BC Calculus

Ch 7 - Area and Volume using Calculus

2009-01-06T16:24:00.002-05:00

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 7.3 Volume of Shapes, Discs & Washers HW p.390-392/1-16
01/08 7.3 Volumes of Shells HW p.392-393/17-33 odd, 39-43
01/09 7.3 Extra Problems HW p.392-394/28-34 even, 35 by shells, 47, 51-53, 66-68

01/13 7.4 Length of Curves HW p.399-400/1-21 odd, 22, 23, 26, 28, 29
01/14 7.3 Surface Area HW handout of problems plus p.371-373/1-11 odd, 12-16, 17-21 odd
01/15 Half-day B A G F
01/16 Review, end of Term 2

01/19 Martin Luther King Day - no school
01/20 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

The rest of the Ch 3 homework

2008-10-14T15:37:00.003-04:00

The rest of Chapter 3 is as follows:
10/14 3.7 Prove power rule for rational powers
            3.8 Derivatives of Inverse Trig Functions
            HW p.156-157/46-51    p.162-163/1-19 by 3's,20,21-33 odd,34
10/15 3.9 Derivatives of Exp and Log Functions
            HW p.170-171/1-41 alternating odds,42,47-50,52
10/16 Professional Development - no school
10/17 3.9 Logarithmic Differentiation   HW p.170/19,20,43-46; p.172/22

10/21 Review or Test Post-Test HW read 4.1, do p.184/1-25 odd
10/22 Test or Start 4.1

More details for the Chapter 3 plan of attack

2008-09-26T21:43:00.006-04:00

Here is a more updated version of what we are doing for the next two weeks (when we actually have class):

9/26 3.4 (Rates of Change) and 3.5 (Trig Differentiation)
         HW p.129-133/1-3,5,8,9,12,13,16,20,21,23-32,34,36
         HW p.140-141/1-13 odd,17-21,23,27-29,31-33,35 (14-16 were CW)

9/30 Rosh Hashanah, no school
10/1 2nd day of Rosh Hashanah, no me
10/2 Review of 3.1-3.5 (all questions answered)
10/3 Test of 3.1-3.5
         HW read 3.6, do p.146-147/1-27 odd

10/07 3.6 Chain Rule (some more)
          HW p.147-148/33-49 odd, 60-65
10/08 Parametrics CW p.147-148/50-58, 66, 68, 71
10/09 Yom Kippur, no school
10/10 3.7 Implicit Differentiation
          HW p.155-156/3, 7, 11-37 odd, 40-45

Next step with derivatives

2008-09-19T15:36:00.004-04:00

This the the syllabus for next week. We will probably have a test after section 3.5.

9/19 Finish up the intro HW p.102-104/16-18,20,22,23,25,26,28
         plus nDeriv Worksheet
9/23 Continuity, Local Linearity, etc.
         HW p.111-112/4-20 by 4's, 21-23,29,30 plus Smoothness Worksheet
9/24 Rules of Differentiation HW p.120/1-19 odd, 20-23, 25
9/25 Proofs of Rules HW p.120-121/27-31 odd, 33-39
9/26 Velocity and Rates of Change
         HW p.129-133/1-3,5,8,9,12,13,16,20,21,23-32,34,36

Upcoming "events"
9/30 Rosh Hashanah (no school)
10/02 Back to School Night
10/09 Yom Kippur
10/13 Columbus Day
10/16 Professional Development Day
10/31 Term 1 ends

Starting Chapter 3

2008-09-18T13:23:00.002-04:00

This is a big chapter so we will start easy. The post-test homework is to read section 3.1 and do p.101/1-6, 11-13.

The Extra Problems Answer Key

2008-09-17T18:44:00.002-04:00

I have uploaded in FirstClass the answer key for the worksheet of extra problems that I handed out today. If you want to download the pdf, you can get that here.

I will probably be on the computer late if you want to email me any questions (though I can't promise anything).

Finishing the Bicycle Lab

2008-09-16T14:05:00.002-04:00

Here is the link for the Bicycle Lab. http://lhs.lexingtonma.org/Teachers/Kelly/calcbc/bikeride/
Remember that you need to fill in the answers on the "Directions" document and email it to me by the end of the day on Thursday (even though we have the test the same day.

Scheduling change

2008-09-14T12:38:00.002-04:00

Since I decided to move the Chapter 2 test to Thursday, the assignments changed slightly.

9/12/08 2.4 p.87-90/3-21 by 3's, 37, 38, 41, 42, 43
9/16/08 Computer Lab 700 (try the Excel tutorial in the Bicycle Lab)
9/17/08 2.4 continued and Review
p.91-93/3-12 by 3's, 15-24, 30, 33, 39-42, 45,47,48,52
9/18/08 Chapter 2 Test and Bicycle Lab homework due
9/19/08 Start Chapter 3 (it's a big one!)

The rest of Ch 2

2008-09-08T16:41:00.003-04:00

Here is the syllabus for the rest of chapter 2. The point of telling you all of this early is that you can see what is coming and budget your time accordingly. Remember, you want to keep up not make up so that you are ready for class every day.

9/09 2.2 Limits with Infinity p.71-73/1,3,5,11-49 odd,52-54,56,58,59
9/10 2.3 Continuity p.80-81/1,5,9,11,14, 15-29 odd, 33-38, 41, 42, 45-47
9/11 Half Day C B A G
9/12 2.4 Rates of Change and Tangents p.87-90/3-21 by 3's, 37,38,41,42
Review p.91-93/3-12 by 3's, 15-24, 30, 33, 39-42, 45,47,48,52
9/16 Bicycle Lab in room 700 (finish for homework, due 9/18)
9/17 Chapter 2 Test

More with limits

2008-09-06T13:46:00.002-04:00

We went over a theorem about the limits of composed functions (with an important exception) and how to use substitution to simplify finding limits.

