Harvard University,FAS
Spring 2004

Mathematics Math1b
Spring 2004

Introduction to Functions and Calculus II
and Differential equations

Course Head: Robin Gottlieb

Office: SciCtr 429
Email: gottlieb@math.harvard.edu
Mainpage Syllabus Sections Calendar Homework Exams Supplements Links

Homework

HW # Assignment Due Solutions
Primer Problem Set 0 Due Thu Feb 12 (TTh) or Fri Feb 13 (MWF) Primer Solution  
Problem Set 1 Section 5.5# 30, 31, 45, 55, 62
Integration Handout #1, 2 (with #1 not due until Problem Set 4 is turned in.)
(TTH classes: Hand in Problem Set 0 with this.)
Reading: Text 5.5 and read about trig integrals on pp. 403-404
W Feb. 11 (MWF) or
Th Feb 12 (TTh)
Solution 1  
Problem Set 2 Section 5.6 # 4, 6, 9, 14, 18, 22, 28
(MWF classes: Hand in Problem Set 0 with this) Extra credit: 5.6 #34
Reading:5.6
F Feb. 13 (MWF) or
T Feb 17 (TTh)
Solution 2  
Problem Set 3 Section 5.7 # 16, 18, 24, 27 (It is easier using substitution - the choice is yours), 29
Integration Handout # 3, 4
Reading:5.7
W Feb 18 (MWF) or
T Feb 17 (TTh)
Solution 3  
Problem Set 4 Integration Handout #5, 6, 7
Plus hand in #1 from the Integration Handout
Reading: 5.7
F Feb 20 (MWF) or
Th Feb 19 (TTh)
Solution 4  
Problem Set 5 Integration Handout # 8, 9
5.2 # 32, 35
6.1 #2, 25
Reading: 5.2 and 6.1
M Feb 23 (MWF) or
T Feb 24 (TTh)
Solution 5  
Problem Set 6 Integration Handout # 11, 12
6.2 #21, 23, 42
Reading:6.2
Optional reading: supplement 27.2 pp. 843-850
Directions for accessing the Supplement can be found under "supplement" in the menu above..
W Feb 25 (MWF) or
T Feb 24 (TTh)
Solution 6  
Problem Set 7 Integration Handout #13, 14, 15, 16, 17
Extra Credit #18 on the Integration Handout
Reading: Supplement pp. 827-842.
F. Feb. 27 (MWF) or
Th. Feb 26 (TTh)
Solution 7  
Problem Set 8 Section 6.2 # 28, 37
Integration Handout #19, 20, 21.
Reading: Supplement 28.1 pp. 853-6
Stewart: 6.2 pp. 453-5.
M. March 1 (MWF) or
T March 2 (TTh)
Solution 8  
Problem Set 9 Section 6.5 # 4, 7, 8, 10, 12, 14
Integration Handout #22
Reading:Section 6.5
Optional: supp. 28.2 pp. 867-871.
W. March 3 (MWF) or
T. March 2 (TTh)
Solution 9  
Problem Set 10 Section 6.5 #13
Integration Handout # 26
Section 5.10 # 2, 6, 12, 14, 20, 51
(Note: one of these requires no computation. Look and think before you plunge in.)
Reading: 5.10
F. March 5 (MWF) or
Th March 4 (TTh)
Solution 10  
Problem Set 11 Section 5.10 # 24, 29
Section 6.7 #2, 4(ab), 6
Extra credit: 6.7 #13
Reading: 6.7
M. March 8 (MWF) or
T. March 9 (TTh).
Solution 11  
Problem Set 12 Section 6.4 # 2, 11 Section 6.3 # 4
Integration Handout # 23, 24
Extra credit: Integration handout # 25.
Reading: 6.3 (omit Ex. 4) and 6.4
Solutions will be posted by the 8th
to assist you in studying.)
Solution 12  
Problem Set 13 Series Handout #1, 3, 5, 6
F Mar 12 (MWF) or
Th Mar 11 (TTh)
Solution 13  
Problem Set 14 Section 8.1 #39; 8.2 #1, 2, 12, 16, 18, 20
Series Handout #2, 4, 7, 8
Reading: Supplement 18.1, 18.2, 18.3. If you need work on summation notation then read 18.4.
Stewart 8.1 and 8.2.
M Mar 15 (MWF) or
T Mar 16(TTh)
Solution 14  
Problem Set 15 Section 8.2 #34, 48, 51 and
8.3 # 3, 4, 9 10

