Record of daily activities,
Math 152, Engineering Mathematics II, Honors
Sections 819820, Fall 2002
 Monday, September 2
 We looked at some motivating examples for studying
calculus (the birdcage problem, understanding
rainbows); we quickly reviewed the fundamental theorem
of calculus stating that differentiation and
integration are inverse operations; we observed that
the method of integration by substitution is just the
fundamental theorem combined with the chain rule for
differentiation.
Homework for Wednesday: Do as many of the oddnumbered review
problems (oddnumbered problems have answers in the
back of the textbook) for Chapter 6 on pages 416418 as
you need to do to be confident that you would get them
right on a quiz. If there are problems that you are
puzzled about or that you don't know how to do, ask
about them in class on Wednesday or in recitation on
Thursday.
 Wednesday, September 4
 We discussed some of the problems in the Review
section at the end of Chapter 6, pages 416418.
Homework for Friday: Read section 7.1
and work the Suggested
Homework problems for section 7.1 that are posted
at the main
Math 152 web site.
 Friday, September 6
 We discussed some illustrative examples of
integration: in particular, how to compute the volume
of the Great
Pyramid of Cheops.
Homework for Monday: Read section 7.2
and work the Suggested
Homework problems for section 7.2 that are posted
at the main
Math 152 web site.
 Monday, September 9
 We discussed various methods for finding the volume
of a truncated pyramid. The formula for the volume can
be interpreted as onethird the height times the sum of
the following
three quantities: the area of the base, the area of the
top, and the geometric mean of those two areas. The
same formula holds (by essentially the same
calculation) for a truncated cone whose base has an
arbitrary shape.
Homework for Wednesday: Read section
7.3 and work the Suggested
Homework problems for section 7.3 that are posted
at the main
Math 152 web site.
 Wednesday, September 11

We worked on various volume problems: number 18 on page
438 (both by washers and by shells); the donut (number
63 on page 439) both by washers and by shells; the
birdcage (number 64 on page 439); and the napkin ring
(number 42 on page 445).
Homework for Friday: In Problems Plus,
pages 454457, do numbers 1, 13, 15, and 18.
 Friday, September 13

We discussed the homework problems.
Homework for Monday: In Problems Plus,
pages 454457, do numbers 3, 7, 19, and 25.
 Monday, September 16
 We discussed the method of integration by parts,
including as examples problems 1, 18, and 44 on page
463 in section 8.1.
Homework for Wednesday: Read section 8.1
and work the Suggested
Homework problems for section 8.1 that
are posted
at the main
Math 152 web site.
 Wednesday, September 18
 We looked at problem 23 on page 456 (in Problems
Plus for Chapter 7) from the point of view of
average value and integration by parts.
Homework: Before recitation on Thursday,
work the Suggested
Homework problems for section 7.5 that are posted
at the main
Math 152 web site. Before class on Friday, read
section 7.4.
 Friday, September 20
 I attended a conference
in Princeton, so Professor
Fulling
substituted and covered section 7.4.
Homework for Monday: Work the Suggested
Homework problems for section 7.4 that are posted
at the main
Math 152 web site.
 Monday, September 23

We discussed integrating rational functions by
the method of partial fractions.
Homework for Wednesday: Read
section 8.4 and work problems 17, 19, 21, and 23
on page 485.
 Wednesday, September 25
 We continued the discussion of integrating rational functions by
the method of partial fractions, with an aside on the
fundamental theorem of algebra.
Homework for Friday: Read
sections 8.2 and 8.3 and work problems 1, 3,
and 5 on page 470 (section 8.2) and problems 3, 7,
and 9 on page 476 (section 8.3).
 Friday, September 27
 The integration of rational functions led us to the
problems of integration via trigonometric substitution
and integration of powers and products of trigonometric
functions.
Homework for Monday: Finish the
Suggested
Homework problems for sections 8.2 and 8.3
that are posted
at the main
Math 152 web site.
 Monday, September 30
 We discussed methods for numerical approximation of
integrals, including the midpoint rule, the trapezoidal
rule, and Simpson's rule. We also saw how integrating
the linear approximation formula leads to an error
bound for the midpoint rule.
Homework for Wednesday: Read
section 8.8 and work problems 1, 5, 29,
and 31 on pages 507508.
 Wednesday, October 2

