BC Calculus 09-10

Review Schedule

2010-03-23T13:59:00.004-04:00

Here is the complete review schedule. Note that starting the week of April 5th, an AP problem quiz could be given on any day and will be given at least 1 - 2 times a week.

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)
4/01 Score the 2008 Exam, review Differential Equations
4/02 Good Friday, no school

4/05 Applications of Diff. Eqtns (Hughes-Hallett 11.6) HW/1,4-8,12-14,21-24
4/06 Systems of Diff. Eqtns (HH 11.8) HW/1-17
4/07 Second Order Diff Eqtns (HH 11.10) HW/1-11 odd, 13-23
(Note: I am out this day.)
4/08 Integration and the Fundamental Theorem of Calculus
4/09 End of Term 3

4/12 Integration Applications (Area & Volume, Rates in and out)
4/13 Trigonometric Substitutions HW p.452-453/35-41 odd, 43-46, 49-53 odd
4/14 Derivatives of Inverse, Curve Sketching, Linearization
4/15 Hard 1998 AP Multiple Choice Questions
(Note: I am out this day.)

4/17 - 4/25 April Vacation

4/26 Go over all questions
4/27 Optimization, Implicit Differentiation, Related Rates
4/28 Power & Maclauren Series, Hyperbolic Trig Functions
4/29 Quiz of Extension Topics

5/03 Fourier Series
5/04 Last Questions
5/05 AP Exam at 8am

Tests for Convergence plus the beginning of the review

2010-03-15T10:14:00.003-04:00

3/15 Starting the Convergence Tests
         n^th term, Direct Comparison, Absolute Convergence
         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 but 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.

Improper Integrals

2010-03-10T09:45:00.001-05:00

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

The approach to the test

2010-03-01T10:24:00.001-05:00

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

Beginning our study of Infinite Series

2010-02-22T09:05:00.002-05:00

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

Dealing with the snow day

2010-02-10T11:12:00.001-05:00

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!

Parametric, Vector and Polar Functions

2010-01-26T12:08:00.002-05:00

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

Ch 7 Review and the Answer Key

2010-01-19T18:44:00.003-05:00

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).

Applications of the Definite Integral

2010-01-05T21:44:00.003-05:00

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

Slope Field Generators

2009-12-19T15:03:00.003-05:00

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.

Separation of Variables HW

2009-12-15T15:07:00.001-05:00

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

Chapter 6 - The indefinite integral, and differential equations

2009-12-03T15:38:00.008-05:00

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 slope of a curve just anywhere - the slope formula (call it the indefinite slope). Well, the same goes for the integral. Chapter 5 was on the Definite Integral and Chapter 6 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.

12/02 Ch 5 Test, Anti-derivative homework p.312-314/1-23 odd, 52
12/03 Intro to Differential Equations (initial value problems)
           HW p.312-315/25, 26, 31-41 odd, 51, 53, 55, 60-62, 67

12/07 Substitution method undoes chain rule differentiation
           HW p.321-323/1 - 19, 45, 46, 50
12/08 Integration Quiz 1; Changing limits of integration
           HW p.321-323/20 - 38, 47, 48, 51
12/09 Int Quiz 2; Integration by Parts undoes the product rule
           HW p.328-329/1-4, 9, 11, 15, 19-24, 27, 29
12/10 Int Quiz 3; More Integration by parts (bring books)
           HW p.329/13, 14, 17, 18, 25, 28, 35-37

12/14 Int Quiz 4; Partial Fraction Decomposition (8.4, ex 1 & 4 only)
           HW p.451-453/1,4, 6-14, 18, 25, 26
12/15 Int Quiz 5; Differential Equations by Separation of Variables
           HW from Hughes-Hallett handout/3-33 by 3's, 35, 36, 39-41
12/16 Int Quiz 6; Exponential Growth and Decay
           HW p.338-341/1-27 odd,28,29,31,35 and p.347-348/1,2,5,6,15,16
                 and enter Slope Field program into calculator
12/17 Logistic Functions
           HW p.347/3, 4, 7, 8, 13, 14, 17-33 odd

12/21 Slope Fields (graphical diff. eq) & Euler's Method (numerical diff. eq)
           HW p.313/27-30,43,44,63,65,66 and p.347/9-12 and
                 p.355-356/2,3,5,7,9,10,15abc,19,20,23 and HH handout/42-47
12/22 Wrap-up of integration techniques and solving differential equations

12/23 Ch 6 Test

12/24-1/4 Christmas vacation (note: Monday, January 4th, is Parent Conferences - no school)

Missing table

2009-12-01T11:32:00.002-05:00

Here is the table of missing data from problem 4.

t (hours)	0	0.1	0.2	0.3	0.4	0.5	0.6	0.7	0.8	0.9	1.0
v(mi/hr)	0	10	20	40	60	50	40	35	40	50	65

Finishing up Ch 5

2009-11-30T13:54:00.003-05:00

The rest of Ch 5 is taken with review and extension material.

