Monthly Schedule

(Honors AP Calculus, Period C)

W 9/3/08

First day of school.

 

Th 9/4/08

HW due:

1. Prepare for quiz on the lower case letters a through z (especially “quite sizzly”) and the lower case Greek letters alpha, beta, gamma, delta, epsilon, zeta, theta, mu, pi, rho, sigma, phi, chi, psi, omega, and upper case sigma. Most of these are shown here.

2. Send me an e-mail with your name as part of the body of the message, so that I can tell who sent it. Be sure to begin your subject line with __C (underscore, underscore, C) so that it cuts through the fog of e-mail clutter.

3. Read §1-1 and the HW guidelines. No written HW is due for today, but I want you to know what the requirements are for the future. Reading notes, which would normally be required whenever there is a reading assignment, are optional this time.

4. Tie up the loose end from the chalkboard: the definition of “a calculus.” It has something to do with pebbles, at least indirectly . . .

 

F 9/5/08

HW due:

1. Read §1-2 and make a few reading notes; write §1-1 #1, 2. Follow the HW guidelines.

2. The entire class will be graded on the issue of whether Michael and Percival send me their e-mail addresses. See #2 from yesterday’s assignment.

 

M 9/8/08

HW due: Read §1-3 (reading notes required, as always); write §1-2 #1-10 all. The first one is done for you as an example. Observe how the use of the word “it” is completely avoided.

1. [You must copy a sketch of the diagram. Assume that the x- and y-axis scales, though not marked, are using units with the same spacing on each axis.]

At x = a, f is increasing. The rate of increase is “slow” since | f '(x) | is only about 0.5.
At x = b, f is increasing. The rate of increase is “fast” since  | f '(x) | is much greater, perhaps 3 or 4.

 

T 9/9/08

HW due: Read §1-4; write §1-2 #15-20 (see instructions below), §1-3 #5, 6, 9.

For #15-20, do parts (a) and (b) as described in the text. Then, for part (c), make an estimate (ballpark guess based on a rough sketch, or you can use the slope of a short secant segment), and add part (d) in which you use MATH 8 to compute the answer. The first one is done for you as an example.

15. f (x) = x2 + 5x + 6
(a) quadratic
(b) f (c) = f (3) = 32 +5(3) + 6 = 30 [work optional]
(c) At x = 3, f is increasing very rapidly. Perhaps f '(3)  20. We also know
    , giving 11 as a reasonable estimate.


(d) By calc., f '(3) = 11.

 

W 9/10/08

HW due: Read §1-5; write §1-4 #9, 10, 11, 13. In #9 and #10, do the (a) part by hand (i.e., using a calculator and recording the results in a table), but use the Thingy or the even more impressive RiemannSums Applet for parts (b) and (c).

 

Th 9/11/08

HW due: Read §1-6 (no reading notes required this time); write §1-5 #15, 16, §1-6 #1.

A quiz (10 points) on recent material is also likely.

 

F 9/12/08

HW due: Read §2-2; write §2-2 #1-6 all, 8, 10, 12. You may omit the sketches for #1-6, but do show sketches for #8-12. Hint: If you are stuck, remember that good students often work an extra problem or two and use the odd-numbered answers in the back of the book to obtain hints.

 

M 9/15/08

HW due: Read §2-3; write §2-3 #7bc-15bc odd, 20. For #7-15, you may omit the (a) part. Here is an example:

8.(b) –13 by inspection


   (c)
      






Other HW (optional): Take the HappyCal Diagnostic Quiz and submit it for grading on Monday. A low score on this quiz and on tomorrow’s test might imply a need to rethink whether HappyCal is the right class for you, but I think most of you could ace the quiz without too much trouble.

In class: Review.

 

T 9/16/08

Test #1 (100 points) on all material discussed in class and all textbook contents through p. 49. The calculus is cumulative. Therefore, all tests are cumulative, and you are expected to be familiar with all important concepts and techniques learned during the entire year. The material to be emphasized will be announced before each test. Test numbers (#1, #2, etc.) do not necessarily correspond to chapter numbers in the textbook.

Warning: Tests frequently include one or more questions that are explicitly not based on examples discussed in class. The purpose is to force you to think under pressure. The more you have prepared your mind by grappling with challenging homework, even going beyond the assigned problems if necessary, the better off you will be.

 

W 9/17/08

HW due: Read §2-4; prepare §2-4 #1-20 orally, and write §2-4 #21-42 mo3.

 

Th 9/18/08

HW due: Read §2-5; write §2-4 #61, 70.

 

F 9/19/08

HW due: Read §2-6; write §2-5 #1-5 all, 8, 9.

 

M 9/22/08

HW due: Read §2-7 (very short); write §2-5 #13, §2-6 #4, 5, 6, 7, 9, 13.

 

T 9/23/08

HW due: Read §§3-2 and 3-3, including the green box after #20 in §3-2; write §3-2 #15abcde, 17abc, 19abc, and the following problem #21:

21. Prove that at any time t, there exist at least two antipodal points on the earth’s surface having the same temperature. You may assume that temperature along any path varies according to a continuous function.

22 (optional). Prove that at any time t, there exist infinitely many pairs of antipodal points having the equal-temperature property. By this we mean that each antipodal pair has equal temperature, but another antipodal pair may have a different temperature. If you have done #21 rigorously, #22 follows as an easy corollary.

 

W 9/24/08

HW due: Read the green box on p. 89 and all of §3-4; write §3-3 #4, 7, 8. For #4, you should store the function q(x) into Y1 and the function nDeriv(Y1,X,X) in Y2. Remember that nDeriv is obtained by MATH 8.

 

Th 9/25/08

HW due: Read §3-5; write §3-4 #1-18 all (setup and answer only; no work needed), 23, 24, 36. Full details are needed for #36. After you have finished #36, compare it against my version, which is posted here. One loose end that is missing from my version is a rigorous proof that power functions with positive integer exponents are continuous, but you can do that as a lemma. (Hint: Use mathematical induction on the power, with the base case satisfied by the identity function.)

 

F 9/26/08

No HW due today. (Everyone should have attended last night’s Political Roundtable event at the Cathedral.)

 

M 9/27/08

No additional HW due today, but be prepared for a quiz on derivative sketching (Friday’s material). Isaac posted this video and this video on YouTube.com for your viewing pleasure. It’s not Emmy-award material, but it’s the best we could do without our Form VI anchor students.

The next step is to try going in reverse. In other words, given a sketch of a function f, sketch a plausible function F such that F ' = f.

 

T 9/30/08

Test #2.

 

 

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Last updated: 30 Sep 2008