BC Calculus

Multivariable Calculus Continues up to the Final

2009-05-12T09:24:00.002-04:00

5/12 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
5/13 13.4 Differentials
          HW problems 1-9 odd, 11-16, 17, 19, 20, 27, 30-32, 34-36, 40
5/14   Half-Day, no class
5/15   13.6 Directional Derivatives and Gradients
          HW problems 1-8, 13-18, 21-24 , 27, 28, 39, 40a-43a

5/19   13.6 Applications of the Gradient (Math MCAS Day 1)
           HW problems 44-52, 55-63 odd, 64, 73
5/20   13.8 Extrema of Functions of Two Variables (Math MCAS Day 2)
           HW problems 1-13 odd, 21, 23, 26, 31, 33, 41, 42, 45-47
5/21   13.9 Applications of Extrema and Review
           CW1, 3, 5, 9, 10, 14, 15
5/22   Multivariable Test

5/26   Last Questions (from you and from me)
5/27   Juniors make groups, start project 1
5/28   Final Day 1
5/29   Final Day 2

Starting Multivariable Calculus

2009-05-09T08:45:00.004-04:00

If you did not take the Extension Material test on Friday, that should be done by Tuesday.

On Thursday we started looking at multivariable calculus - though only the function aspect of it. Here is the homework:

"13.1 Introduction to Functions of Several Variables,"
exercises 31, 33, 35, 37, 43 (skip confirming), 45-48, 49-59 odd, 63-66.

We will spend the next two weeks on this material, culminating in a test on May 22nd.

Trig Substitutions

2009-04-16T14:56:00.002-04:00

Trig Substitutions is the last bit of 8.4 that we never got to. We have now done the whole book! Make sure you try these because there are almost impossible to understand without trying a few.

HW p.452-453/35-41 odd, 43-46

See sample problems!

2009-04-13T17:06:00.002-04:00

I have uploaded a document with some sample AP problems on Integration and the Fundamental Theorem of Calculus. Download the document here. Be ready for the quiz.

Here are some FTC AP problems for you to try...

2009-04-09T13:27:00.002-04:00

2007 AB3
2006 AB3
2004 AB5
2003 AB4

Review Topics, etc.

2009-04-08T22:48:00.006-04:00

Here is a proposed syllabus for review and extensions (it might change):

4/08 Second-Order Differential Equations (HH 11.10/1-11 odd, 13-23)
4/09 Integration and the Fundamental Theorem of Calculus

4/14 Integration & its Applications (area & volume, rates in & out, etc)
4/15 Trigonometric Substitutions for Integration
4/16 Derivative of the inverse, Curve Sketching, Linarization
4/17 Optimization, Implicit Differentiation, Related Rates

4/28 Power and MacLauren series
4/29 Hyperbolic Trig Functions
4/30 Fourier Series
5/01 the hard 1998 Multiple Choice Questions

5/05 last questions from you
5/06 AP Exam at 8am
5/07 Review Extension material
5/08 Test of Extension Material

After this we will study Multivariable Calculus for a few weeks, have a test on that, then the final. Projects for juniors after the seniors leave.

First topic for Review/Extensions

2009-04-02T22:17:00.002-04:00

First up: Differential Equations

4/02 Review Differential Equations Graphically (Slope Fields),
          Numerically (Euler's Method), Algebraically (straight integration
          with initial value, separation of variables, known format of
          outcome) HW 5 AP problems
4/03 Application problems (Hughes-Hallett section 11.6)
          HW handout/1, 4-8, 12-14, 21-24
4/07 AP Problem Quiz
          Systems of Differential Equations (Hughes-Hallett section 11.8)
          HW handout/1-17

Wrapping up the Series Convergence Section

2009-03-21T12:10:00.002-04:00

The last of the assigned convergence homework is from the chapter review.

p.509/1-16, 41-52 odd (evens are optional, any extra problems are helpful)

Next week's syllabus
3/24 2 more AP problems
3/25 Test of Series Convergence (9b)
3/26 Multiple Choice portion of 2003 AP Exam (1A in class, 1B for HW)
3/27 Open Response portion of 2003 AP Exam (2A in class, 2B for HW)

We will score the 2003 exam on Tuesday, 3/31. I will collect the score sheets so make sure you do the test and bring the answers. Next week is MCAS. We will meet at 12:30 on Tuesday, not meet on Wednesday. Thursday and Friday classes meet at the usual time.

