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W 9/6/06
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First
day of class.
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Th 9/7/06
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Quiz (10 pts.) on the alphabet.
Double HW due (4 pts. each):
1. Send me an e-mail stating what you hope to achieve from the course (1 or 2
sentences). Remember to begin your subject line with a double underscore and
to sign your name at the end of your e-mail. I will ignore any e-mail that is
missing the proper subject or that is unsigned. Important: If you have
more than one e-mail address, send your message from the location that you
check most frequently.
2. Read §1.1. Brief reading notes are required. Read the HW
guidelines to earn full credit.
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F 9/8/06
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HW due: Write §1.1 QR 1-9 odd, Exercises 1-39 odd. After
you have finished, check all answers against the back of the book and write corrections
in the right margin of your paper. Remember, you should be keeping the
right-hand column open as you write out your work.
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M 9/11/06
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HW due: Read §1.2; write §1.2 #1-7 all; also repeat §1.1
#39, this time writing down the r
and r2 values after
making sure that your calculator is set up with “DiagnosticOn.” In case you
have forgotten how to do this, here are the steps:
1. Press 2nd Quit and/or CLR so that you are in what I call the “full-screen
immediate mode” of your calculator. In other words, you should get to a
situation where the screen is entirely blank except for a flashing cursor in
the upper left corner.
2. Press 2nd CATALOG. Note that the “A” (alpha) indicator lights up.
3. Press the letter D, which is a shortcut to skip you to the first command
that starts with the letter D. There is no need to press ALPHA first, since
you are already in the alphabetic mode.
4. Use your down arrow to scroll down to the DiagnosticOn choice.
5. Press ENTER twice. Your calculator should display the message, “Done.”
From now on, every time you perform a linear regression, the calculator will
display the r and r2 values. As you probably
remember from PreCal, r is the
“linear correlation coefficient,” a number between –1 and 1 that measures the
strength of the linear correlation between x and y. If r = 1, we know that there is a perfect
straight-line relationship. If r =
–1, we know that there is a perfect straight-line relationship but with
negative association (i.e., as x
increases, y decreases). If r = 0, there is no correlation between
x and y, which is another way of saying either (a) that different x values produce a random scattering
of y values, with no trend visible,
or (b) that there may be a trend, but it is not linear.
Reminder: Be sure to state your r and r2 values when you redo §1.1 #39.
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T 9/12/06
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HW due: Sketch a velocity function, labeling the axes with
letters and units. Then use the “counting squares” technique to estimate the total
distance covered over a closed interval. Show your work, and write a sentence
or two to describe what you did.
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W 9/13/06
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HW due: §1.2 #37-50 all, 64a, 66a. Note: For #64a, power regression is STAT CALC A.
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Th 9/14/06
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HW due: §1.2 #66 all parts, plus the additional exercise
described below. Since this does not require a full 35 minutes, please use
any additional time to get fully caught up with HW.
Additional exercise related to #66:
After you have found the locus of Q that minimizes the cost, change the
problem slightly. Make the cost across the river be $150 per foot instead of
$180. Then try several other choices for the cost across the river. At what
value of the per-foot cost does it become a rational decision to go directly
across the river (i.e., to make point Q coincide with P) to minimize cost? At
what value of the per-foot cost should we decide to skip the land segment
altogether (i.e., to make point Q coincide with Dayton)?
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F 9/15/06
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Important Bulletin: Class will meet today in Steuart 201. That is the
room immediately above the room where we have been meeting.
HW due: Read §1.3 and prepare yesterday’s assignment for collection. Also
write out the following: §1.2 #35, 64bcd (64a was previously assigned), §1.3
#1-6.
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M 9/18/06
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Bulletin: We are back to our regular classroom (Steuart 101).
Señor Muñoz’s clock is simply too loud, and our partition has been repaired.
HW due: Read about the Rule of 72. Then write §1.3 #23-29 all
(review of Precal), solving each problem 2 ways:
(a) by using the techniques of §1.3 (i.e., the techniques of Precal), and
(b) by applying the Rule of 72 to make
a reasonable estimate.
I will also be collecting problem the modified problem 66 (i.e., last
Wednesday’s HW) one more time. If you are happy with your submission last
Friday, and several papers were quite good, you need not resubmit it. If you
would like to improve your grade, you may submit a new paper today and I will
average it with last Friday’s submission.
