Last bit for non-seniors

You will have all of the time after the final to work on one of two projects: Fourier Series and Music, and S-I-R (spread of disease) differential equation system.  The end result will be a write-up and verbal presentation (on June 13th if you are ready, June 17th if you are not).

A bit of Multivariable Calculus and the Final

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

5/09  13.1 Introduction to Functions of Several Variables 
         HW problems 31,33,35,37,43 (skip confirming),45-48,49-59 odd,63-66.

5/12  AP Physics Exam
5/13  Math MCAS Day 1: A G H B
5/14  13.3 Partial Derivatives of a Function of Two Variables   (Math MCAS Day 2: C E F H D)     

         HW problems 1-4, 6-27 by 3's, 29, 35, 37-40, 45, 47, 89-91
5/16  13.4  Differentials         

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

5/19  13.6 Directional Derivatives and Gradients
         HW problems 1-8, 13-18, 21-24 , 27, 28, 39, 40a-43a
5/20  13.6 Applications of the Gradient  CW problems 71, 72
         HW problems 44-52, 55-63 odd, 64, 73
5/21   13.8 Extrema of Functions of Two Variables, and Review
          HW problems 1-13 odd, 21, 23, 26, 31, 33, 41, 42, 45-47 
5/23   Multivariable Test

5/26   Memorial Day

5/27   Last Questions (from you and from me)
5/28   Final Day 1
5/30   Final Day 2

Review for the AP exam

Here is the complete review schedule.  Note that starting the week of April 7th, 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, 4/07.  I will collect the score sheets so make sure you do the test and bring your answers.

4/02  Multiple Choice portion of 2008 AP Exam (1A in class, 1B for HW)

4/04  Open Response portion of 2008 AP Exam (2A in class, 2B for HW)

4/07  Score the 2008 Exam, Overview of Topics to review

4/08  Derivatives of Inverse, Curve Sketching, Linearization

4/09  Differential Equations

4/11  Optimization, Implicit Differentiation, Related Rates

4/14  Integration and the Fundamental Theorem of Calculus

4/15  Integration Applications (Area and Volume, Rates in and out)

4/16  Hyperbolic Trig (enough review for a bit - let's do an extension topic!)

4/18 - 4/27  Good Friday, April Vacation

4/28  Hard 1998 AP Multiple Choice Questions

4/29  Go over Hard 1998 AP Multiple Choice Questions

4/30  Work on 2003 AP Exam

5/02  Work on 2003 AP Exam - submit questions/topics you would like covered on Monday 5/05

5/05  Topics chosen by you

5/06  Last Questions

5/07  AP Exam at 7:30am

5/08  Half Day C A G F

Series Part 2 - Tests for Convergence

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.  Homework listed in blue needs updating.

3/19  Recap of Infinite Sequences and Series, n^th term, Integral Test

         HW p.511/29, 30, 34, 38  and  p.523/1-5, 7, 8, 10-14,17, 19, 21

3/21  Limit and Direct Comparison Test

         HW p.511-512/3, 4, 49, 51, 53  and  p.523-524/9, 15, 16, 22, 59  

               also try some of the previous problems using these tests

3/24  Ratio Test and the Radius of Convergence         

         HW p.511/9-27 by 3's, 31-47 odd

3/25  Alternating Series, Liebniz Error Bound
         HW p.523-524/27-32, 55, 56, 58, 63-65

3/26  Absolute and Conditional Convergence

         HW p.523-524/23-26, 35-47 odd, 54, 61, 66-71

3/28  Fourier Series, Review and 2 AP Problems  (End of Term 3)

         HW p.526-529/1-16, 41-51 odd (evens are optional but helpful)

3/31  Five more AP Problems

4/01  Test of Series Convergence (9b)

Improper Integrals (a bit of chapter 8)

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.

3/14  Horizontally and Vertically Infinite Improper Integrals
3/17  The Direct Comparison Test and some extra improper integral problems

Homework: By the end of the 2 days, you should have done p.467-469/1 - 44, 55, and 59-61.

