Harvard University,FAS
Summer 2006

Mathematics Math1b
Summer 2006

Introduction to Functions and Calculus II
and Differential equations

Course Head: Robin Gottlieb

Office: SciCtr 430
Email: gottlieb@math.harvard.edu
Mainpage Syllabus Calendar Homework Exams Supplements Links

Homework

HW Assignment Due Solutions
#1 Stewart 7.1 #1, 4, 6, 16, 27, 32, 34
Integration handout B #1, 3, 6, 7, 8, 9, 10
(download from the supplements page)
Reading: S: 5.1-5.5 and 7.1 (Ignore the part of Ex. 3 that refers to Simpson's Rule.) Read the supplement Gottlieb 27.1 which is available on the supplements page.
June 30 Solutions
#2 Stewart: 7.2 #4, 9, 12, 27 (careful with constants versus variables!), 32, 48
7.3: #1, 22
Stewart 5.5 #10, 14, 24, 30, 32, 33, 34, 36, 49, 62
Integration Handout B: # 4, 5, 13, 14, 19
July 6 Solutions
#3 Stewart 6.1 ( At least one of these won't require parts!)# 8, 10, 13, 17 (many altermatives), 20, 22, 25, 34
6.2 #6
6.3 # 1, 2, 12, 18, 31, 35, 39.
Integration Handout #20, 21, 22
Stewart 7.5 #10.
For the reading in 7.5 read 384-387, no further.
July 12 Solutions
#4 Integration Handout B : #15, 17, 18, 26
Stewart: 7.5 #6, 12(you can eliminate time), 14, 17
7.4 #1, 6, 16
6.6 #2, 8, 9, 22, 41, 42, 44
July 14 Solutions
#5 Series Handout (download from Supplements page) #1, 2, 3, 4, 5, 6
Stewart: 8.1 #2, 10, 26, 28, 29
8.2 #1, 2, 6, 18, 27, 40
with 8.2 #33 as extra credit for those economists in the class and 8.1 #40 as a challenge problem for those who wish.
July 19 Solutions
#6 Series Handout: #7, 10
Read 30.1 from the supplement (It is on the supplements page ) and do
p. 931-932 # 1, 2, 4, 8, 13 (use your work from 2)
Stewart 8.2 #19, 30
July 21 Solutions
#7
Stewart 8.3 #2, 5, 12, 14, 16, 24, 29, 30, 35, 37 (hint: compare the values of a_n to those of sin(a_n)), 41
8.4 # 5, 6, 8, 9, 20, 22, 39ab
Series Handout #9, 15, 18, 25
July 25 Solutions
#8 Series handout #12, 13, 14, 16, 17, 21
8.4# 26, 30, 32, 37;
8.5 # 8, 10, 16, 17, 18, 20
July 28 Solutions
#9 Series Handout #11, 20, 22
8.5 #23a (b optional)
8.6: #8, 14, 23, 26, 28, 38ab;
8.7# 6, 8, 10 (cosh x is defined to be (1/2)[e^x + e^{-x}] - add the two series term by term and divide by two,) 23, 47(error <.0005), 50, 62 ;
Start trying some practice exams and review problems!
August 1 Solutions
#10 Read Stewart 7.6 pp. 397-400 and 403-404 plus supplement 3.1, 3.2
stewart: 7.6 # 21-256
31.1 #4 and 31.2 #1, 3
Differential Equations handout (see supplements page) #1,2,3, 4, 5
August 4
Solutions
#11 Read stewart 7.6 and the supplement 31.3 and 31.4
Differential Equations Handout #6, 7, 8, 9, 10, 11
Stewart: 7.6 #6, 8 (solve for y explicitly), 10, 12, 14, 33, 34, 39, 44, 46; (optional: #36 )

Supplement 31.3 # 1 (no need to compute the 2nd derivative), 6, 7, 17, 21 Extra credit: #23
August 8 Solutions
Solution2
#12 Read the supplement 31.5
Differential Equations Handout # 12,13, 14, 15 with a = 3/2, 16
Supplement 31.5: #1, 13 with the following correction for #13:
in (a) dy/dt = x, not -4x (as written there are no answers to (a)).
Try the applet dfield and pplane on the supplements page of the website. Fool around with it and use it to check your work on the rest of the homework.
August 11 Solutions
#13 Differential Equations Handout #17, 18, 21, 22, 26, 27a
Supplement p. 1049 -50 # 5, 12 (look at the instructions above 12), 14, 17

Longer assignment: Add any or all of Differential Equations handout #23, 24, 27b, 28 plus this worksheet relating vibrating springs to a phase plane representation.
August 14  
#14 Study for the final 9:00 am - noon on Thursday, 8/17 in SC E (in the basement)




Maths 1b, Summer, 2006, maths1b@fas.harvard.edu, Department of Mathematics, Faculty of Art and Sciences, Summer School, Harvard University