Harvard University,FAS
Fall 2002

Mathematics Math1b
Fall 2002

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 September 27 (MWF) or Th. September 26 (TTh) Primer Solution  
Problem Set 1 Section 5.2 #18,20,32,35
Section 6.1 # 2,25
# 1,2 on Integration Handout A
Reading: Text 6.1 and Supp 27.2 pp843-850
Directions for accessing the Supplement.
W Sep 25 (MWF) or
Th Sep 26 (TTh)
Solution 1  
Problem Set 2 # 3, 4, 5, 6, 7, 9 on Integration Handout A
(#9 is missing a delta x!)
Reading: Supp. 27.1 (pp. 827-842)
F Sep 27 (MWF) or
T Oct 1 (TTh)
Solution 2  
Problem Set 3 # 8, 10, 11, 12 on Integration Handout A
(the density units in #10 should be gm/cm^3 not cm^2)
Section 6.2 #28, 37
Reading: Supp. 28.1 (pp. 853-6)
Section 6.2 pp. 453-5.
M Sep 30 (MWF) or
T Oct 1 (TTh)
Solution 3  
Problem Set 4 # 13, 14 on Integration Handout A
Section 6.2 #21, 23, 42
Reading: Section 6.2
Optional: suppl. 28.1 pp 856-62.
W Oct 2 (MWF) or
Th Oct 3 (TTh)
Solution 4 
Problem Set 5 Section 6.1 #22; Section 6.3 #1, 4
Section 6.4 #2, 11
# 16 on Integration Handout A
Extra Credit: #18 on Integration Handout A (Do the updated version with parts (a)-(d))
Reading: Section 6.3 (omit Ex. 4) and 6.4
F Oct 4 (MWF) or
T Oct 8 (TTh)
Solution 5  
Problem Set 6 # 17 on Integration Handout A
Section 6.5 1, 4, 7, 8, 10, 12
Reading: Section 6.5
Optional: suppl. 28.2 pp 867-71.
M Oct 7 (MWF) or
T Oct 8 (TTh)
Solution 6  
Problem Set 7 Section 5.5 # 24, 27, 28, 32, 45, 55, 62
#20 on Integration Handout A
Section 5.7 #2
#19 on Integration Handout A should be started now but won't be due for a week. Typo on "Claim 2". That should be sin(x^2) not cos(x^2).
Reading: Section 5.5 and trig integrals pp 403-404
W Oct 9 (MWF) or
Th Oct 10 (TTh)
Solution 7 
Problem Set 8 Section 5.6 #6, 8, 9, 11, 14, 18, 22, 28
Extra credit: Section 5.6 #34
Reading: Section 5.6
F Oct 11 (MWF) or
T Oct 15 (TTh)
Solution 8  
Problem Set 9 Section 5.7 #16, 18, 24, 27 (you can do this more easily via substitution: the choice is yours), and #29.
#21, 22, 23 on Integration Handout A
Remember that #19 on the integration handout is due W or Th.
Reading: 5.7 partial fractions pp. 405 (last 3 lines) - 407.
W Oct 16 (MWF) or
T Oct 15 (TTh)
Solution 9  
#19 on Integration Handout A now due.
Claim 2 should have a sin(x^2) not a cos(x^2).
W Oct 16 (MWF) or
Th Oct 17 (TTh)
Solution #19  
Problem Set 10 #24, 25, 26 on Integration Handout A where the instructions on 24 should be "Evaluate the following integrals. Each of them can be done with a trigonometric substitution; all but one can also be done in other ways."
#26 is in the refreshed version of the integration handout.
Reading: 5.7 pp. 404-405 plus 5.10 through p. 432.
F Oct 18 (MWF) or
T Oct 22 (TTh)
Solution 10  
Problem Set 11 5.10 #2, 6, 12, 14, 20, 24, 29, 51
(Note: one of these requires no computation. Look and think before you plunge in.)
Reading: 5.10
M Oct 21 (MWF) or
T Oct 22 (TTh)
Solution 11  
Problem Set 12 6.7 #2, 4, 6
Extra credit: 6.7 #13
Reading: 6.7
W Oct 23 (MWF) or
Th Oct 24 (TTh)
Solution 12 
Problem Set 13 #1, 3, 5, 6 on Series Handout A
F Oct 25 (MWF) or
Th Oct 24 (TTh)
Solution 13 
Problem Set 14 # 2, 4, 7, 8 on Series Handout A
8.1 #39; 8.2 #1, 2, 12, 16, 18, 20
Reading: Supp 18.1, 18.2, 18.3 and if you need work on summation notation then 18.4. Stewart 8.1, 8.2.
M Oct 28 (MWF) or
T Oct 29 (TTh)
Solution 14  
Problem Set 15 8.2 #34, 48, 51
8.3 #3, 4, 10, 19, 20
Extra credit: 8.2 #52
Reading:8.3 "Testing by Comparison" pp. 586-587 (through Ex. 3)
W Oct 30 (MWF) or
Th Oct 31 (TTh)
Solution 15  
Problem Set 16 # 9 on Series Handout A
8.3 \#1, 2, 5, 9, 15, 16, 18, 22
Reading:8.3 pp. 583-588 (through Ex. 5)
F Nov. 1 (MWF) or
T Nov 5 (TTH)
Solution 16  
Problem Set 17 In the supplement on the web do S 30.1 #1, 2, 9, 11, 12, 13 (use your work from 2), 16
# 10 on Series Handout A
Reading: Section 30.1 in the supplement on the web.
M Nov 4 (MWF) or
T Nov 5 (TTh)
Solution 17  
Problem Set 18 8.7 in Stewart #7, 13, 18, 20, 22
# 11, 12 on Series Handout A
Reading: 8.7 pp. 613-mid 614. (We'll return to 8.7.) In the supplement on the web middle of page 947 through mid p.948.
W Nov 6 (MWF) or
Th Nov 7 (TTh)
Solution 18  
Problem Set 19 8.4 #12, 13, 19 (explain your reasoning carefully)
# 13, 14 (typo! see Mainpage), 15 on Series Handout A
Reading: 8.4 pp. 592-597 (alternating series and absolute convergence)
F Nov 8 (MWF)
or
T Nov 12 (TTh)
Solution 19 
Problem Set 20 8.4 #2, 20, 22, 31, 33(notice that this is the Taylor series for e^x)
# 17, 18 on Series Handout A
Reading: 8.4 pp. 597-8 (ratio test)
W Nov 13 (MWF)
or
T Nov 12 (TTh)
Solution 20  
Problem Set 21 8.5 #4, 12, 14, 16, 20
8.6 #11
#20 on Series Handout A
Reading: 8.5 and 8.6
F Nov 15 (MWF)
or
Th Nov 14 (TTh)
Solution 21  
Problem Set 22 8.7 #11, 23, 29, 36
#21, 22(see mainpage for minor corrections), 23 on Series Handout A
Reading: 8.7
M Nov 18 (MWF)
or
T Nov 19 (TTh)
Solution 22  
Problem Set 23 8.7 #34
8.8 #1,9
8.9 #20, 22
8.6 #6, 16
#24 on Series Handout A
Reading: 8.8 and .9
W Nov 20 (MWF)
or
T Nov 19 (TTh)
Solution 23  
Problem Set 24 8.5 #23a
8.7 #38
8.9 #23
Concept Check on p. 640 (Stewart) #3,4,10, 11a-d and the True/False Quiz # 1-7 and 11
#25 Series Handout A
Extra Credit 8.9 #25
F Nov 22 (MWF)
or
Th Nov 21 (TTh)
Solution 24  
Problem Set 25 Study for the exam.
M Nov 25 (MWF/ TTh)
 
