Last Bit for Non-Seniors

You will be presenting a lesson on some topic in advanced mathematics.  You may work with someone else on the same topic but you must have a self-contained, unique lesson of your own to present.  I will kick things off with a lesson on hyperbolic trig functions sinh(x) and cosh(x).  The presentations will be on 6/11, 6/12 and 6/15.  You 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.

6/01  Hyperbolic Trig Functions  HW pick a topic
6/02  Get rubric, start researching your topic (you may elect to change it)
6/04  Last day to change your topic
6/05  Keep working on researching your topic and putting together your lesson, pick day of presentation

6/08  Keep working on researching your topic and putting together your lesson
6/09  Go to the library to research, the computer lab to type, the classroom to practice, the staff room to make copies
6/11  Presentations (Matthew and Eric)
6/12  Presentations (Devin and Louie)

6/15  Presentations (Emily, Richard, Bharat, Brian)

6/22  Last day of class
6/23  Come to get your grades

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:

5/07  13.1 Introduction to Functions of Several Variables   Half Day C A G F
         HW problems 31,33,35,37,43 (skip confirming),45-48,49-59 odd,63-66.

5/08  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

5/11  13.4 Differentials (Proof of the Clairault Theorem)        

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

5/12  13.6 Directional Derivatives and Gradients   Math MCAS Day 1: A G H B
         HW problems 1-8, 13-18, 21-24 , 27, 28, 39, 40a-43a

5/13  Math MCAS Day 2: D E F H 
5/14  13.6 Applications of the Gradient  CW problems 71, 72
         HW problems 44-52, 55-63 odd, 64, 73
5/15  13.8 Extrema of Functions of Two Variables, and Review
         HW problems 1-13 odd, 21, 23, 26, 31, 33, 41, 42, 45-47

5/18  13.9 Applications of Extrema
         HW problems 1, 3, 5, 9, 10, 14, 15
5/19  Extra Multivariable Problems (answer key)
5/21  Review and 13.9 problems 19, 21, 22 (handout and answer key)

5/22  Multivariable Test

5/25   Memorial Day

5/26   Last Questions (from you and from me)
5/28   Final Day 1 - No Calculator
5/29   Final Day 2 - Calculator ok

Review for the AP Exam

Here is the complete review schedule.  Note that starting the week of April 6th, 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 Thursday, 4/09.  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)

4/07  Open Response portion of 2008 AP Exam (2A in class, 2B for HW)

4/09  Score the 2008 Exam, Overview of Topics to review

4/10  Derivatives of Inverse, Curve Sketching, Linearization

4/13  Differential Equations

4/14  Optimization, Implicit Differentiation, Related Rates

4/16  Integration and the Fundamental Theorem of Calculus

4/17  Integration Applications (Area and Volume, Rates in and out)

4/18 - 4/26 April Vacation

4/27  Hard 1998 AP Multiple Choice Questions

4/28  Go over Hard 1998 AP Multiple Choice Questions

4/30  Work on 2003 AP Exam

5/01  Work on 2003 AP Exam - submit questions/topics you would like covered on Monday 5/04

5/04  Topics chosen by you and Last Questions

5/05  AP Exam at 7:30am

5/07  Half Day C A G F

Series Part 2 - Testing for Convergence

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.

3/19  Horizontally Infinite Improper Integrals
3/20  Vertically Infinite Improper Integrals

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

3/23  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

3/24  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

3/26  Ratio Test and the Radius of Convergence         

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

3/27  Alternating Series, Liebniz Error Bound  (End of Term 3)
         HW p.523-524/27-32, 55, 56, 58, 63-65

3/30  Absolute and Conditional Convergence

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

3/31  Fourier Series, Gamma Functions, Review and many AP Problems

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

4/02  Test of Series Convergence (9b) - NO CALCULATORS

Important Dates

3/24  MCAS Day 1 (G H A)

3/25  MCAS Day 2 (E F C D)

3/26  MCAS Day 3 (C B G H A)

3/27  End of Term 3

4/03  1st night of Passover

4/03  Good Friday - no school

4/18-4/26 April Vacation

5/05  AP Calculus BC Exam

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. 

3/02  9.1  Infinite series, power series, intervals of convergence
               HW p.481-482/1, 2, 3-35 odd, 48-53

3/03  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

3/05  9.2  Taylor and Maclaurin series
               HW p.492-493/1, 3, 5-18, 20-24, 26, 27, 32, 33, 36, 43

3/06  HH  10.3  Finding and using Taylor series
               HW handout/1-22

3/09  9.2  More with Taylor series

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

3/10  HH 10.4 The Error in Taylor Polynomial Approximations/1 - 14 except 3

3/12  (Half Day - C B H F)

3/13  Extra Problems  HW finish handout (answer key)

3/16  Review (more extra problems plus 2 AP problems - answer key)

3/17  Series Approximation Test
        HW read pp.459-462 (Horizontally Improper Integrals)

MCAS on Tues, 3/24 - Thur, 3/26
Term 3 Ends on Friday, 3/27

Vector, Parametric and Polar Calculus (Chapter 10)

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

2/06  10.1  Parametric Review with Calculus
                 HW p.535-537/1-15 odd, 18-33 by 3's, 35, 36, 39-44, 57, 59

2/09  SNOW DAY
2/10  10.2  Vector Review with Calculus
                 HW p.545-547/3-24 by 3's, 25, 26, 27-49 odd, 57-60

2/12  10.3  Polar Review with Calculus

                 HW p.557-558/1, 3-36 by 3's, handout of Stewart problems 54-66, 68, 75, 76, 81, 82 
                       plus text p.558/39-42, 71 if you need more practice 

2/13  10.3  Polar Area (and Singing Valentines?)

                 HW p.558/43-60

2/14-22  February Break

2/23  10.3  Polar Curve Length and Surface Area

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

2/24  Extra Problems (answer key to Extension problems)

2/26  Review of Parametric/Vector and Polar Caluclus

                 HW AP Problems

2/27  Ch 10 Test 

Applications of Integration (Chapter 7)

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

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
1/16  7.1  Integration as Net Change  (Classwork and homework - I am out taking a course - first day)
               CW and HW p. 386/1-21

1/19  Martin Luther King Day - no school

1/20  7.3  Volume of solids with specific, non-circular cross sections  (End of Term 2)
               HW p.406-408/1-6, 39-44

1/22  7.3  Volumes of solids of revolution: Discs and Washers
               HW p.407/7-16,  finish washer worksheet
1/23  7.3  Volumes of solids of revolution: Shells
               HW p.407-408/17-27 odd, 29 by shells, 33-38

1/26  7.3  Extra Problems [Larson book] and AP Problems  (I am out taking a course - last day)
               HW p.406-408/18-28 even, 47, 50, 51, 53, 70, 72-74
1/27  SNOW DAY
1/28  SNOW DAY

1/29  7.4  Length of Curves
               HW p.416-417/1-21 odd, 22, 23, 25, 27, 28
1/30  Surface Area  

               HW finish handout of problems from the Stewart book

2/02  SNOW DAY 2/03  Review and Extra Problems (answer key)

2/05  Ch 7 Test