We did some review problems in preparation for the
upcoming examination on Wednesday, October 9, on
Chapters 6, 7, and 8.
Homework for Friday: Read
section 8.9 about improper integrals.
 Friday, October 4

In preparation for the upcoming examination on Wednesday, October 9, on
Chapters 6, 7, and 8, we looked at two sample problems.
 Monday, October 7
 We further discussed improper integrals.
Reminder:
The first examination is Wednesday, October 9, at
the usual meeting time in the usual room.
 Wednesday, October 9
 First examination
 Friday, October 11
 We discussed firstorder linear ordinary
differential equations.
Homework for Monday: Read
section 9.2 and do problems 5, 9, 15, 17, 25,
and 33 on pages 540541.
 Monday, October 14
 Some discussion of the normal distribution
accompanied the return of the graded examinations.
Also we continued the discussion of firstorder
differential equations, including an example of a
Bernoulli equation.
Homework for Wednesday: Read sections
9.1 and 9.3. Do problems 3, 5, 9, 17, and 35 on pages
533535 in section 9.1, and problems 1 and 6
on page 573 in Problems Plus.
 Wednesday, October 16
 We discussed some homework problems (the logistic
equation, slicing pizzas into equalarea portions, a
sneaky substitution for integrating 1/(x^7x)) and the
length of curves.
Homework for Friday: Read
section 9.4. In section 9.3, pages 546547,
do problems 3, 5, 7, 9, and 27. In Problems Plus,
page 573, do problems 9 and 12.
 Friday, October 18