The last of the convergence tests

2009-03-17T15:07:00.002-04:00

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

Convergence - the first set of tests

2009-03-12T15:34:00.002-04:00

After a discussion of Convergence and some "Guess-Who" tests to determine if it is happening,

3/12 p.492/Exploration1 and p.495/1-15 odd (not 5, 11), 23-29 odd
3/13 p.495-6/33, 34-40 even, 52 and p.506/1-11 all

Post Test Homework

2009-03-11T13:27:00.002-04:00

We will be starting section 9.4 - Convergence of Series. To be ready you need to come into class with some idea of what is going on. †To that end, here is the post-test homework:

read 9.4 to mid page 490 then do p.495/5,11,17-21,35,37,39

The rest of the easy part of series

2009-03-04T14:39:00.003-05:00

3/04 Error and Error Bounds HW do Explorations 1 & 2 in Section 9.3 plus
p.486-7/16-23, 27, 28, 30, 32 and (optional challenge) 29, 33, 34
3/05 Half-Day C B H F More with error - Hughes-Hallett 10.4 (third ed.)
HW problems 1-15 in handout
3/06 Extra Problems HW finish handout

3/10 Go over extra problems, AP problem, review
3/11 Test of 9.1-9.3 plus HH 10.3 and 10.4

Beginning our study of Infinite Series

2009-02-24T14:50:00.002-05:00

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. The date of the test is, tentatively, Wednesday, March 11.

2/24 9.1 Infinite series, power series, intervals of convergence
                HW p.466-7/1, 2, 3-15 odd, 17-23, 36-41
2/25 9.1 Finding series that represent functions
                HW p.468/42-53; read p.469-474; do Explorations 1 and 2
2/26 9.2 Taylor and Maclaurin series
                HW p.478/1-18, 20, 21, 26, 27, 30, 31
2/27 HH 10.3 Finding and using Taylor series
                HW handout/1-22
3/03 9.2 More with Taylor series
                HW p.478-9/19, 22, 24, 25, 28, 29, 32 and p.486/1-10

Improper Integrals and Vacation

2009-02-10T13:01:00.003-05:00

The leadup to February vacation is one section of Chapter 8 - Improper Integrals. These are integrals that go to infinity, either vertically or horizontally.

2/10 Post-test HW read 8.3 pp.433-435 and
do p.442/1,4,7,12-14,20,21,23-25
2/11 Vertically Infinite HW p.442/remaining odd #'s of 3-21, 33, 37, 43
2/12 Comparison Tests HW p.442/rest of 27 - 46
2/13 CW p.443/49, 52, 53, 54

More with Chapter 10 (up to vacation!)

2009-01-26T22:34:00.002-05:00

Here is the proposed syllabus for the rest of the chapter. Snow days (and any discretionary decisions on my part) may change things.

1/23 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
1/29 10.4 Modeling Projectile Motion (p.539-545)
          HW p.549-550/3, 5-8, 13, 19-21
1/30 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
2/05 10.6 Polar Curve Length and Surface Area
          HW p.567-568/31-39, 41-47 odd
2/06   Review

2/10   Ch 10 Test

There will be some Improper Integrals (oh boy!) up to vacation.
2/14-2/22 February Break

The start to Chapter 10, more later

2009-01-22T21:59:00.004-05:00

Chapter 10 is calculus with parametric and polar curves. We start with the parametric.

1/22 10.1 Parametric Review
HW p.518-519/1-19 odd, 23-27, 31, 32, 35, 37 and
p.520-526/read review of vectors in the plane (not ex. 6)

The derivation of our surface area formula

2009-01-18T21:29:00.003-05:00

I felt that my presentation of the formula for the surface area involved too much hand waving and not enough validation for the formula that we were using. To that end I have typed up a derivation of the lateral surface area for a frumstum. You can download the pdf here. If you still have questions, send me an email.

Ch 7 - Area and Volume using Calculus

2009-01-06T16:24:00.006-05:00

Here is the Chapter 7 syllabus. Plan accordingly. We lose a day of class due to the half-day so I am putting the non-lecture homework on that day.

01/06 7.2 Area between Curves HW p.380-382/1-35 odd, 43
01/07 Snow Day
01/08 7.3 Volume of Shapes, Discs & Washers HW p.390-392/1-16
01/09 7.3 Volumes of Shells HW p.392-393/17-33 odd, 39-43

01/13 7.3 Extra Problems HW p.392-394/28-34 even, 35 (by shells),
47, 51-53, 66-68
01/14 7.4 Length of Curves HW p.399-400/1-21 odd, 22, 23, 26, 28, 29
plus 7.1 p.371-373/1-11 odd, 12-16, 17-21 odd
01/15 Half-day B A G F
01/16 7.3 Surface Area HW handout of problems

01/19 Martin Luther King Day - no school
01/20 Review, end of Term 2
01/21 Ch 7 Test HW read pp.404-407, do p.410/27-30 and p.415/42, 43

Chapter 6 - The indefinite integral

2008-11-25T12:22:00.006-05:00

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. The [tight] schedule is posted so early because of the post-Ch 5 test homework.

