Record of daily activities, Math 172, Section 502, Calculus, Fall 2005
- Monday, December 12
- The final examination was given. Solutions are available online.
- Monday, December 5
- This was the last class meeting. We reviewed for the final
examination to be given on Monday, December 12, from 8:00 to
10:00am.
- Friday, December 2
- The graded examination papers were returned. After a 10-point
curve, the average score was 75. We started reviewing for the
comprehensive final examination, which is scheduled for Monday,
December 12, from 8:00 to 10:00am.
- Wednesday, November 30
- The third examination was given. Solutions are available online.
- Tuesday, November 29
- We continued reviewing for the third examination.
- Monday, November 28
- We reviewed for the third examination, which is scheduled for
Wednesday, November 30.
- Wednesday, November 23
- No class meeting today. Have a safe Thanksgiving break.
- Tuesday, November 22
- We looked at some applications of the binomial formula,
including an excerpt from the story "Lucky Numbers" in Richard
Feynman's memoirs "Surely You're Joking,
Mr. Feynman!"
- Monday, November 21
- We worked an example of expanding a function in a binomial
series, recognizing the pattern of the general term, and estimating
the error in truncating the series.
Reminders: Homework 13a on iLrn is due today, November 21, at
11:59pm. The third examination, covering chapter 10, is
scheduled for Wednesday, November 30 (after the Thanksgiving
break).
- Friday, November 18
- We looked at Newton's binomial series (section 10.8) and
worked on Homework 13a on iLrn, which is due on Monday,
November 21, at 11:59pm.
- Wednesday, November 16
- We looked at some examples of recognizing special infinite
series (exercises 45-48 in section 10.7 on pages 633-634) and
some examples of calculating limits by using series expansions
instead of l'Hôpital's rule (exercises 38 and 39 on
page 633).
Assignment: Homework 12b on iLrn is due on Thursday,
November 17, at 11:59pm. Also you should work on the
suggested homework problems for section 10.7.
- Tuesday, November 15
- We worked some examples of finding Maclaurin series and Taylor
series, and we computed an integral to three-decimal-place accuracy
by using a series expansion of the integrand.
Assignment: Homework 12b on iLrn is due on Thursday,
November 17, at 11:59pm.
- Monday, November 14
- We discussed Maclaurin series and Taylor series
(section 10.7 in the textbook).
Assignment: Homework 12a on iLrn is due on Monday, November 14,
at 11:59pm. Homework 12b on iLrn is due on Thursday,
November 17, at 11:59pm.
- Friday, November 11
- We worked on homework 12a on iLrn, which is due on Monday,
November 14, at 11:59pm. (Homework 12b, which is not yet
available, will be due on Thursday, November 17.)
- Wednesday, November 9
- We looked at an example of finding a power series
representation of a function, and we compared the graphs of several
partial sums with the graph of the function on the interval of
convergence of the series. We also compared the integral of the
function (computed exactly via a substitution) with the integral of
a partial sum.
Assignment: Homework 11 on iLrn is due on Thursday,
November 10, at 11:59pm. Also you should work on the
suggested homework problems for Chapter 10.
- Tuesday, November 8
- We discussed power series representations of functions. In
particular, we computed that
Σn2nxn/n equals -ln(1-2x)
for x between -1/2 and 1/2, and we showed that the alternating sum
of reciprocals of odd counting numbers equals π/4.
Assignment: Homework 11 on iLrn is due on Thursday,
November 10, at 11:59pm.
- Monday, November 7
- We discussed the interval of convergence of a power series
(section 10.5).
Assignment: Homework 10 on iLrn is due on Monday, November 7,
at 11:59pm, and homework 11 is due on Thursday,
November 10, at 11:59pm.
- Friday, November 4
- We discussed the ratio test and worked on homework 10 on
iLrn, which is due on Monday,
November 7, at 11:59pm.
- Wednesday, November 2
- We discussed absolute convergence and the alternating series
test (section 10.4).
Reminder: Both parts of homework 9 on
iLrn are due on Thursday,
November 3, at 11:59pm.
- Tuesday, November 1
- We discussed the limit comparison test and worked on some
exercises from section 10.3 on convergence of infinite
series.
- Monday, October 31
- We discussed the comparison test and the integral test for
infinite series.
Assignment: Both parts of homework 9 on
iLrn are due on Thursday,
November 3, at 11:59pm.
- Friday, October 28
- The graded examination papers were returned. The median score
was 66. One student made a score of 100: good job! We
worked on an exercise about convergence of
infinite series, partly by hand and partly using Maple.
- Wednesday, October 26
- The second examination was given. Solutions are available online.
- Tuesday, October 25
- We reviewed for tomorrow's examination, which is based on the
following sections in the textbook: 8.8 (approximate integration),
8.9 (improper integrals), 9.1 (separable differential equations),
9.2 (first-order linear differential equations), 9.3 (arc length),
9.4 (surface area), 9.6 (hydrostatic pressure and force), 10.1
(sequences), and 10.2 (series).