Extra credit: 8.2 #52 Reading:8/3 (through p. 588 Ex.5
W Mar.17 (MWF) or
Th Mar 18 (TTh)
Solution 15  
Problem Set 16 Section 8.3 #1, 2, 5, 15, 16, 18, 19, 20, 22
Reading: 8.3
Series Handout #9 a,b,c -part (d) is extra credit).
F Mar 19 (MWF) or
T Mar 23 (TTh)
Solution 16  
Problem Set 17 In the supplement on the web: Section 30.1 #1, 2, 9, 11, 12, 13(use your work from #2), 16
Series Handout # 10
Reading:Section 30.1 from the supplement on the web.
M Mar 22 (MWF) or
T Mar 23 (TTh)
Solution 17  
Problem Set 18 Section 8.7 #7(ignore references to R_n(x) here and throughtout the assignment) 13, 18, 20, 22
Series Handout # 11, 12
Reading: 8.7 pp 613 -mid 614
(In the supplement on the web middle of p. 947-mid 948)
W Mar 24 (MWF) or
Th Mar 25 (TTh)
Solution 18  
Problem Set 19 Section 8.4 #12, 13, 19 (explain your reasoning carefully)
Series Handout #13, 14, 15
Reading:8.4 pp. 592-597 (alternating series and absolute convergence
F Mar 26 (MWF) or
T Apr. 6 (TTh)
Solution 19  
Problem Set 20 Section 8.4 #2, 20, 22, 31, 33 (notice that this is the Taylor series for e^x)
Series Handout #17, 18
Reading:8.4 pp. 597-8 (ratio test)
M Apr. 5 (MWF) or
T Apr. 6 (TTh)
Solution 20  
Problem Set 21 Section 8.5 # 4, 12, 14, 16, 20
Series Handout #20, 21
Reading:8.5
W Apr 7 (MWF) or
Th Apr 8 (TTh)
Solution 21  
Problem Set 22 Section 8.6 # 9, 11
SEction 8.7 # 11 (no R_n(x)), 29, 36
Series Handout #22, 24
Reading:8.6 and 8.7
F Apr 9 (MWF) or
T Apr. 13 (TTh)
Solution 22  
Problem Set 23 Section 8.7 # 34 section 8.8 # 1, 9 section 8.9 #22.
Series Handout #23a-c (no Taylor remainder) and 25.
Reading:8.8 and 8.9
M Apr 12 (MWF) or
T Apr. 13 (TTh)
Solution 23  
Problem Set 24 Problems for Review: (answers to be posted before the exam)
Concept Check on p. 640 (stewart) #3, 4, 10, 11a-d
True/False quiz # 1-7 and 11 on p. 640
8.6 # 6, 16 and 8.5 # 23a and 8.7 #38 and 8.9#23
W Apr 14 (MWF) or
Th Apr. 15 (TTh)
Solution 24  
Problem Set 25 Study for the exam
 
Problem Set 26 Differential equations Handout #1, 2, 3, 4, 5
(use the web applet under the supplements page: dfield.)
7.2 # 3, 4, 5, 6 (you can check this using the web applet!)
M Apr 19 (MWF) or
T Apr. 20 (TTh)
Solution 26  
Problem Set 27 Differential equations Handout #6, 7, 8, 9
7.1 # 7, 11; and 7.3 #4, 10
Reading: 7.1, 7.2 (without Euler's method) and 7.3 or the supplement 31.1, 31.2 and 31.4
W Apr 21 (MWF) or
Th Apr. 22 (TTh)
Solution 27  
Problem Set 28 From the supplement on the web, 31.3 (pp. 1014 -16) #1,2,3,6 and
From Stewart 7.4 #19bcd
Reading: Supplement 31.3 (p.1002-1012)
F Apr 23 (MWF) or
T Apr. 27 (TTh)
Solution 28  
Problem Set 29 Differential equations Handout #10(part (b) should refer to 10ai not 4ai), 11, 12
First Order Linear handout #1, 2, 3
7.3 # 34, 36
Reading: First Order Linear Handout
M Apr 26 (MWF) or
T Apr. 27 (TTh)
Solution 29  
Problem Set 30 Differential equations Handout #13, 15 Use the pplane applet to check your work.
Be prepared to put your answer to 15 on the board on the date the assignment is due. Full credit will be given for 15 as long as you turn in a thoughtful answer.
7.6 # 1, 2 plus Chapter 7 Review #20 and 21 where in (20(d) the trajectories are closed curves.)

TTH classes: do Stewart 7.1 #4 and 5 for Thursday as well.
Reading: Stewart 7.6 and the supplement 31.5 ( pp 1024-1040).
W Apr 28 (MWF) or
Th Apr. 29 (TTh)
Solution 30
Problem Set 31 In the supplement on p. 1042-5 do #9. 13bc, 14
Differential equations Handout #14, 16
MWF classes: In Stewart 7.1 do #4, 5
F Apr 30 (MWF) or
T May. 4 (TTh)
Solution 31
Problem Set 32 Differential equations Handout #19(a,c), 20(a,c), 21
Reading: Supplement 31.6 pp. 1045-middle of page 1047.
M May 3 (MWF) or
T May 4 (TTh)
Solution 32  
Problem Set 33 Differential equations Handout #19b, 20b, 22, 23, 24(abd)

TTH classes: do ALL of #24 and do 26 from the Differential Equations Handout and #17 from the supplement p. 1050. (These should be subtracted from the subesquent assignment.
Reading: Supplement 31.6 pp. 1047 1049.
W May 5 (MWF) or
Th May 6 (TTh)
Solution 33
Problem Set 34 Supplement p. 1050 #12, 13, 16, 17
Differential equations Handout #24 (c. e. f), 25, 26.
Plus Extra Credit:
I. Use series to solve y'' = -4y where at t=0 y = 2 (NOT 0) and y'=0.
II. Analyze 2 differential eqns from two perspectives: first, using what you know about solving second order differential equations and second, writing each as a system of first order differential equations. Details will be found on the supplements page under "last problem of the term".
Reading: Supplement 30.4 (pp. 960-961) or Stewart 8.10.
F May 7 (MWF) or
T May 11 (TTh) (in your CA's mailbox)
Solution 34  


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