^{lambda t}, not $e^{lambda^t}) and #29
Plus: Handout H
Monday, December 10 Solution 33
34 Do: Handout I Wednesday, December 12 Solution 34
35 Do: Handout J   Solution 35

Note:We will have the solutions to both problem set #10 and 11 up on the web by Saturday. This way students can check and correct their answers while studying for the exam. This problem set will not have to be handed in for a grade, but should be done. Students will be held responsible for the material on it!

Last update, 12/05/2001, math1b@fas.harvard.edu