Monthly Schedule

(Honors AP Calculus, Period A)

Th 11/1/012

HW due: Prepare for our review day. Bring a list of your unsolved (or at least, challenging but unchecked) problems from the previously assigned problems. You need to be prepared, so that when you are called upon, you can instantly point us to a section number and problem number, and you can justify concisely exactly what it is about the problem that makes it challenging. By the way, your justification must be connected to the technical obstacles, not to how you feel about the problem. “This problem frightens me” may be a truthful explanation, but if you use it, you must still be prepared to explain precisely what it is about the instructions, the content, or the solution that you found frightening. Vagueness = failure.

In class: Review, review, review.

 

F 11/2/012

Big Quiz (30 minutes, 60 points) on all material from the year to date. You are responsible for all terminology and notation presented in the book and/or discussed in class, all textbook material and assigned exercises through the end of §5-10), the fractals video, and the additional in-class discussions of famous mathematicians and their contributions.

 

M 11/5/012

HW due (optional, but you should really try to do it): Please re-do #2 from last Friday’s Big Quiz. There was an unfortunate typo in the original version.

 

T 11/6/012

HW due: Be prepared for a possible quiz over the same material as last Friday’s quiz.

In class: Monte Carlo simulations.

 

W 11/7/012

(The day after Election Day.) No additional HW is due today, so that you have the option of watching the election returns if you wish.

 

Th 11/8/012

HW due: Sleep!

 

F 11/9/012

No school (teacher workday).

 

M 11/12/012

HW due:

1. Use Newton’s Method, and the tabular recording style demonstrated in class, to find a root of each of the following functions. Answers should be correct to at least 3 decimal places after the decimal point. If the method is ill-behaved, be sure to say so. Use a “sensible” starting value for x0 in each case. For example, since part (a) is attempting to find the cube root of 6, you know that the answer must be between 1 and 2; therefore, 1.5 is a sensible starting value.

   (a) y = f (x) = x3 – 6
   (b) y = f (x) = cos(3x) + 11x2/3 – 12
   (c) y = f (x) = cos(3x) + 11x2/3 – 1
   (d) Repeat part (a), except this time use a starting value of –1.5.

2. Use Simpson’s Rule,


to estimate each of the following definite integrals. Use 8 subintervals (i.e., 9 mesh points) in each case. Use the tabular recording style demonstrated in class to show your intermediate work.

   (a)

   (b)

3. Use FTC1 to find the exact value of each integral in #2.

4. Demonstrate that for the integrals in #2, Simpson’s rule with 8 subintervals is more accurate than either the midpoint rule (using 4 subintervals) or the trapezoid rule (using 4 subintervals). Use the tabular recording style demonstrated in class to show your intermediate work.

5. Prove, algebraically, that the midpoint rule (using n subintervals) and the trapezoid rule (using n subintervals) can be combined in a weighted average,



in order to achieve the Simpson’s Rule formula.

6. Show that the result of #5 holds for the integrals you estimated. In other words, show that for both (a) and (b), the weighted average formula given in #5 gives the same results that you obtained in #2.

7. Explain why FTC1 fails for .

8. Do any of the following work for the integral in #7: midpoint rule, trapezoid rule, Simpson’s Rule, Riemann sum? Explain.

 

T 11/13/012

HW due: Read §5-11; write §5-11 #1, 2, 12.

 

W 11/14/012

HW due: Read §6-3; write (on pp. 241-245) #R1abc, R2abc, R3abcd, R4ab, R6abde, R7, R11c, C5abcde. For #C5e, you can record the fact on your HW sheet. (You don’t need to have a separate journal.)

 

Th 11/15/012

HW due:

1. Finish yesterday’s assignment if you have not already done so.

2. Write §6-3 #1-50 (mo2  mo3). These should all go very quickly. If not, you are doing something wrong. Omit the problems that are neither a multiple of 2 nor a multiple of 3 (i.e., #1, 5, 7, 11, 13, 17, 19, 23, 25, 29, 31, 35, 37, 41, 43, 47, 49).

 

F 11/16/012

HW due: Read §§6-5 and 6-6. Reading notes are required, as always.

 

M 11/19/012

HW due: Be prepared for an open-notes quiz on the Simpson’s Paradox video. You may watch the video as many times as you wish.

In class: Guest speaker, Mr. Joe Morris ’62, MITRE Corporation.

 

T 11/20/012

No additional written HW due. Re-scans of previously assigned problems, especially those that have been covered in class, are possible.

 

W 11/21/012

Thanksgiving break begins.

 

M 11/26/012

HW due: Sleep and recharge your internal batteries.

 

T 11/27/012

HW due: Read §6-8; write §6-5 #3-18 mo3, 24, 27-33 odd, §6-6 #19, 20, 21, §6-8 #11, 22.

 

W 11/28/012

HW due: Write §6-8 #6-30 mo3, 35, 36.

 

Th 11/29/012

Test (100 pts.), cumulative. You need to know, for example, who Newton, Leibniz, Mandelbrot, Gödel, Cantor, and Riemann were. You need to know the statements (including hypotheses) for EVT, IVT, MVT, FTC1, and FTC2. You need to memorize the green boxes on pp. 142 and 150. You need to know the definitions in the green boxes on pp. 196-198. You need to know the 3-part definition of continuity (limit exists, function value exists, and they equal each other) and the proof on p. 154 that diff.  cont. This is not a comprehensive list by any means.

If you have been paying attention in class, you should not have to study a great deal except to refresh your memory. Questions will be similar to those found at the ends of Chapters 3, 4, 5, and 6. You can solve “R” problems, “T” problems, or a mixture. “C”-type problems will not be featured on the test.

 

F 11/30/012

HW due: Sleep. Form V students are on a field trip today. We will have class, but it will start at 8:10 instead of the usual 8:00 time.

 

 

Return to the HappyCal Zone

Return to Mr. Hansen’s home page

Return to Mathematics Department home page

Return to St. Albans home page

Last updated: 07 Feb 2013