|
W 12/01/010
|
HW due: Do as many of the
review problems listed below as possible. If you do not finish them all by
today, then record your time and finish the rest for Thursday. The test will
probably be moved to Friday, and the final decision will be posted here by
Thursday morning.
p. 296 #81-90 all
p. 297 #R1abc, R3ab
p. 298 #R5abc, R6d, R7c
p. 299 #R7f, R9ab
In class: Half of the period will be review for the test. The other half will
be devoted to our guest speaker, Mr. Joe Morris of MITRE Corporation.
|
|
|
Th 12/02/010
|
HW due: Entire set of
review problems assigned previously.
In class: Review.
Warning: The solution I gave at the
very end of the period, for R5a(iii) on p. 298, was wrong! Perhaps because I
was writing near the top of the whiteboard, my hand slipped while I was
writing r(t) = t tan t = e tan t · ln t, and it came out instead as etan t · ln t, which is
of course nonsense. Everything that followed that mistake was also erroneous.
Here is the correct solution:
|
|
|
F 12/03/010
|
Test (100 pts.) on Simpson’s Rule and Chapter 6. Note: Because
of the Christmas House Tour, this test will be held in MH-102, not in our
usual testing room. We will start at 8:00 a.m., since there is no assembly
period afterward, and you can have essentially as much time as you wish.
Please also note the correction in yesterday’s calendar entry to the problem
we were working on as time ran out.
In addition to the material represented by the review problems, you need to
be thoroughly familiar with the items on the study guide below.
- Famous mathematicians (including correct
pronunciation): Euler, L’Hôpital, Riemann.
- Proofs you must be able to reproduce if asked:
− standard proof of FTC1 using MVT (pp.
216-217)
− change-of-base formula (#21 on p. 278)
− proof that 
For the third proof, you can choose either the original method (using
the definition of e on p. 272)
or the streamlined method (using L’Hôpital’s Rule).
- Theorems you are required to be able to state
correctly, including hypotheses and conclusions:
− EVT (Warning! This tripped up many
people on the last test.)
− IVT
− MVT
− FTC1 and FTC2
− CRI
− L’Hôpital’s Rule.
- All derivative and integral formulas we have
learned up to this point, including trig functions (derivatives and
antiderivatives) and inverse trig functions (derivatives only). Antiderivatives
of the inverse trig functions will not be covered until later in the
course.
- Derivatives and antiderivatives of xp (including special
case if p = −1), ln x, and ex. The antiderivative of ln x is x ln x − x + C.
- Substitution rule: qr = exp(r
ln q).
- Antidifferentiaion by “u substitution,” including showing your work if asked.
- Derivative of an inverse (green box on p. 153,
though many people, myself included, find it easier to “reason it out”
without using the formula).
- Rule of 72: derivation, statement, and
application.
- Implicit differentiation (covered in
Puzzlemania but not represented on any test yet).
|
|
|
M 12/6/010
|
HW due: Read §§7-1 and 7-2;
write §7-1 #5, 6.
|
|
|
T 12/7/010
|
HW due: Read §7-3; write
§7-2 #2.
|
|
|
W 12/8/010
|
HW due: Read §7-4; write
§7-3 #3, 4.
|
|
|
Th 12/9/010
|
HW due: Read §7-5; write
§7-4 #2, 4.
In #2, you do not need to purchase “dot paper.” Simply make a reasonable
lattice of points by using your pencil.
In #4, a photocopy is not required. Instead, practice making a rough
transcription of the diagram onto your paper. (This is a skill you will need
for tests as well.)
|
|
|
F 12/10/010
|
HW due:
1. Read §7-6; write §7-5 #1, 3, 5, §7-6 #13-15 all. (In §7-6, R = rabbit population in hundreds, and
F = fox population in hundreds.)
There is no need to make photocopies; simply practice your skill of making
quick sketches. When making tables for Euler’s method, use more columns than
your book shows. You need columns for i
(starting with 0), xi, yi, dy/dx (computed by the
given diffeq.), dy = (dy/dx) , and yi
+ 1 = yi + dy. Then copy the result from the yi + 1 column
into the yi cell on the
next row. Remember that the x value
for the next row is merely the old x
incremented by  .
2. Write a comment for each line of the following calculator program. (This
program will be distributed at the start of class; there is no need to key it
in unless you wish to have it sooner.) It is especially important for you to
document the purpose of the variables X, Y, N, and H.
PROGRAM:EULER
:ClrHome
:Disp "PROGRAM: EULER"
:Output(3,1,"WRITTEN BY E.M.")
:Output(4,1,"HANSEN, ST.")
:Output(5,1,"ALBANS SCHOOL.")
:Output(6,1,"Y1 IS ASSUMED TO")
:Output(7,1,"CONTAIN DY/DX.")
:Output(8,1," ")
:0 I
:ClrList L1,L2
:Prompt X,Y,N,H
:Lbl A
:I+1I
:Y+HY1Y
:X+HX
:XL1(I)
:YL2(I)
:If I<N
:Then
:Goto A
:End
:Disp "CHECK L1,L2"
3. If you have not already downloaded the working
version of BIGSLOPE,
do that before the start of class.
|
|
|
M 12/13/010
|
HW due: Read §8-1, §8-2,
and the green box on p. 368; write §8-2 #19, 20.
|
|
|
T 12/14/010
|
HW due: Write #1-12 all,
14, and 17 from the 2008 test on
Chapters 7 and 8, plus #T1 and T2 on p.431. If you have any remaining time,
please work a selection of review problems (your choice) from pp. 341-343.
|
|
|
W 12/15/010
|
Test on Chapter 7, Critical Points, and Points of
Inflection. This test covers,
potentially, all material from the beginning of the year through §8-2. However,
no famous mathematicians are on this test. This is a warm-up for your midterm
exam.
Solutions to #17 from the 2008 test, as well as #T1 and T2 on p. 431, were
supposed to be posted here late Tuesday evening. Unfortunately, I forgot.
(Sorry!) Luckily, there are no problems testing those exact points on the
test.
|
|
|
Th 12/16/010
|
HW due: Read §8-3; write
§8-2 #24, 25, 33, 41.
|
|
|
F 12/17/010
|
HW due: Attend Lessons and
Carols service at the Cathedral if you possibly can.
|
|