11/25 Simpson's Rule
           HW finish handout
11/30 Recap and review CW Review probs/2-6,37,49,50
           HW p.298-300/9, 15-29 odd, 30, 38-43, 54
12/01 Review and Extension CW finish handout
12/02 Ch 5 Test of the Definite Integral
           HW p.312-314/1-23 odd, 52

Ch 5 - The Definite Integral

2009-11-16T14:27:00.002-05:00

Here's the syllabus up to Thanksgiving (mostly).

11/16 Defining the Definite Integral and looking at integration properties
           HW 5.2 p.267-268/29-47 odd and 5.3 p.274-275/1-6
11/17 Average Value
           HW 5.3 p.275-276/26, 29-42, 46
11/18 Fundamental Theorem of Calculus
           HW 5.3 p.275/7-27 odd and 5.4 p.286/1-17 odd
11/19 Derivatives of integrals with the Chain Rule
           HW 5.4 p.286-287/19-35 odd, 37-46

11/23 More problems to practice
           CW/HW 5.4 p.287-288/47-56, 60-64
11/24 Trapezoidal Rule
           HW 5.5 p.295-297/1, 3, 5-9, 11, 12, 17 (not d), 22, 23

The first sections of Ch 5

2009-11-12T20:03:00.002-05:00

11/12 Area and Riemann Sums (5.1, 5.2)
HW p.254-257/1-5,7,8,10-13,22-26 and p.267/7-27 odd

RAM Program

2009-11-10T10:07:00.002-05:00

The RAM program may be downloaded here. Please enter it into your calculator for class on Thursday.

The rest of the post test homework is p.229-231/16-18, 50, 51

More applications for derivatives

2009-10-26T09:38:00.002-04:00

Note: The sheet of extra problems was from the book: p.185/52; p.193/36, 39, 40, 50, 51

We are starting to get into the actual applications of derivatives.

10/26 4.3 Using derivatives to graph
                  HW p.204-206/8-29 by 3's, 31-39 odd, 41-48
10/27 4.4 Optimization (derivatives to find min/max)
                  HW p.214-217/1,5,7,9,15,17,20,22,25,26,28,32,34,36
10/28 4.4 AP Problem Quiz
                  HW p.217-219/39-43, 45, 47, 49
10/29 4.5 Linear Approximations (using a different book!)
                  HW HH/1-10, 14-17 and p.229-231/11-14, 52

11/02 4.5 Using the approximation
                  HW HH/11-13 and p.230-231/31-45 odd
11/03 8.1 L'Hopital's Rule (derivatives to find limits)
                  HW p.423-425/1-47 odd, 50, 52
11/04 4.6 Quick Quiz; Related Rates (everything depends on t)
                  HW p.237-239/3, 5, 6, 9, 11-13, 15, 18-22, 24
11/05 4.6 More Related Rates (because everything depends on t)
                  HW p.240-241/27, 28, 30, 32, 34, 35, 37, 39, 40, 41

11/09 Review and extra questions
11/10 Ch. 4 Test
                   HW Enter RAM program in calculator, p.229-231/16-18, 50, 51
11/11 Veterans Day - no school

Starting Derivative Applications (Ch 4)

2009-10-21T10:21:00.002-04:00

The first two sections of Chapter 4 mesh together so the homework will be a bit back-and-forth.

10/21 p.192-193/3, 5, 9, 13, 15-20, 21a, 24a, 25-33 odd
10/22 p.184-185/27-35 odd, 36, 37-43 odd, 45-51 plus a sheet of extras

Answers to today's extra questions

2009-10-19T15:35:00.002-04:00

1. For the ellipse problem today (4x^2 + 9y^2 = 36) with the generic first quadrant point (p, q), you should find the following:

xT = 9/p
yT = 4/q
xN = 5p/9
yN = -5q/4

Given that p goes from 0 to 3 and q goes from 0 to 2, we can say the following about possible values of the tangent and normal intercepts:

xT = (3, infinity)
yT = (2, infinity)
xN = (0, 5/3)
yN = (-5/2, 0)

2. For e^(2x) = k*sqrt(x) then it happens at x = 1/4 when k = 2/sqrt(e
(if you need a hint, you have two equations (original and slopes) for the two unknowns (k and x))

More with Derivatives

2009-10-06T12:20:00.002-04:00

Here is the syllabus for the rest of the chapter.