Problem Set 26 #1, 2,3,4 on Differential Equations Handout A
Stewart 7.2 #3-6
W Nov 27 or M Dec.2 (your choice) (MWF)
or
T Nov 26 or T Dec 3 (your choice) (TTh)
Solution 26 
Problem Set 27 Enjoy Thanksgiving Break!

Problem Set 28 #6, 7, 8, 9 on Differential Equations Handout A version II (Get it by clicking here - it's different from the old one - throw the old one out.)
Stewart 7.3 #4, 10, 16, 29 and 7.5 #7
W Dec. 4 (MWF)
or
Th Dec 5 (TTh)
Solution 28  
Problem Set 29 Supplement 31.3 (p. 1014-1016) #1,2,3,5,6, 7
Stewart 7.3 #33 and 7.4 #19
Relevant reading is section 31.3 (pp. 1002-1017 in the supplement. At this point we've covered 31.1-31.4 in the differential equations chapter in the supplement.
F Dec. 6 (MWF)
or
T Dec 10 (TTh)
Solution 29  
Problem Set 30 Read the First Order Linear Diff Eqns handout under "supplements" and do problems 1,2 (with the condition that $x>0$), and 3 at the end of the handout.
Do #10, 11, 12, and 13 on< Differential Equations Handout A version II
M Dec. 9 (MWF)
or
T Dec 10 (TTh)
Solution 30 
Problem Set 31 Stewart 7.6 #1,2 plus Chapter 7 Rev. p. 559 #20 (in (d) the trajectories are closed) and 21
Do #14, 16 on Differential Equations Handout A version II
Read the supplement 31.5 (pp. 1024 - 1040) and Stewart 7.6
W Dec. 11 (MWF)
or
Th Dec 12 (TTh)
Solution 31 A more detailed solution to #16 is available in supplements
Problem Set 32 In the supplement on p. 1042-1045 do #9, 13bc, 14
Do #15, 17 on Differential Equations Handout A version II
In the supplement p. 1023 #12, 13ab (mixture review)
F Dec. 13 (MWF)
or
T Dec 17 (TTh)
Solution 32  
Problem Set 33 Do #20, 21, 22, 23, and 24 on Differential Equations Handout A version II
Read the supplement 31.6 (pp. 1045 - 1047)
M Dec. 16 (MWF)
or
T Dec 17 (TTh)
Solution 33  
Problem Set 34 In the supplement do #12 and 13 on p. 1050
Do #25, 26, 27 on Differential Equations Handout A version II
Read the supplement 31.6 (pp. 1048 - 1049)
W Dec. 18 (MWF)
or
self-correct (TTh)
Solution 34 
Problem Set 35 (1.) Use series to solve y'' = k^2y.
(2.a) Find the first three non-zero terms of a power series solution to y' = xy +y +1
(2.b) Suppose y(0) = 0. Use your answer to (a) to approximate y(0.1).
(We'll do #18, 19 on Differential Equations Handout A version II in class.)
Read the supplement 30.4 (pp.959-961) and / or Stewart 8.10
self-correct Solution 35  
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