- Monday, October 24
- We looked at an example (exercise 24 on page 604 in
section 10.3) of estimating the sum of an infinite series by
comparing the tail of the series with an improper integral.
Reminders: Homework 8 on iLrn is due today, October 24, at
11:59pm. The second examination is scheduled for Wednesday,
October 26.
- Friday, October 21
- We worked on the first part of online homework 8 (about
infinite series).
Assignment: Both parts of homework 8 on
iLrn are due on Monday,
October 24, at 11:59pm.
- Wednesday, October 19
- We discussed geometric series (section 10.2).
Reminders: The second examination is scheduled for
Wednesday, October 26. Homework 7 on iLrn is due Thursday, October 20,
at 11:59pm.
- Tuesday, October 18
- We continued the discussion of sequences (section 10.1).
We talked about the limit laws for convergent sequences, the
squeeze theorem, and the monotonic sequence theorem.
Assignment: Homework 7 on iLrn is due Thursday, October 20,
at 11:59pm.
- Monday, October 17
- We started a new topic: sequences and series (Chapter 10).
We looked at some examples of sequences and limits of
sequences.
- Friday, October 14
- We worked on areas of surfaces of revolution (exercises 2
and 8 on page 553 of section 9.4 in the textbook),
partly by hand and partly with Maple.
Assignment: It is a good exercise to work out the
integrals by hand (and check your answers with Maple or with a
calculator). Also you should look at the
suggested homework problems for section 9.4 (but don't
worry about exercise 17 on page 553, since we skipped
Simpson's rule).
- Wednesday, October 12
- We looked at some of the homework problems on iLrn that are due tomorrow, Thursday,
October 13 at 11:59pm.
- Tuesday, October 11
- We discussed hydrostatic pressure and force (section 9.6
in the textbook).
Assignment: Homework 6 on iLrn is due Thursday, October 13 at
11:59pm.
- Monday, October 10
- We discussed the computation of arc length (section 9.3 in
the textbook).
Assignment: Homework 6 on iLrn is due Thursday, October 13 at
11:59pm.
- Friday, October 7
- We worked on an exercise about
approximate integration, partly by hand and partly using
Maple.
- Wednesday, October 5
- We looked at a solution of exercise 74 on page 518 in
section 8.9 about improper integrals, and we discussed the
method of integrating factors for solving first-order linear
differential equations (section 9.2).
Assignment: Homework 5 on iLrn is due tomorrow, Thursday,
October 6, at 11:59pm.
- Tuesday, October 4
- We worked examples of solving differential equations by the
method of separation of variables (section 9.1 in the
textbook).
Assignment: Both parts of the fifth online
homework are available on iLrn.
The assignment is due on Thursday, October 6, at 11:59pm.
- Monday, October 3
- We discussed the approximation of definite integrals
(section 8.8 in the textbook) by the left-hand-endpoint rule,
the right-hand-endpoint rule, the trapezoidal rule, and the
midpoint rule. We did an example of applying the error estimate for
the midpoint rule.
Assignment: The first part of the fifth online
homework is available on iLrn.
The assignment is due on Thursday, October 6, at 11:59pm.
- Friday, September 30
- The graded examination papers were returned. The average score
was 66. Two students made a score of 100: good job! We
discussed the notion of improper integrals (section 8.9 in the
textbook).
Assignment: Try the
suggested homework problems for section 8.9. I will send
an email announcement when the next online homework is
available.
- Wednesday, September 28
- The first examination was given. Solutions are available online.
- Tuesday, September 27
- We reviewed for the first examination to be given on Wednesday,
September 28.
- Monday, September 26
- We discussed the method of partial fractions (section 8.4
in the textbook).
Reminders: The fourth homework on iLrn is due tonight, September 26,
at 11:59pm. The first examination is Wednesday, September 28,
in class.
- Friday, September 23
- President Gates cancelled classes for Friday, September 23
because of Hurricane Rita.
- Wednesday, September 21
- We worked examples of integration via trigonometric
substitution (exercises 2 and 6 on page 476 in
section 8.3).
Assignment: The fourth online homework on iLrn is due on Sunday,
September 25 Monday, September 26 at
11:59pm. Note that iLrn technical support is available on Sunday
from 4:00pm to midnight at the toll-free telephone number (866)
267-4984. Also there is a Math 152/172 help session on Sundays from
7:30pm to 9:30pm in Blocker 165.
- Tuesday, September 20
- We worked examples of integrating products of powers of
trigonometric functions (section 8.2). The techniques come
into play in the integration of rational functions (the topic of
section 8.4).
Assignment: Work on the
suggested homework problems for sections 8.1 and 8.2.
- Monday, September 19
- We worked exercise 13 on page 451 in section 7.5
about average value, and we discussed the method of integration by
parts (section 8.1).
Assignment: The third online homework assignment
on iLrn is due today,
September 19, at 10:00pm. You should also work on the
suggested homework problems for section 8.1.
- Friday, September 16
- We worked on two problems about the work required to pump water
out of a tank (exercises 17 and 19 on page 449 in
section 7.4).