Please note that the homework after the Chain Rule class is slightly different from that posted on the board!

10/06 3.6 Chain Rule (some more)
            HW p.147-148/33-39 odd, 57, 58, 60-65, 68, 71
10/07 3.7 Implicit Differentiation
            HW p.155-156/3, 7, 11-37 odd, 40-45
10/08 3.7 Prove power rule for rational powers HW p.156-157/46-51
            3.8 Derivatives of Inverse Trig Functions
             HW p.162-163/1-19 by 3's,20,21-33 odd,34

10/12 Columbus Day, no school
10/13 3.9 Derivatives of Exp and Log Functions
            HW p.170-171/1-41 alternating odds,42,47-50,52
10/14 Professional Development - no school
10/15 3.9 Logarithmic Differentiation   HW p.170/19,20,43-46; p.172/22
           3.6 Parametrics CW p.147-148/50-58, 66, 68, 71

10/19 Review
10/20 Test of Chapter 3 Post-Test HW read 4.1, do p.184/1-25 odd

Post test homework - intro to the Chain Rule

2009-10-05T16:21:00.002-04:00

You homework is to take a peak at the Chain Rule - the last of our derivative rules. Read section 3.6 and do p.146-147/1-27 odd. I will prove it tomorrow.

Questions from today's handout

2009-10-01T20:07:00.002-04:00

You may have already noticed but at the top of today's handout of problems it mentions that you can get worked solutions for the odd problems from www.CalcChat.com (though you may need to download Shockwave to use it).

I noticed also that problem 6 is really a Chain Rule problem (sneaky cx) so you can skip that one.

Here are my answers for the even problems:
2. y - 4 = 4(x - 2) and y - 1 = -2(x + 1)
4. a] tangent y - 4 = 4(x - 2)
    b] normal   y - 4 = =0.25(x - 2)
    c] y = 0
    d] normal = curve: y = (-1/2a)(x - a) + b = x^2 (where b = a^2)
         if you use the quadratic formula to solve for x you find the
          discriminant is positive so there are two solutions.
6. skip it
14.a] v = (-27/5)t + 27 and a = -27/5
    b] v = 27(1 - .2t) = 0 so t = 5
    c] a = 5.4 ft/sec^2 rather than 32 ft/sec^2, about 1/6^th

The first half of Chapter 3

2009-09-21T14:07:00.002-04:00

This the the syllabus up to the next test. We will probably have a test after section 3.5.

9/21 Finish up the intro HW p.102-104/16-18,20,22,23,25,26,28 plus nDeriv Worksheet
9/22 Continuity, Local Linearity, etc. HW p.111-112/4-20 by 4's, 21-23,29,30 plus Smoothness Worksheet
9/23 Rules of Differentiation HW p.120/1-19 odd, 20-23, 25
9/24 Proofs of Rules HW p.120-121/27-31 odd, 33-39

9/28 Yom Kippur (no school)
9/29 3.4 (Rates of Change)
          HW p.129-133/1-3,5,8,9,12,13,16,20,21,23-32,34,36
9/30 3.5 (Trig Differentiation)
          HW p.140-141/1-13 odd,17-21,23,27-29,31-33,35
10/1 Review of 3.1-3.5 (all questions answered)

10/5 Test of 3.1-3.5
          HW read 3.6, do p.146-147/1-27 odd

Upcoming "events"
10/01 Back to School Night
10/12 Columbus Day
10/14 Professional Development Day
11/06 Term 1 ends

Computer Lab Links

2009-09-14T22:09:00.001-04:00

The computer lab deals with rate of change using actual data recorded by Mr. Richardson when he used to ride his bike from his old apartment in Bedford.

http://lhs.lexingtonma.org/Teachers/Kelly/calcbc/bikeride/

The link is to a page of Mr. Kelly's. His page mentions that the directions were handed out in class. I am going paperless with this. You will open the directions, type your answers directly into the document, and email it to me, along with any other work required. Please use a different font or color so it is easy to find your answers.