Monthly Schedule

(AP Calculus AB, Period D)

W 12/1/04

HW due: Personal selection—use your own judgment—from the review problems on pp. 242-245. A minimum of 35 minutes’ worth is required, though of course you may wish to spend more time and effort if you hope to do well on the test. I would recommend choosing a mixture of easy problems (to warm up) and harder problems (to provide challenge and learning opportunities).

 

Th 12/2/04

Test on Chapter 4. Everybody will be taking the test today, even those of you who already have two tests scheduled. Under the rules of the test system, teachers are required to list their tests in the test book, and it is on a first-come, first-served basis. Since my test is listed ahead of all but one of the courses in which you are enrolled, any other tests will have lower priority than mine. The other teacher(s) must have forgotten to use the test book.

 

F 12/3/04

Class will be held as usual today. To (perhaps) put your mind at ease, let me say that because the test was missing any indication of the relative point values of the problems, I have decided to grade the test somewhat leniently (i.e., out of more than 100 points possible, but counting as 100). I am not making this decision because the test was too long. On the contrary: You need to develop proficiency and speed through your homework, and you need to understand that in any college course, thinking on your feet is required during exams. It is never sufficient simply to “plug and chug” homework-style problems.

There is no additional HW due. Please get a good night’s sleep!

 

M 12/6/04

HW due: Read §5.1; write §5.1 #1, 2, 12.

 

T 12/7/04

HW due: Same problems, except add Simpson’s Rule (discussed in class) as a method to perform. Feel free to use the Thingy to check your answers. Show work in tabular or formulaic style (your choice). For #12, you will need to ask yourself if you have the correct number of mesh points. Do you? (Answer in your HW paper.) If not, then use the data point of 130 sec and 38 ft/sec to help you compute your Simpson’s Rule answer. If you do have the correct number of mesh points in the problem as stated, simply proceed with the data shown in your book.

 

W 12/8/04

HW due: Read §5.2; write §5.2 #1-28 all, 41-46 all.

 

Th 12/9/04

HW due: Read §5.3 (at least through bottom of p. 270); write §5.3 #1-12 all, 17-20 all. Do at least two of problems #7-12 geometrically, i.e., without using MATH 9.

 

F 12/10/04

HW due: Finish reading §5.3; write §5.3 #25-30 in addition to the other problems previously assigned.

 

M 12/13/04

HW due: Read §5.4; finish all previously assigned problems.

 

T 12/14/04

HW due (4 parts, or do all 5 if time permits):

1. Read Braxton’s proof of FTC2 and the proof that FTC1 is equivalent to FTC2.
2. Prepare a list of questions; everything on those two handouts is fair game for the test.
3. Restate FTC1 and FTC2 in your own words.
4. Write a selection (your choice) of odd-numbered problems from §5.4 and §5.5.
5. Optional reading: HappyCal proof that Simpson’s Rule equals (2M + T)/3.

In class: Review.

 

W 12/15/04

HW due: pp. 298-299 #11, 12, 13, 14, 15-30 mo3, 31-33 all, 38, 39, 41, and the additional problem below. Important: For #13-32, use your calculator only for purposes of checking your answer. Show your work. When using FTC1, use the vertical-line notation given in class for indicating the upper and lower evaluation limits for the antiderivative.

Additional problem (easy if you know the trick—no work needed!): Find G(x) such that
G(–1.4) = 7.288 and G′(x) = f (x) = exp(cos (17x4 – 12 ln (x2 + 38 sin2 2x))) for all x Î Â.

Reminder: The notation exp means “e to the . . .” For example, exp(48x + 2) means e48x + 2.

In class: More review.

 

Th 12/16/04

Test on Chapter 5. Ben (Salmon) and Max are the only people with conflicts; both should double-check to make sure that we are clear on our alternate testing schedule. Everyone else should plan for a 40-minute test during the normal class period.

Important: Bring all second quarter HW both today and tomorrow for scanning.

You need to know the following:

 

  • FTC1 and FTC2 (statement, applications)
  • FTC2 proof (general knowledge only)
  • Accumulator function: what it represents, how to form it, how it links the differential and integral calculus
  • Proof that FTC1 Û FTC2 (complete knowledge, especially justification for each step)
  • Riemann sums: definition, applications, conversion to and from definite integrals
  • Trapezoidal Rule: derivation, applications, proof that T = (L + R)/2
  • Simpson’s Rule: statement, applications; derivation and S = (2M + T)/2 not required
  • Definite integrals: definition, conversion to and from finite sum approximations
  • Adaptive quadrature: what it is, what its purpose is
  • D Þ C Þ I (differentiability, continuity, Riemann integrability)
  • Antiderivatives: finding a general antiderivative, finding a particular antiderivative that satisfies an initial condition
  • The “u substitution procedure” given in class for finding an antiderivative
  • Average value of a function on a closed interval (p. 271: yellow box and Example 3).

 

F 12/17/04

No additional HW (because of Lessons & Carols service 12/16). However, bring all previous HW from the second quarter for scanning.

 

 

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Last updated: 17 Dec 2004