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Th 12/1/05
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HW due:
Modify a “cloned” version of your program so that it handles upper sums,
lower sums, left endpoint sums, right endpoint sums, midpoint sums, and the
trapezoid rule. I recommend working on a copy so that if you make a huge
mistake, you always have a good version you can go back to. Remember that 2nd
Rcl allows you to paste code from other programs into your current program. Hint: There is a shortcut you may use
for the trapezoid rule. In fact, I would encourage you to use it.
Bonus opportunity: Program the
other method of the trapezoid rule (as a check on your first method), as well
as Simpson’s Rule.
Technical note: It is difficult to
program a true upper or lower
Riemann sum, as described in the 11/30 calendar entry. I have decided, in
response to a student e-mail late this week, to accept a program that
considers as rectangle heights the maximum (resp., minimum) of the values
found at each subinterval’s endpoints. However, I need to remind you in class
that that approach is not technically correct. When the number of intervals
is large, the discrepancy between that method and a true upper or lower Riemann sum calculation will be small for all
but the most ill-behaved functions.
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F 12/2/05
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Class will meet today in Steuart 101.
No additional HW due, but today I expect everyone to have a working and
essentially bug-free Riemann sum program. For the second day in a row, there
were no visitors in Math Lab yesterday.
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M 12/5/05
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HW due:
Complete Mathcross #3 and Mathcross #4, which were distributed Friday
in class. If you really enjoy these puzzles, you can get started on Mathcross #5 (due at the end of the week).
Reading assignment: There is also
an article (not related to the calculus) that I would like you to read in
yesterday’s Washington Post Outlook
section. The main article, starting on page B1, discusses the shortage of
males in college and describes the “industrial classroom,” which seems to
favor female learning styles at the expense of male learning styles. What I
would like from you is some concrete suggestions (written down if possible,
but oral suggestions are acceptable) about how I can make our classroom more
male friendly. We have an all-male school, and we might as well take
advantage of the opportunity! Here is a
link to the article in case you do not have access to the newspaper
itself.
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T 12/6/05
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HW due: Read
§5-6; write §5-6 #3, 4, 5, 6, 30.
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W 12/7/05
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HW due:
Read §5-7 and answer the following questions.
1. Without referring to your notes, write the full, correct statement of MVT.
Then check it for accuracy.
2. Show that if the hypothesis of MVT is altered to include the phrase
“continuous on the open interval,” then the conclusion may or may not be
satisfied. In other words, provide two sketches (or two function
definitions), one of which works and one of which does not.
3. Show that if the hypothesis of MVT is altered to delete the phrase
concerning differentiability, then the conclusion may or may not be
satisfied. Again, two sketches or function definitions are required.
4. Show that if the hypothesis of MVT is altered to delete the phrase
concerning continuity altogether, then the conclusion may or may not be
satisfied. Again, two sketches or function definitions are required.
5. Show that if the conclusion of MVT is altered so that c can be claimed to exist in a closed interval, then the altered
MVT would be weaker, i.e., would have a conclusion that is less interesting.
6. Show that if the hypothesis of the MVT is altered to require only that f is a step function, then the
conclusion may or may not be satisfied. Again, two sketches or function
definitions are required.
7. In March of 1988, I drove from Northern Virginia to Kings Dominion, a
distance of about 80 miles, in an hour and 15 minutes.
(a) What does the MVT allow you to conclude about my speedometer reading,
assuming my speedometer was accurate?
(b) If I give you the additional fact that I was traveling 65 mph (the speed
limit) shortly before reaching the Kings Dominion exit, what additional
conclusion can you make?
(c) Name any theorem(s) you used in reaching your conclusion in part (b).
(d) List the conditions of the theorem(s) listed in part (c). Are all the
conditions satisfied?
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Th 12/8/05
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HW due:
Read §5-8 (the highlight of the year); write §5-7 all problems.
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F 12/9/05
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HW due: If
there is school, then you need a morale booster. Therefore, if school is
held, then there is no homework. However, if there is no school, then the
assignment for today is to read §5-9 and write §5-8 #1, 3, 7.
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M 12/12/05
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HW due: The
assignment from last Friday, namely to read §5-9 and write §5-8 #1, 3, 7.
Then, if you would really like to flatter me, you could work on some Mathcross puzzles. The newest one includes
Seinfeld and Monty Python references.
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T 12/13/05
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HW due:
Read §5-10; write §5-9 #3-36 mo3.
In class: Evaluation of Test 4 corrections.
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W 12/14/05
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HW due:
§5-10 #3-7 all, §5-11 #9, 12.
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Th 12/15/05
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Big Quiz on Chapter 5.
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F 12/16/05
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Optional HW due: Elephant’s Wheels puzzles
(prize to the winner).
Equipment and/or old HW assignments may be checked as well. If you have zeros
from previous assignments, this would be a chance to make them up.
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