We looked at examples of arc lengths and surface
areas, including Gabriel's Horn.
Homework for Monday: Read sections 9.5
and 9.6. Do problems 1, 9, 11, 19, 23, and 27 on
page 553 in section 9.4.
 Monday, October 21
 We looked at some problems from sections 9.5 and 9.6
in the textbook (centroids and hydrostatic force).
Homework for Wednesday: Do the Suggested
Homework problems for sections 9.5 and 9.6 that are
posted at the main
Math 152 web site.
 Wednesday, October 23
 We discussed the notion of an infinite sequence and
some examples of convergent sequences.
Homework for Friday: Read sections
10.1 and 10.2 and do problems 15, 19, 21, 23, 31,
43, 45, and 47 on page 585 in
section 10.1.
 Friday, October 25
 After discussing the arithmeticgeometric
mean (see also problem 47 on page 585 in
section 10.1 in the textbook), we looked at some
examples of infinite series, in particular the
geometric series.
Homework for Monday: Do problems 11,
13, 19, 21, 27, 33, 43, 47, 53, and 55 on pages
593595 in section 10.2.
 Monday, October 28
 We discussed the Cantor set (see problem 53 on
page 594 in section 10.2 of the textbook)
from the point of view of geometric series, and we
looked at approximating the sum of the series
1/n(ln(n)^2) by integrals (see problem 28 on
page 604 in section 10.3 of the textbook).
Homework for Wednesday: Read
section 10.3. Do problems 1, 3, 5, 7, 9, 11,
and 31 on pages 603604 in section 10.3,
and problem 5 on page 649 in Problems Plus (about
the snowflake curve).
 Wednesday, October 30
 We discussed comparison tests for
convergence/divergence of infinite series, including
(not in the textbook) the Cauchy condensation test for
series with positive, decreasing terms.
Homework for Friday: Do problems 13,
15, 17, 19, 21, 23, and 29 on page 604 in
section 10.3 and problem 6 on page 649
in Problems Plus (about summing the series whose terms
are the reciprocals of the positive integers whose only
prime factors are 2 and 3).
 Friday, November 1
 We discussed the ratio test and
the alternating series test (material in
section 10.4 of the textbook).
Homework for Monday: Read
section 10.4. Do problems
5, 7, 9, 11, 19, 21, 29, 31, and 33 on pages 611612 in
section 10.4
and problem 4 in Problems Plus on page 648.
 Monday, November 4
 We discussed finding the radius of convergence of a
power series by using the ratio test and the (not in
the book) root test.
Homework for Wednesday: Read
section 10.5. Do problems 3, 5, 7, 9, 19, 23,
and 25 on page 617 in section 10.5 and
problems 9 and 15 on pages 650651 in Problems
Plus.
 Wednesday, November 6
 We discussed differentiation and integration of
power series.
Homework for Friday: Read
section 10.6 and do problems 1, 5, 7, 11, 13, 19,
25, 29, and 31 on pages 622623.
 Friday, November 8
 We discussed polynomial approximations to functions
and error estimates for the approximations.
Homework for Monday: Read
section 10.7. Know the boxed formulas on
page 630. Do problems 3, 9, 19, 33, 39, 41,
and 45 on page 633 in section 10.7.
 Monday, November 11
 We continued the discussion of how to obtain power
series expansions of functions.
Homework for Wednesday: Read
section 10.8. On page 570 in the
Chapter 9 review problems, do the oddnumbered
problems 111.
 Wednesday, November 13
 We discussed Pascal's triangle and the binomial
expansion.
Homework for Friday: Do problems 3, 5,
9, 11, and 13 on pages 636637 in
section 10.8 and the oddnumbered problems 123 on
page 646 in the Chapter 10 review.
 Friday, November 15
 We discussed applications of power series and
remainder estimates in the context of the story "Lucky
Numbers" from Richard Feynman's memoirs "Surely
You're Joking, Mr. Feynman!"
Homework for Monday: Do problems 19,
23, 25, and 27 on pages 644645 in
section 10.9
and problems 15, 19, 21, 25, and 27 on pages
570571 in the Chapter 9 Review.
 Monday, November 18
 We discussed some problems about surface area and
looked at two
sample problems for the
second examination to take place on Friday, November 22.
The homework is to continue reviewing
for the examination.
 Wednesday, November 20
 We discussed
solutions to the sample
problems for the second examination.
The homework is to prepare for the
examination to be given Friday.
 Friday, November 22
 Second examination
 Monday, November 25
 We discussed the second
examination and began talking about
threedimensional geometry.
 Wednesday, November 27
 No class meeting. Enjoy the Thanksgiving holiday!
 Monday, December 2
 We discussed threedimensional coordinate systems.
Homework for Wednesday: Read sections
11.1 and 11.2 and do the Suggested
Homework problems for section 11.1 that are posted
at the main
Math 152 web site.
 Wednesday, December 4
 We discussed product operations on
threedimensional vectors: the scalar (dot) product and
the vector (cross) product.
By popular demand, the due date for the project is
pushed back to Tuesday, December 10, the last day
of classes for the semester. (Note,
however, that the university has used the HumptyDumpty
principle to redefine that day to
be a Thursday.)
Homework for Friday: Read
section 11.3 and do the Suggested
Homework problems for section 11.2 that are posted
at the main
Math 152 web site.
 Friday, December 6
 We discussed the analytic description of planes in
space.
Homework for Monday: Do problems 13,
15, 19, 23, 29, 31, and 37 in section 11.4
(page 681) and problems 111 (odd numbers) and
1925 (odd numbers) in section 11.3
(page 673).
 Monday, December 9
 We filled out the course evaluation forms and
continued the discussion of lines and planes in
threedimensional space.
Special office hours for final exam period:
1:003:00 on Friday, December 13 and Monday,
December 16 in Milner 202.