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

Ch 7 - The Indefinite Integral and Differential Equations

Just as we sometimes want to know the slope of a curve at a certain point (call it the definite slope), we also want to know the formula to calculate the slope of a curve anywhere - the slope formula (call it the indefinite slope). The same goes for the integral.  Chapter 6 was on the Definite Integral and Chapter 7 is on the Indefinite Integral.  We will learn how to find it algebraically, graphically and numerically (of course). The algebraic portion will take some time and you will be subjected to almost daily quizzes to make sure you are getting it.

Note:  We will not be able to finish this chapter before Christmas break.

12/07  Ch 6 Test
12/08  Intro to Differential Equations (initial value problems)
           HW p.335-339/1-23 odd, 59, 60, 75-80 and download slope field calculator

12/09  Substitution method undoes chain rule differentiation (this will happen on 12/11 for G-Block)
           HW p.346-348/1 - 39 odd, 69, 77 (the last one will be turned in - be neat)

12/11  Slope Fields (graphical diff. eq) & Euler's Method (numerical diff. eq) (on 12/10 for G-Block)

           HW finish handout and p.335-338/25, 27, 35-47 odd, 51-57 odd, 61, 63, 65

12/14  Integration  Quiz 1;  Changing limits of integration
           HW p.347-348/41, 43, 45, 53-67 odd, 68, 79

12/15  Int  Quiz 2;  Integration by Parts undoes the product rule
           HW p.354-355/1-16, 33, 36, 39, 41

12/16  More (Harder) Integration by parts
           HW p.355-356/17-31 odd, 34, 35, 42, 43, 47-56

12/18  Int Quiz 3;  Higher Powers of Trig Functions (additional notes) and 
           Trig Substitution (additional notes)

           HW p.347, 348/47-52, 81-84 and packet problems 1-3,7,13,17,22,27,34,35,38,39

12/21  Differential Equations by Separation of Variables
           HW from Hughes-Hallett handout/3-42 by 3's, 28, 43-47 (download page 1 and page 2)
12/22  Int Quiz 4;  Exponential Growth and Decay

           HW p.364-368/3-11 odd, 21, 23, 25, 29, 31, 39, 41, 43, 44, 53, 54, 57

12/23  Calculus Jeopardy

12/24-1/3  Christmas vacation (just for fun, watch this!)

01/04  Recap
           HW finish handout

01/05  Partial Fraction Decomposition

           HW handout problems 7-31 odd, 41, 43, 45, 47-50 
           (see textbook p.369-371/1-14, 47, 48 for more practice)
           Longterm HW Mixed Integrals Worksheet (finish by January 15th)

01/06  Logistic Functions

           HW p.375-377/15-35 odd, 36, 37, 44-46

01/08  Int Quiz 5;  Laplace Transforms (Day 1 - Intro)

           HW finish problems in handout 

01/11  Laplace Transforms (Day 2 - Additional Transforms) 
           HW finish problems in handout

01/12  Int Quiz 6;  Laplace Transforms (Day 3 - Applications)

           HW finish application problems in handout (some answers included)
01/13  Wrap-up of integration techniques and solving differential equations

01/14  Half Day B A G F

01/15  Ch 7 Test, End of Term 2

01/18  Martin Luther King Day

The Definite Integral (Ch 6)

We began looking at anti-derivatives in the last chapter, now we will look more closely and formally.  We need some new vocabulary, starting with another verb for finding the anti-derivative: integrating.

11/16  Post Ch 5 Test, enter a version of the RAM program (or look up a fancier one online - for

           example rsum.zip or riemann.zip at http://www.ticalc.org/pub/83plus/basic/math/calculus/ -

           and download it right into your calculator)
11/17  Area and Riemann Sums (6.1, 6.2)

           HW p.277-280/1, 4, 6-14, 19, 21, 28, 31-38, 40, 41  and  p.291/9-27 by 3's

11/18  Defining the Definite Integral and looking at Integration Properties (6.2, 6.3)

           CW Explorations on p. 274 & p.286  HW p.291-292/37-43 odd, 51-57 odd  and p.298-299/1-6

11/20  Average Value and the Mean Value Theorem for Integrals (6.3)

           HW p.299-300/7-10, 14-18, 37-42, 47

11/23  The Fundamental Theorem of Calculus and Antiderivatives (6.3, 6.4)

           HW p.299-300/19-35 odd, 49-51 and p.311/27-43 odd

11/24  Derivatives of Integrals with the Chain Rule (6.4)

           HW p.310-311/3-24 by 3's, 45-54

11/25  Half-day A C F H

11/26  Thanksgiving

11/27  Black Friday

11/30  Parent Conferences

12/01  Write test problems to review 

           HW p.311-313/55-64, 68-71, 73, 75-79

12/02  Trapezoidal Rule and Simpson's Rule (6.5)

           HW p.320-321/1, 3, 5-7, 9-11, 20, 21, 27, 30, and finish handout
12/04  Review and Extension (handout with answer key)

12/07  Ch 6 Test of the Definite Integral

Applications of the Derivative (Ch 5)

We have spent a month learning how to find the derivative for any function.  Now we will start using those derivatives to solve problems or explain phenomena.

10/23  Post-Ch3 Test HW: download and do handout on Curve Analysis

10/26  5.1  Extreme Values of Functions

                 HW p.200-201/15-30 by 3's, 31-43 odd, 44, 51, 53, 55

10/27  5.2  Mean Value Theorem and Antiderivatives (proof of the MVT)

                 HW p.208-210/3-27 by 3's, 30-35, 41-49 odd, 60, 62, 63

10/28  5.3  Curve Sketching from f ' and f ''

                 HW p.220-222/2, 4, 5, 7, 11-33 odd, 43-47, 51, 59, 60

10/30  5.4  Optimization (using derivatives to find min/max) (end of Term 1)

                  HW p.231-234/1, 5-7, 12, 15-17, 19, 20-26 even, 27, 31-34, 36

11/02  5.4  More Optimization

                  HW p.234-237/39-41, 45, 47, 48, 50, 58-61, 63

11/03  5.5  AP Problem Quiz, Linear Approximation (using a different book)

                  HW handout/1-12 18-20, 24, 25

11/04  5.5  Using the Approximation

                  HW handout/21-23, 26, 27  and book p.248-250/37-41, 45-47, 51, 66, 69

11/06  9.2  L'Hopital's Rule (using derivatives to find limits)

                  HW p.458-460/13-47 odd, 53, 55, 58, 68, 70-72

11/09  5.6  Related Rates (everything depends on t)

                  HW p.257-260/3-39 by 3's

11/10  5.6  More Related Rates (because everything depends on t)

                  HW p.257-261/5, 7, 10, 17, 19, 20, 22, 26, 31, 32, 35, 42-46
11/11  Veterans' Day - no school

11/13  Review and extra problems (links: review, its answer key, a practice test, that answer key)

11/16  Chapter 5 Test