Tests for Convergence plus the beginning of the review

3/15  Starting the Convergence Tests (n^th term, Direct Comparison, Abs. Conv.)

        HW p.492/Exploration1 and  p.495/1-15 odd, 17-21, 23-29 odd

3/16  Ratio Test, Integral Test, Limit Comparison

        HW p.495-6/33 -40, 52  and  p.506/1-11 all

3/17  Alternating Series, Liebniz Error Bound

        HW p.507/12-16, 28a-42a even (part a only), 43,47,48,50

3/18  Absolute and Conditional Convergence

        HW p.507-508/17-26, 27-41 odd, 51-55

3/22  Review plus 2 AP Problems

        HW p.509/1-16, 41-51 odd (evens are optional, any extra problems are helpful)

3/23  3 more AP problems  (MCAS schedule - class meets at 1:30)

3/24  MCAS schedule - no class

3/25  2 more AP problems  (MCAS schedule - class meets at 10:10)

3/29  Test of Series Convergence (9b)

3/30  Multiple Choice portion of 2008 AP Exam (1A in class, 1B for HW)

3/31  Open Response portion of 2008 AP Exam (2A in class, 2B for HW)

We will score the 2008 exam on Thursday, 4/01.  I will collect the score sheets so make sure you do the test and bring the answers.

Dea Haupt

Mathematics Department

Lexington High School

Improper Integrals

Here is another bit of Ch 8 which introduces the idea of convergence and divergence for functions. Three nights of homework on this and then on to the rest of Ch 9 - Convergence of Series.

3/09  Post-test, Horizontally Infinite Improper Integrals (read pp.433-435)
         HW p.442/1, 4, 7, 12-14, 20, 21, 23 - 25
3/10  Vertically Infinite Improper Integrals and the Direct Comparison Test
         HW p.442/remaining odd of 3 - 21, 33, 37, 43
3/11  Limit Comparison Test
         HW p.442/rest of 27 - 46, 49

The approach to the test

The last few lessons until the first Series Test are as follows:

3/02  HH 10.4 The Error in Taylor Polynomial Approximations/ 1- 14 except 3
3/03  Extra Problems  HW finish handout
3/04  Half Day - no class  (C B H F)

3/08  Review
3/09  Series Approximation Test

Beginning our study of Infinite Series

We are starting Chapter 9 - the study of infinite series. The first test is on sections 9.1-9.3 plus two handouts of sections from the Hughes-Hallett book.

2/22  9.1  Infinite series, power series, intervals of convergence
               HW p.466-7/1, 2, 3-15 odd, 17-23, 36-41
2/23  9.1  Finding series that represent functions
               HW p.468/42-53;  read p.469-474; do Explorations 1 and 2
2/24  9.2  Taylor and Maclaurin series
               HW p.478/1-18, 20, 21, 26, 27, 30, 31
2/25  HH   10.3  Finding and using Taylor series
               HW handout/1-22
3/01  9.2  More with Taylor series
               HW p.478-9/19, 22, 24, 25, 28, 29, 32  and  p.486/1-10

Dealing with the snow day

Given that we were just going to spend the 10th doing AP problems for review, we will still be having the test on the 11th.   Enjoy the day off!

Parametric, Vector and Polar Functions

Chapter 10 is calculus with parametric, vector and polar curves.  Here is the proposed syllabus for the rest of the chapter.  Snow days (and any discretionary decisions on my part) may change things.

1/25  10.1  Parametric Review
                HW p.518-519/1-19 odd, 23-27, 31, 32, 35, 37
1/26  10.2  Vector Calculus
                HW p.528-529/23-25, 35-37, 39-43, 45, 47-49, 52-54
1/27  10.3  Vector-Valued Functions
                HW p.537-538/1-23 odd
1/28  10.3  More practice
                CW/HW p.538-539/25-37 odd, 34, 41a, 42, 45

2/01  10.4 Modeling Projectile Motion (handout from another book)
                HW p.549-550/3, 5-8, 13, 19-21
2/02  10.5 Polar Review
                HW p.558-559/1, 3, 5-61 alternating odds, 63-68
2/03  10.6  Derivatives of Polar Curves
                HW p.566/1-12
2/04  10.6  Polar Area
                HW p.566-567/13-27 odd, 29, 30, 44

2/08  10.6  Polar Curve Length and Surface Area
                HW p.567-568/31-39, 41-47 odd
2/09  Extra Problems
2/10  Review with AP problems
2/11  Ch 10 Test

2/13-22  February Break

Ch 7 Review and the Answer Key

The answer key to the Review/Extra Problems can be downloaded here. Remember, the snowflake problems won't hurt but are not due until Monday.

Please note:  there is a typo in the integral formula for problem 4a.  It should have the sine inverse of u over a (not u over 2).

Applications of the Definite Integral

Ch 7 involves using integration to solve problems, particularly geometry problems. We will spend several days finding the volumes of solids - and one method includes cake!

1/05  7.1  Integration as Net Change
                 HW p. 371-373/1-11 odd, 12-16, 17-21 odd
1/06  7.2  Area between Curves  CW Garden handout
                 HW finish handout plus p.380-382/1-35 odd, 43
1/07  7.3  Volume of solids with specific, non-circular cross sections
                 HW pl.390-391/1-12

1/11  7.3  Volumes of solids of revolution: Discs and Washers
                 HW p.392/13-22,  finish washer worksheet
1/12  7.3  Volumes of solids of revolution: Shells
                 HW p.392-393/23-33 odd, 39-43
1/13  7.3  Extra Problems and AP Problems
                  HW p.392-394/24-34 even, 35 by shells, 47, 51-53, 66-68
1/14  7.4  Length of Curves  (and a half-day B A G F)
                  HW p.399-400/1-21 odd, 22, 23, 26, 28, 29

1/18  Martin Luther King Day - no school
1/19  Surface Area  HW handout/1-4, 6-12 even, 13-15, 28, 31, 32, 36
1/20  Review and Extra Problems
1/21  Ch 7 Test
1/22  End of Term 2

Slope Field Generators

A slope field is a graphical method for solving differential equations. While you will be required to generate then by hand, usually we want to just look at them.  There are several ways to generate them electronically:

Calculator:  Download slopefields.zip from http://www.ticalc.org/pub/83plus/basic/math/calculus/
                   There are seven (!) slope field programs but this one seemed the easiest to use (and
                  get out of).  It is the one dated 05-07-01.

Computer Applet:  http://alamos.math.arizona.edu/~rychlik/JOde/JOdeApplet.html

Mac Application:  http://www.colby.edu/personal/s/sataylor/teaching/F08/MA121/SlopeFields.pdf

You want to have something on your calculator by Monday (the 21st). You need the cable that connects your calculator to the computer or (if you have a friend that has successfully downloaded the program) a cable to connect your calculator to a friends calculator.  You can also type the program into the calculator.

Separation of Variables HW

Download the pdfs of the pages for the homework: (first page) - (second page). (Mr. Harris and I were unable to combine them - stupid computers!)
They are scans from section 11.4 of the third edition of Calculus by Hughes-Hallett, Gleason, McCallum, et al.
Do problems 3-33 by 3s, 35, 36, 39-41