Assignment: The third online homework assignment
on iLrn is due on Monday,
September 19 at 10:00pm.
- Wednesday, September 14
- We discussed the notion of average value of a function and the
mean-value theorem for integrals (section 7.5). Also we did an
example of computing the work required to pump water out of a tank
(exercise 16 on page 448 in section 7.4).
Assignment: An online homework will be
forthcoming; watch for an announcement. Meanwhile, work on the
suggested homework problems for sections 7.4 and 7.5.
- Tuesday, September 13
- We looked at another example of volumes using the shell method
(exercise 29 on page 444 in section 7.3), and we did
some examples of problems involving the computation of work
(exercises 2 and 10 on page 448 in
section 7.4).
Assignment: Because of technical problems at
iLrn last night, the due date
for the second online homework assignment is extended to 10:00pm
tonight, September 13.
- Monday, September 12
- We discussed computation of volumes of revolution by the method
of shells, illustrated by exercises 1, 18, and 28 on
page 444 in section 7.3.
Assignment: Complete the second online homework
assignment on iLrn, which is due
today by 10:00pm. Then work on the
suggested homework problems for section 7.3.
- Friday, September 9
- We looked at solutions of exercise 50 on page 439
(section 7.2) about the volume of a frustum of a cone, both by
integrating using the disc method and by using similar triangles
and the formula for the volume of a cone (see the geometry formulas
inside the front cover of the textbook). Then we worked on the
even-numbered problems 8-48 on page 407 (section 6.5)
about integration via substitution, using Maple to check and get
hints. For example, the Maple command
int(x*sqrt(1+x2),x); produces an
anti-derivative of the function
x√(1+x2). The Maple command
with(Student[Calculus1]): followed by the command
IntTutor(); starts the integration tutor, which can give
hints and solve integration problems step-by-step.
Assignment: The second online homework assignment
on iLrn is due Monday,
September 12, by 10:00pm. You should also do some more
practice on integration by substitution.
- Wednesday, September 7
- We worked in groups on exercises 13-24 on page 438 in
section 7.2 about volumes of revolution.
Assignment: You now have all the tools to do the
second online homework assignment on iLrn. The assignment is due Monday,
September 12, by 10:00pm. You should also try the
suggested homework problems for section 7.2.
- Tuesday, September 6
- We looked at examples of computing volume by the method of
integrating the area of a cross section.
Assignment: Read section 7.2. The first
online homework assignment is due Wednesday, September 7, by
10:00pm. The second online homework assignment is due Monday,
September 12, by 10:00pm.
- Monday, September 5
- We looked at an example of combining the fundamental theorem of
calculus with the chain rule, discussed the idea behind the
inflection-point problem in the first online homework, and did some
examples of computing areas between curves.
Assignment: Read section 7.1 in the textbook
about areas between curves. Work on the first online homework on
iLrn. If you have finished that,
try the
suggested homework problems for section 7.1.
- Friday, September 2
- We started with an example of the method of substitution for
computing definite integrals and the statement of both parts of the
fundamental theorem of calculus. Then we logged in to the
computers, opened Maple, and worked on getting Maple to do the
following three computations.
- ∫01 √(1+x2)dx
(Maple syntax: int(sqrt(1+x^2),x=0..1);)
- √2 to 100 decimal places
(Maple syntax: evalf[100](sqrt(2));)
- plot the function x sin(x) e-x on the interval
[0,2π]
(Maple syntax: plot(x*sin(x)*exp(-x), x=0..2*Pi);)
A further exercise is to find the first positive x for which
the graph of y=x intersects the graph of y=tan(x). (Some things to
try are the plot command
plot({x,tan(x)},x=0..6,y=-5..5); and the
fsolve command with an interval for x read off from
the plot.)
Assignment: Work on the first online homework on
iLrn.
- Wednesday, August 31
- We looked at solutions of problems 34 and 35 on
page 387 at the end of section 6.3. Then we discussed one
half of the fundamental theorem of calculus and the method of
substitution.
Assignment: Read sections 6.4 and 6.5 and
watch for an email announcing the first online homework using
iLrn.
- Tuesday, August 30
- We looked at a solution of problem 40 on page 369
about the sum of cubes of integers. Then we looked at the
definition of the area under a curve (equivalently, the integral of
a positive function) as a limit of sums of areas of rectangles
(Riemann sums).
Assignment: Read section 6.3 and do problems
29-35 on page 387 at the end of section 6.3.
- Monday, August 29
- We started with some warm-up exercises on the chain rule for
derivatives. If you are shaky on this, review section 3.5 in
the textbook. If you need to review trigonometric functions, see
Appendix D in the textbook; the derivatives of trigonometric
functions are covered in section 3.4. Also we did some warm-up
exercises on summation notation. Then we looked at the fundamental
idea behind integration: namely, approximating the area under a
curve by sums of areas of rectangles.
Assignment: Read sections 6.1 and 6.2 in the
textbook and work on exercise 40 on page 369 at the end
of section 6.1 (not to hand in).