Monday, March 15, 2010
3/15 Starting the Convergence Tests (nth 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
Wednesday, March 10, 2010
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
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
Monday, March 1, 2010
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
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
Monday, February 22, 2010
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
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
Wednesday, February 10, 2010
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!
Tuesday, January 26, 2010
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
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
Tuesday, January 19, 2010
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).
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).
Tuesday, January 5, 2010
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
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
Saturday, December 19, 2009
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.
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.
Tuesday, December 15, 2009
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
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