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T 9/19/06
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HW due:
1. By means of a careful sketch (graph paper recommended but not required),
show that the derivative of the function y
= –cos 2x appears to be 2 sin 2x.
2.(a) Graph the absolute value function y
= |x|, either by hand or by using
your calculator and carefully transferring the sketch to your paper.
(b) Sketch the function f
(x) = x2(sgn x)/2.
Could f ¢ be the same function as the function y in part (a)? Why or why not? [Note: sgn x means the signum function, namely –1 if x < 0, 0 if x = 0,
and 1 if x > 0.]
(c) Now sketch y ¢.
(d) Does y ¢ have a name? Explain your answer.
3. Do #38 on p. 25. There is not much work to show, but be sure to explain
your results clearly. I may randomly choose a few to read.
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W 9/20/06
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Test
on §§1.1 through 1.3 and Class Discussion. This test has a few problems that are similar to problems seen on Monday’s HappyCal test.
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Th 9/21/06
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HW due: Correct yesterday’s
test to 100%. You may work in groups if you wish, but if you are called
upon to answer, you need to provide an explanation, not just the answer. This
is true even for the multiple-choice questions. Therefore, it is in your best
interest to learn from your classmates, not simply to parrot their answers.
Important: Save a tree! Try
working from the on-screen copy of the test if you can. (Obviously, if you
need to work while waiting for a ride after sports, or something like that,
you will need to make a printout for reference. Please use common sense.)
Write all answers, even the free-response answers, on regular HW paper
(3-hole punched). Answers written on a copy of the test will not qualify for
full credit.
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F 9/22/06
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HW due:
1. Read §1.4, including working through explorations 1, 2, and 3 with your
graphing calculator. If you do not remember how to plot parametric functions
(hint: use the MODE key), please see me or consult your calculator manual.
Answer the questions posed in the explorations.
2. If you did not turn in your Wednesday test
answers yesterday, I will accept them today for partial credit. Because this
is such an important assignment, I have decided to count it much more heavily
than a normal HW assignment. Don’t accept a zero on this assignment. If you
would like to amend an earlier submission, that is also OK. You may work with
friends, but make sure that you really learn what is going on. Write all
answers on 3-hole punched notebook paper.
In class: Oral Quiz (graded) on
your HW test corrections.
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M 9/25/06
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HW due: Read §1.5; write §1-4 #1-4 all (state viewing
window in format
[__, __] ´ [__, __]
and parameter interval in format
[__, __] with step size indicated), 27-32 all, 40.
Explanation of notation: If you are
not familiar with the “cross” notation, here is what it means. It is a
convenient way of summarizing a viewing window, shown as “domain cross
range.” For example, instead of writing xmin
= 7, xmax = 9, ymin = 3.5, ymax = 4.5, I can simply
write
[7, 9] ´ [3.5, 4.5]
and all mathematicians will know what is meant. We pronounce this as follows:
“The interval [7, 9] cross (or ‘crossed with’) the interval [3.5, 4.5].”
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T 9/26/06
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Please spread the word: Starting today, and continuing until the end of the
year, we will meet in LS-G5, a geology/chemistry classroom on the ground
floor of the Lower School. This is a well-equipped modern classroom that
should be a significant improvement over Steuart 101.
HW due: Read §1.6; write §1.5 #2-24 even, 41, 42. In #14-24, “verify”
means to show the work clearly. Follow the example below. Be sure to state
the original function and to identify which is the original and which is the
inverse. Show every step, just as in this example!
13. f (x) = 2x + 3
In f, y = 2x + 3.
In f –1,
x = 2y + 3 Þ y = (x – 3)/2.
\ f –1(x) = (x – 3)/2.
Check 1: f
(f –1(x)) = f ((x – 3)/2) = 2(x – 3)/2 + 3 = (x – 3) + 3 = x, Q.E.D.
Check 2: f –1(f (x))
= f –1(2x + 3) = ((2x + 3) – 3)/2 = 2x/2 = x, Q.E.D.
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W 9/27/06
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HW due: (1) Patch up all previously assigned HW. (2) Get
adequate sleep.
In class: “Quizlet” (or propose a
better name) on the course up to this point. Grade will be based on how well
you learn or, if you already know just about everything, on how well you help
your fellow students learn. While you are working on your quizlet, I will
spot-check your HW binder, so be sure to bring it to class.
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Th 9/28/06
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HW due: §1.6 #21-32 all, 34.
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F 9/29/06
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HW due: Read §2.1; write §2.1 #31, 32.
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