Last Bit for Non-Seniors

You will be presenting a lesson on some topic in advanced mathematics.  You must have a self-contained, unique lesson to present.  The presentations will be on 6/13, 6/14 and 6/15 or 6/16.  Your presentation must include your lesson plan, a handout that includes notes and problems for the students, and a worked solution key (not just answers!).  I have some suggestions if you are having trouble finding a topic.

The rubric is available here.

5/31  Start researching your topic (you may elect to change it)
6/01  Declare your topic, get the rubric
6/03  Keep working on researching your topic and putting together your lesson, pick day of presentation

6/06  Keep working on researching your topic and putting together your lesson
6/07  Keep working on researching your topic and putting together your lesson
6/08  Prepare your presentation
6/10  Prepare your supplementary materials (G-Block)

D-Block
6/10  Presentations (Rachel and Markus)
6/13  Presentations (Nirmal and Ravi)
6/14  Presentations (Krishna and Daniel)
6/16  Presentations (Luke, Emily and Sabrina)

G-Block
6/14  Presentations (Jason and Rohan)
6/15  Presentations (Maggie, Peter and Kaushal)

6/23  Last day of class

A Little Bit of Multivariable in the Night...

Post AP we start looking at multivariable calculus - though only the function aspect of it.  Here is the syllabus:

5/06  13.1 Introduction to Functions of Several Variables 
         HW problems 31,33,35,37,43 (skip confirming),45-48,49-59 odd,63-66.

5/09  13.3 Partial Derivatives of a Function of Two Variables    

         HW problems 1-4, 6-27 by 3's, 29, 35, 37-40, 45, 47, 89-91

5/10  13.4 Differentials (Proof of the Clairault Theorem)        

         HW problems 1-9 odd, 11-16, 17, 19, 20, 27, 30-32, 34-36, 40

5/11  13.6 Directional Derivatives and Gradients
         HW problems 1-8, 13-18, 21-24 , 27, 28, 39, 40a-43a

5/13  13.6 Applications of the Gradient  CW problems 71, 72
         HW problems 44-52, 55-63 odd, 64, 73

5/16  13.8 Extrema of Functions of Two Variables
         HW problems 1-13 odd, 21, 23, 26, 31, 33, 41, 42, 45-47
5/17  13.9 Applications of Extrema   Math MCAS Day 1: E B A G H D
         HW problems 1, 3, 5, 9, 10, 14, 15
5/18  Review and 13.9 problems 19, 21, 22 (handout and answer key)  Math MCAS Day 2: A H D E F C B
           D-Block meets in room 408
5/19  Half Day C A G B
5/20  Extension problems (answer key)

5/23   Multivariable Test

5/26   Last Questions (from you and from me)
5/25   D-Block Final Day 1 - No Calculator
5/26   G-Block Final Day 1 - No Calculator
5/27   Final Day 2 - Calculator ok

5/30   Memorial Day
6/05   Graduation

Review for the AP Exam

Here is the complete review schedule.  Note that starting the week of April 11th, an AP problem quiz could be given on any day and will be given at least 1-2 times per week.

We will score the 2008 exam on Monday, 4/11.  I will collect the score sheets so make sure you do the test and bring your answers.

4/06  Multiple Choice portion of 2008 AP Exam (1A in class, 1B for HW)

4/08  Open Response portion of 2008 AP Exam (2A in class, 2B for HW)

4/11  Score the 2008 Exam, Overview of Topics to review, upload 2008 results here

4/12  Derivatives of Inverse, Curve Sketching, Linearization

4/13  Optimization, Implicit Differentiation, Related Rates

4/15  Integration and the Fundamental Theorem of Calculus

4/16 - 4/24 April Vacation

4/25  Hard 1998 AP Multiple Choice Questions

4/26  Integration Applications (Area and Volume, Rates in and out)
4/27  Differential Equations

4/29  Go over Hard 1998 AP Multiple Choice Questions, Work on 2003 AP Exam

5/02  Work on 2003 AP Exam - submit questions/topics you would like covered on 5/03

5/03  Topics chosen by you and Last Questions

5/05  AP Exam at 7:30am

Series Part 2 - Testing for Convergence (more Ch 10)

Here is another bit of Ch 9 which introduces the idea of convergence and divergence for functions. Three nights of homework on this and then on to the rest of Ch 10 - Convergence of Series.

3/18  Horizontally Infinite Improper Integrals
3/21  Vertically Infinite Improper Integrals

Homework: By the end of the 2 days, you should have done p.475-477/1 - 44, 55, and 59-61.

The last unit is on Convergence Tests.  There are several - all with their own plusses and minuses.  The challenge is to choose the correct test in each situation.

