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

Ch 4 - The Derivative, part 2

We finish up our study of finding derivatives by adding one more general derivative rule and taking the derivatives of inverses, exponential and logarithmic functions and functions for which we cannot solve for y.  Homework in red needs editing.

10/06  Post test homework: read 4.1, do p.160/1-27 odd

10/07  4.1  Chain Rule

           HW p.160-163/30-39 by 3's, 53-56, 58, 59, 61, 62, 67-69, 76-79
10/09  Professional Development Day - no school

10/12  Columbus Day - no school

10/13  4.2  Implicit Differentiation

           HW p.170-172/3-42 by 3's, 43, 46, 48-53, 56, 65

At this point, the PSAT day puts the two classes on a different schedule and G-Block will have an extra day of review before the test. Just follow along.

Day 3  4.3  Derivatives of Inverse Trig Functions

           HW p.178-179/3-27 by 3's, 28, 29, 31-34, 47-49

Day 4 4.4  Derivatives of Exponential and Logarithmic Functions, Prove Power Rule for all n

           HW p.186-188/3-42 by 3's, 49-51, 53, 64, 65

Day 5 4.5 Log Differentiation and Parametric Differentiation (4.1)

           HW p.187/43-48, 52, 54-56  and  p.161-162/41-49 odd, 50-52, 63, 66

           Here is a worksheet that puts the parametric/vector ideas together.

Day 6 Review and Extra Problems

10/22  Suggested Review Problems from the book: p.189-191/1-53 odd, 66, 67, 71, 73-75, 77, 78

10/23  Chapter 3 Test

           HW download and do handout on Curve Analysis

Ch 3 - The Derivative

This the the syllabus up to the next test.

9/21  Introduction to Differentiation HW do p.107/1-12

9/22  3.1 Finish up the intro HW p.107-110/19, 20, 22-24, 26, 27, 32-34, 42, 44 plus nDeriv Worksheet

9/23  Yom Kippur - no school
9/25  3.2 Continuity, Local Linearity, etc. HW p.116-117/4-12 by 4's, 13, 14, 31-33, 35-37, 39 plus Smoothness Worksheet
9/25  G-Block will do the nDeriv and Smoothness worksheets in class on Friday, section 3.2 on Thursday

9/28  3.3 Rules of Differentiation  HW p.126/3-21 by 3's, 13, 14, 23, 27-35 odd, 39, 41

9/29  3.3 Proofs of Rules  HW p.126-128/42-49, 50-59

9/30  3.4 Rates of Change  CW p.140-142/31,32,35,49  HW p.137-142/1,3,5,8-13,18-20,24-29, 46-48, 50

10/2  3.5 Trig Differentiation  CW p.148-149/24-26,50,51  HW p.147-149/1-9 odd,17-23 odd,27-31,33,36,37,39-42

10/5  Review (all questions answered) (Review Worksheet with Answer Key)

10/6  Test of Ch 3
         HW read 4.1, do p.160/1-27 odd

Upcoming "events"
9/30 Back to School Night
10/9 Professional Development Day - no school
10/12 Columbus Day - no school
10/14 PSAT Day - altered schedule

Chapter 2 - Limits and Continuity

Chapter 1 is prerequisite material that you are expected to remember so we will start with chapter 2...

Here is the plan for the whole chapter (to infinity and beyond!).  

9/03  Introduction to Calculus: slope of curves, area under curves

9/07  Labor Day - no school

9/08  Limits Handout to remember: what they are, notation, rules for operations, ways of finding limits
              HW Worksheet of limit problems and a Squeeze Theorem Proof

9/10  2.1 Limit of Composed Functions, substitution
              HW finish worksheet and p.68/65-68, read section 2.2     
9/11  2.2 Horizontal & Vertical Asymptotes, End Behavior
              HW p.76-77/1, 3, 5, 9-12, 15-55 odd, 65, 67, 69, 70

9/14  Rosh Hashanah - no school

9/15  2.3 Continuity, 4 Kinds of Discontinuities and the IVT

               HW p.84-86/1, 3, 8-11, 14, 15, 17-29 odd, 38-44, 47, 50-52, 60-62

9/17  2.4 Rate of Change and Tangent lines   Half Day C B A G
               HW p.93-96/3-21 by 3's, 47, 49, 50, 53-55

9/18  2.4 and Review  (Answer Key for Extra Rate-of-Change Problems)
               HW (suggested) p.97-99/3-15 by 3's, 16-24, 30, 33, 39-42, 45, 47, 48, 54

9/21  Ch 2 Test (list of topics)

               HW read section 3.1, do p.107/1-12
9/23  Yom Kippur - no school

Welcome!

I would like to welcome you to the fast paced world of BC Calculus.  Together we will go through a year of college calculus in a year of high school.  Calculus is the study of change and we will look at how many functions change and how we can apply these ideas to real problems.  Enjoy (and keep up with your homework!)!!