Important Dates

3/18  MCAS Day 1 (Hr G H A)

3/19  MCAS Day 2 (E F H D)

3/21  MCAS Day 3 (D E F B C)

3/28  End of Term 3

4/14  1st night of Passover

4/18  Good Friday - no school

4/19-4/27 April Vacation

Series Part 1 - Finding Series to model functions

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 Calculus book. 

2/26  9.1  Infinite series, power series, intervals of convergence
               HW p.481-482/1, 2, 3-35 odd, 48-53

2/28  9.1  Finding series that represent functions

               HW p.482-483/54-61, 63-65, 72;  read p.484-488; do Explorations 1 and 2

3/03  9.2  Taylor and Maclaurin series
               HW p.492-493/1, 3, 5-18, 20-24, 26, 27, 32, 33, 36, 43

3/04  HH   10.3  Finding and using Taylor series
               HW handout/1-22

3/05  9.2  More with Taylor series

               HW p.492-494/25, 28, 30, 31, 34-36, 44  and p.500/1 - 10

3/07  HH 10.4 The Error in Taylor Polynomial Approximations/1 - 14 except 3

3/10  Extra Problems  HW finish handout (answer key)
3/11  Review (more extra problems plus 2 AP problems - answer key)

3/12  Series Approximation Test
        HW read pp.459-462 (Horizontally Improper Integrals)

3/13  (Half Day - C B H F)

Ch 10 - Calculus for Parametric and Polar Functions

Chapter 10 is calculus with parametric, vector and polar curves.  Here is the proposed syllabus for the rest of the chapter.

2/03  10.1  Parametric Review with Calculus
                 HW p.535-537/1-15 odd, 18-33 by 3's, 35, 36, 39-44, 57, 59
2/04  10.2  Vector Review (Half-Day for Parent Conferences B A G H)
                 HW p.545/3-24 by 3's
2/05  10.2  Vector Calculus (Snow Day - give it a try, I will answer questions next week)
                 HW p.546-547/25, 26, 27-49 odd, 57-60

2/07  10.3  Polar Review  (I will be out taking a course - last day)

                 HW p.557-558/1-37 odd

2/10  10.3  Derivatives of Polar Curves

                 HW handout of Stewart problems 54-66, 68, 75, 76, 81, 82 
                       plus text p.558/39-42, 71 if you need more practice 

2/11  10.3  Polar Area

                 HW p.558/43-60
2/12  10.3  Polar Curve Length and Surface Area

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

2/14  Extra Problems (answer key to Extension problems)

2/15-23  February Break

2/24  Recap and Review of Parametric and Polar Caluclus

                 HW AP Problems

2/25  Ch 10 Test 

Ch 7 - Applications of Integration

Ch 7 involves using integration to solve problems, particularly geometry problems. We will spend several days finding the volumes of solids.

1/14  7.1  Integration as Net Change  (Post-Test reading and homework)
               HW p. 386/1-11 odd, 12-16, 17-21 odd
1/15  7.2  Area between Curves  CW Garden handout
               HW finish handout plus p.395-397/1-17 odd, 21-39 by 3's, 40, 41, 49

1/17  7.3  Volume of solids with specific, non-circular cross sections  (End of Term 2)
               HW p.406-408/1-6, 39-44

1/20  Martin Luther King Day - no school

1/21  7.3  Volumes of solids of revolution: Discs and Washers
               HW p.407/7-16,  finish washer worksheet
1/22  7.3  Volumes of solids of revolution: Shells
               HW p.407-408/17-27 odd, 33-38

1/24  7.3  Extra Problems [from Larson book] and AP Problems  (I will be out taking a course - day 1)
               HW p.406-408/18-28 even, 29 by shells, 47, 50, 51, 53, 70, 72-74

1/27  7.4  Length of Curves
               HW p.416-417/1-21 odd, 22, 23, 25, 27, 28
1/28  Surface Area  

               HW [Stewart book] handout/1-4, 6-12 even, 13-15, 28, 31, 32, 36
1/29  Review and Extra Problems (answer key)

1/31  Ch 7 Test  (I will be out taking a course - day 2)