(Note: D-Block will meet in room 408 on 3/22 and 3/23 due to MCAS)
3/22  Recap of Infinite Sequences and Series, n^th term, Integral Test

         HW p.521/29, 30, 34, 38  and  p.534/1-5, 7, 8, 10-14,17, 19, 21
3/24  Half Day F C A H  (End of Term 3)

3/28  Limit and Direct Comparison Test

         HW p.521-522/3, 4, 49, 51, 53  and  p.534-535/9, 15, 16, 22, 59  

               also try some of the previous problems using these tests

3/29  Ratio Test and the Radius of Convergence         

         HW p.521/9-27 by 3's, 31-47 odd

3/30  Alternating Series, Liebniz Error Bound
         HW p.534-535/27-32, 55, 56, 58, 63-65

4/01  Absolute and Conditional Convergence

         HW p.534-535/23-26, 35-47 odd, 54, 61, 66-71

4/04  Fourier Series, Gamma Functions, Review and many AP Problems

         HW p.537-538/1-16, 41-51 odd (evens are optional but helpful)

4/05  Test of Series Convergence (9b) - NO CALCULATORS

Important Dates

3/22  MCAS Day 1 (E B A Hr G H D)

3/23  MCAS Day 2 (A H D E F C B)

3/24  MCAS Day 3 (F C A H)

3/24  End of Term 3 and Half Day

3/25  Good Friday - no school

4/16-4/24 April Vacation (includes Passover)

5/05  AP Calculus BC Exam

Series Part 1 - Modeling functions with Series (Ch 10)

We are starting Chapter 10 - the study of infinite series. The first test is on sections 10.1-10.3 plus two handouts of sections from the Hughes-Hallett Calculus book. 

3/02  10.1  Infinite series, power series, intervals of convergence
                  HW p.489-490/1, 2, 3-35 odd, 48-53

3/04  10.1  Finding series that represent functions

                  HW p.490-491/54-61, 63-65, 72;  read p.492-496; do Explorations 1 and 2

3/07  10.2  Taylor and Maclaurin series
                  HW p.500-502/1, 3, 5-18, 20-24, 26, 27, 32, 33, 36, 43

3/09  HH  10.3  Finding and using Taylor series
                  HW handout/1-22

3/10  10.2  More with Taylor series

                  HW p.501-502/25, 28, 31, 34-36, 44  and p.509/1 - 10

3/12  HH 10.4 The Error in Taylor Polynomial Approximations/1 - 14 except 3

3/14  Extra Problems  HW finish handout (answer key)
3/15  Review (more extra problems plus 2 AP problems - answer key)

3/16  Series Approximation Test (NO CALCULATOR)

         HW read pp.467-470 (Horizontally Improper Integrals)

MCAS on Tues, 3/22 - Thur, 3/24 (D-Block will meet in room 408)
Thur, 3/24 Half Day - F C A H, and End of Term 3

Fri, 3/27 Good Friday, no school

Vector, Parametric and Polar Calculus (Ch 11)

Chapter 11 is calculus with parametric, vector and polar curves.  Here is the proposed syllabus for the rest of the chapter.

2/10  11.1  Parametric Review with Calculus
                 HW p.547-549/1-15 odd, 18-33 by 3's, 35, 36, 39-44, 57, 59
2/12  11.2  Vector Review with Calculus
                 CW p.558-560/3-24 by 3's, 25, 26, 27-51 odd, 53, 54, 59-62

2/13 - 2/21  February Break

2/22  11.3  Polar Review with Calculus

                 HW p.571-572/1, 3-36 by 3's, 39-42, 72

2/23  11.3  Polar Area

                 HW p.572/43-60
2/24  Extra Problems (including Stewart problems) 
                 HW area: 54-66, 68, 75, 76, 81, 82   length: odds (not 55) and 56
2/26  11.3  Polar Curve Length and Surface Area

                 HW handout of Larson problems 41-43, 45-49, 51, 53-60, 62, 63

2/29  Review of Parametric/Vector and Polar Caluclus (answer key to Extension problems)

                 HW AP Problems

3/01  Ch 11 Test 

Ch 8 - Applications of Integration

Ch 8 involves using integration to solve problems, particularly geometry problems. We will spend several days finding the volumes of solids.

1/18  Martin Luther King Day - no school  

1/19  8.1  Integration as Net Change
                CW and HW p. 392-394/1-21, 25, 26, 30, 33
1/20  8.2  Area between Curves  CW Garden handout
                HW finish handout plus p.402-404/1-17 odd, 21-39 by 3's, 40, 41, 49
1/22  8.3  Volume of solids with specific, non-circular cross sections
                HW p.414-416/1-6, 41-46

1/25  8.3  Volumes of solids of revolution: Discs and Washers

                HW p.415/7-16, finish washer worksheet
1/26  8.3  Volumes of solids of revolution: Shells
                HW p.415-416/17-29 odd, 31 by shells, 35-40
1/27  8.3  Extra Problems [Larson book] and AP Problems
                HW p.415-418/18-30 even, 49, 52, 53, 55, 72, 74-76

1/29  8.4  Length of Curves
                HW p.424-425/1-21 odd, 22, 23, 25, 27, 28

2/01  8.4  Surface Area (D-Block, G-Block is canceled)
                HW finish handout of problems from the Stewart book

2/02  D-Block: Review and Extra Problems (handout and answer key)
        G-Block: Surface Area
2/03  D-Block: More review problems
2/04  G-Block: Review

2/05  Snow Day

2/08  Snow Day
2/09  Ch 8 Test