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
Mon, Wed, Fri Homework                      Main page

Homework
Tuesday and Thursday Sections

HW # Assignment Due Solutions
Primer Problem Set 0 Tuesday, September 18 Solution 0
1 Problem Set 1 Thursday, September 20 Solution 1
2 Problem Set 2
Problem Set 3
Tuesday, September 25 Solution 2
3 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
Thursday, September 27 Solution 3
4 Read Section 8.5 and 8.6
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, 16 (but don't worry about the endpoints of the interval), 20abc, 22, 23ab, 28
Section 8.6 #6, 12, 16, 28
Plus: Problems 2, 3 and 4 from Handout A
Tuesday, October 2 Solution 4
5 Read the Series handout
Do (from the handout, pg. 931): #1, 2, 4, 9, 12, 13
Plus: All of Handout B
Thursday, October 4 Solution 5
6 Read Section 8.7 and 8.8
Do: Section 8.7 #12, 14, 18, 20, 23, 25, 27, 29, 34, 36, 38
Section 8.8 #1, 4, 9, 16a (b and c are extra credit)
Tuesday, October 9 Solution 6
7 Read Section 8.9
Do: Section 8.9 #3, 19, 20, 22, pg. 641 #40
Plus: Problems 1 and 2 from Handout C.
Thursday, October 11 Solution 7
8 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 on Handout C.

Good Luck on the Exam!

See Note Below Solution 8
9 Do: Section 5.5 #4, 5, 8, 10, 14, 16, 20, 24, 27, 28, 32, 57, 60
Section 5.6 #4, 5, 8, 14, 22, 28, and pg. 438 #5 (as a review)
Plus: Looking at Integration from a Graphical Perspective
Extra credit: Section 5.6 #34
Tuesday, October 23 Solution 9
10 Do: Section 5.6 #6, 18
Section 5.7 #18, 20, 24, 27, 29
Plus: Problem 1 from Handout D
Thursday, October 25  
11 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.)
Section 5.9 #2, 13, 23, 24
Plus: Problems 2-6 from Handout D
Extra credit: pg. 441 #72 OR Problem 7 on Handout D
Tuesday, October 30 Solution 11:
Part I
Part II
12 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
Thursday, November 1 Solution 12
13 Do: Section 5.10 #53
Plus: Problems 2-6 from Handout E
And: 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, 27 (for Extra Credit)
Tuesday, November 6 Solution 13:
Part I
Part II
14 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
Thursday, November 8 Solution 14
15 Do: Section 6.3 #1, 4, 21
Section 6.4 #2, 5, 11
Section 6.5 #1, 4, 7, 10, 12, 19, 22
Extra Credit: Section 6.4 #16; Section 6.5 # 17, 18
Tuesday, November 13 Solution 15:
Part I
Part II
16 Do: Section Section 6.7 # 2, 3, 4, 6, 8, and Chapter 6 Review #29 (pg. 501)
Extra Credit: Section 6.7 # 13
Thursday, November 15 Solution 16
17 Read: Text Section 7.1 and 7.2, Supplementary Materials packet p. 1-9 (working through the worksheet), and Handout p. 983 - 992
Do: Section 7.1 #1, 3, 4, 6, 9, 11, 12, 14
Section 7.2 #1
Handout p.990 # 1, 2, 4
Plus: Problems 1-3 from Handout F
Tuesday, November 20 Solution 17
18 Happy Thanksgiving! - -
19 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
Tuesday, November 27 Solution 19
20 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)
Thursday, November 29 Solution 20
21 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
Tuesday, December 4 Solution 21
(Please use to study for the exam)
22 Read: Section 8.10
Do: Section 8.10 #3 (express as a familiar function), 5 (which cannot be expressed as a familiar function)
Thursday, December 6 Solution 22
23 Read the supplement pp. 16-40
In the text, do Section 7.6 #1,2
Plus: Problem 4 from Handout G
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: All of Handout H (including the Additional problems)
Tuesday, December 11 Please see MWF Solution 32 and 33
24 Do: Handout I Thursday, December 13 Solution 24
25 Do: Handout J   Solution 25

Note: We will have the solutions to both problem set #7 and 8 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