Homework: text p.64/53-56, read section 2.2 (p.65-71), finish worksheet of limit problems.

Note: If you are checking your answers for the worksheet, they are 1. 1, 2. 2, 3. 1, 4. 0 and 5. -1/4

Our first homework assignment

2008-08-27T20:37:00.002-04:00

We reviewed limits today (section 2.1 in the text) - specifically looking at ways to evaluate them or determine if no limit exists. Finish the worksheet from class and do the following problems:
pp.63-64/12, 16, 20, 23, 26-28, 31, 41, 42, 43-51 odd
Tomorrow is the sandwich theorem.

Welcome!

2008-08-26T13:11:00.008-04:00

Welcome to BC Calculus. This year we will do two semesters of college calculus by May 6th, 2009 (the date of the AP Exam). After that we will do some other fun things because the math never ends...

This class goes very quickly so there are many homework problems each night, certainly more than you want to do the night before a test. KEEP UP!!! We learn lots of cool stuff and you don't want to waste time not understanding it.

Let's go!

Final Projects for non-seniors

2008-05-30T14:20:00.000-04:00

Our schedule for the rest of the year is as follows:

5/28 Pick groups and projects, assign initial research duties

6/03 MCAS (Hr G H E) Work on project
6/04 MCAS (E F A D) no class
6/05 Work on project
6/06 Finish up project, assign presentation duties

6/10 Oral and written presentation of project

6/16 Last Day of School
6/17 Get your grades

3D Extrema Homework

2008-05-19T16:02:00.001-04:00

Our last two sections of Multivariable Calculus concern extrema and their applications.

5/20 13.8 Extrema of Functions of Two Variables
           HW p.958-959/1-13 odd, 21, 23, 26, 31, 33, 41, 42, 45-47

5/21 Return AP Open Response Problems
          13.9 Applications of Extrema
           HW p.964-965/1-5 odd, 9, 10, 14, 15

5/22 Review with classwork problems

5/27 Multivariable Test

Multivariable Calculus

2008-05-09T12:53:00.001-04:00

We will be spending the rest of the time studying multivariable calculus. This is not in our book (the college version of our textbook with all three terms of calculus has it) so you will be getting handouts of pertinent sections. We will be using a different book (by Larson) which has better notation. Here is the syllabus and the first week of homework assignments:

5/09 13.1 Intro to Multivariable HW p.892-894/31-37 odd, 43 (skip
                                                       confirming), 4-48, 49-49 odd, 63-66

5/13 13.3 Partial Derivatives HW p.912-913/1-4, 6-27 by 3's,
                                                       29, 35, 37-40, 45, 47, 89-91
5/14 13.4 Increments and Differentials HW p.921-922/1-9 odd, 11-16,
                                                17,19,20,27,30-32,34-36,40 (see extra
                                                handout for specific instructions)
5/15 13.6 Directional Derivatives and Gradients HW p.940/1-8,13-18,
                                               21-24,27,28,39,40a-43a (just part a here)
5/16 13.6 Apps of the Gradient HW p.940-942/44-52, 55-63 odd, 64, 73

5/20 13.8 Extrema of Functions of Two Variables
5/21 13.9 Applications of Extrema
5/22 Review
5/23 No class (MCAS)

5/27 Multivariable Test
5/28 Sophomores and Juniors have class
5/29 Final Day 1 (Multiple Choice)
5/30 Final Day 2 (Open Response)

More review in the lead-up to the AP Exam

2008-04-18T21:59:00.000-04:00

More review of topics:

4/15 Integration and the Fundamental Theorem of Calculus
4/16 Integration & its Applications (area & volumes, rates in & out, etc.)
4/17 Curve Sketching (broadly defined)
4/18 Derivative of the inverse, Implicit differentiation

4/29 Power and MacLauren series
4/30 Related Rates, Linearization
5/01 Hyperbolic Trig functions
5/02 the hard 1998 Multiple Choice Questions

5/06 Last questions from you
5/07 AP Exam at 8am

This week in review: Differential Equations

2008-04-08T14:13:00.000-04:00

We start our AP Exam review with differential equations, as per your request.

4/08 Numerical and Graphical solutions (Euler's Method and Slope Fields)
           CW/HW AP Problems 2006B/AB5, 2006/BC5, 2001/BC5

4/09 Analytical Solutions (Separation of Variables, Partial Fractions, etc.)
           CW/HW AP Problems 1999/6, 2006B/5, 2007/4

4/10 AP Problem Quiz; Applications and Modeling (Hughes-Hallett 11.6)
           HW Handout problems 1, 4-8, 12-14, 21-24

4/11 Systems of Differential Equations (Hughes-Hallett 11.8)
           HW Handout problems 1-17

The AP Test as syllabus

2008-03-31T09:25:00.000-04:00

This week we will spend our time working through the 2003 AP Test to get a feel for what an entire test feels like and to determine what topics need special reviewing. The plan is below and timely completion counts.

4/1 CW Multiple Choice Part 1A (55 minutes, 28 questions, no calculator)
        HW finish Part 1A

4/2 CW Multiple Choice Part 1B (50 minutes, 17 questions, calculator)
        HW finish Part 1B

4/3 CW Free Response Part 2A (45 minutes, 3 questions, calculator)
        HW Free Response Part 2B (45 minutes, 3 questions, no calculator)

4/4 Score your partner's exam. Look over your scored exam and list
        what topics you would like reviewed. Turn in your scored answer
        sheet with the list.

We will review, with a couple of breaks for applications problems, until the
AP Exam on May 7th.