Parametric, Vector and Polar Functions

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  Review
2/10  Extra Problems
2/11  Ch 10 Test

2/13-22  February Break

Ch 7 Review and the Answer Key

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

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

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

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

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

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

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

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

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