12/02 Ch 5 Test, Anti-derivative homework p.312-314/1-23 odd, 52
12/03 Substitution method undoes chain rule differentiation
           HW p.321-323/1-38, 45-48, 50, 51 all due 12/05
12/04 CW: Bring books to work while many are at the band field trip
12/05 Integration Quiz 1; Integration by Parts undoes the product rule
           HW p.328-329/1-4, 9, 11, 15, 19-24, 27, 29

12/09 Int Quiz 2; More Integration by parts (bring books)
           HW p.329/13, 14, 17, 18, 25, 28, 35-37
12/10 Int Quiz 3; Partial Fraction Decomposition (8.4, ex 1 & 4 only)
           HW p.451-453/1,4, 6-16, 25, 26
12/11 Int Quiz 4; Intro to Differential Equations (initial value problems)
           HW p.312-315/25,26,31-41 odd, 51, 53, 55, 60-63, 65, 67
12/12 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.347-8/1,2,5,6,9,15,16
12/17 Logistic Functions (& put Slope Field program in calculator)
           HW p.347/3,4,7,8,11-14,17-33 odd
12/18 Slope Fields (graphical diff. eqtns) & Euler's Method
           (numerical diff. eqtns) HW p.313/27-30,43,44,65,66
           & p.355-6/2,3,5,7,9,10,15abc,19,20,23 & HH handout/42-47
12/19 Wrap-up of Integration techniques and solving differential equations

12/23 Ch 6 Test

12/24-1/5 Christmas vacation
           (note: Monday, January 5th, is Parent Conferences - no school)

Finishing up Ch 5

2008-11-17T10:58:00.003-05:00

The rest of the chapter straddles the Thanksgiving break.

11/25 Trapezoidal Rule (5.5), Review
           HW p.295-297/1, 3, 5-9,1 1, 12, 17 (not d), 22, 23
11/26 Half-Day A C F H    Simpson's Rule
11/27 Thanksgiving

12/02   Chapter 5 Test

The beginning of Chapter 5

2008-11-13T21:20:00.001-05:00

This is the proposal. It might change but I hope not. Chapter 5 is when we start looking at going the other way - e.g. if you start with the derivative, what is the function? To be ready, you need a rectangular area approximation program in your calculator.

11/12 HW Enter RAM program in calculator plus p.229-231/16-18,50,51
11/13 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
11/14 Integration and Integral Properties (5.2, 5.3)
             HW p.267-268/29-47 odd and p.274-275/1-6

11/18   Average Value of a Function (5.3)
              HW p.275-276/26, 29-42, 46
11/19   Fundamental Theorem of Calculus (5.3, 5.4)
              HW p.275/7-27 odd and p.286/1-17 odd
11/20   More tricky integrals with the Fundamental Theorem (5.4)
              HW p.286-287/19-35 odd, 37-46 (bring your book)
11/21   And more... (5.4, bring your book)
              HW p.287-288/47-56, 60-64

Post-test homework

2008-11-12T17:20:00.001-05:00

To be ready for the start of Chapter 5 tomorrow, you need to enter the RAM program in your calculator (a copy of the program is on my desk if you didn't get it). Also, do the following Newton's Method problems:
p. 229-231/16-18, 50, 51

The rest of the derivative application problems

2008-11-01T10:30:00.003-04:00

Here are the rest of the assignments for the derivative applications in Chapter 4 (and a bit of 8)

10/31 Linear Approximation (remember: read the handout, not the book)
            HW handout/1-10,14-17 and p.229-231/11-14, 52

11/04 Linear Approximation cont. (percent change problems)
            HW handout/11-13 and p.230-231/31-45 odd
11/05 L'Hopital's Rule (using derivatives to find limits)
            HW p.423-425/1-47 odd, 50, 52
11/06 Related Rates (derivatives with implicit parametrics)
            HW p.237-239/3,5,6,9,11-13,15,18-22,24
11/07 Related Rates cont. (bring your books)
            HW p.240-241/27,28,30,32,34,35,37,39,40,41

11/11 Veteran's Day - no school
11/12 Proposed date for the test

Optimization Homework

2008-10-30T09:24:00.002-04:00

10/29 p.214-217/1,5,7,9,15,17,20,22,25,26,28,32,34,36

10/30 p.217-219/39-42, 43- 49 odd

Some Chapter 4 homework

2008-10-27T14:45:00.004-04:00

The first part of Chapter 4 is conceptual, the rest is applications. Here is the conceptual homework (sorry I didn't post this earlier, I thought I had).

10/23 4.1 cont. Local & Absolute Extreme and Critical Points
             HW p.184-185/27-43 odd, 36, 45-53

10/24 4.2 Mean Value Theorem
             HW p.192-193/3,5,9,13,15-20,21a,24a,25-33 odd,
                   36,39,40,50,51a

10/28 4.3 Second Derivative Test
             HW p.204-206/8-29 by 3's, 31-39 odd, 41-48