The Indefinite Integral and Differential Equations (Chapter 6)

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.

Note:  We will not be able to finish this chapter before Christmas break.

12/01  Parent Conferences
12/02  Ch 5 Test
12/04  Intro to Differential Equations (initial value problems)
          HW p.327-330/1-23 odd, 65-70 and download slope field calculator

12/05  Slope Fields (graphical diff. eq) & Euler's Method (numerical diff. eq)

          HW finish handout and p.328-329/41-49 odd, 51-58

12/08  Substitution method undoes chain rule differentiation
          HW p.337-339/1 - 39 odd, 69, 77 (the last one will be turned in - be neat)

12/09  Integration  Quiz 1;  Changing limits of integration
          HW p.338-340/41, 43, 45, 53-67 odd, 68, 79

12/11  Int  Quiz 2;  Integration by Parts undoes the product rule
          HW p.346-347/1-16, 33, 36, 39, 41

12/12  More (Harder) Integration by parts
          HW p.347-348/17-31 odd, 34, 35, 43, 47-56

12/15  Int Quiz 3;  Higher Powers of Trig Functions (additional notes) and Trig Substitution (additional notes)

          HW p.338, 340/47-52, 81-84 and packet problems 1-3,7,13,17,22,27,34,35,38,39

12/16  Differential Equations by Separation of Variables
          HW from Hughes-Hallett handout/3-42 by 3's, 28, 43-47

12/18  Int Quiz 4;  Exponential Growth and Decay

          HW p.357-361/3-11 odd, 21, 23, 25, 29, 31, 39, 41, 43, 44, 53, 54, 58

          Longterm HW Mixed Integrals Worksheet (finish by January 14th)
12/19  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)

12/22 Logistic Functions

          HW p.369-371/15-35 odd, 36, 37, 44-46

12/23  Calculus Jeopardy

12/24-1/4  Christmas vacation

01/05  Recap
          HW finish handout

01/06  Int Quiz 5;  Laplace Transforms (Day 1 - Intro)

          HW finish proofs in handout

01/08  Laplace Transforms (Day 2 - Technical Skills) [Half Day B A G F]

          HW finish problems in handout (copy of my answer key)

01/09  Int Quiz 6;  Laplace Transforms (Day 3 - Applications)

          HW finish application problems in handout

01/12  Wrap-up of integration techniques and solving differential equations

01/13  Ch 6 Test

01/16  End of Term 2

The Definite Integral (Chapter 5)

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.

11/07  Post Ch 4 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)

11/10  Area and Riemann Sums (5.1, 5.2)

           HW p.270-273/1, 4-12, 17, 19, 26, 29-36, 38, 39 (note, problem 6 refers to 5b, not 1b)

           and  p.282-283/9-27 by 3's
11/11  Veterans' Day - no school

11/13  Defining the Definite Integral and looking at Integration Properties (5.2, 5.3)

           CW Explorations on  p. 267 & p.279  HW p.283-284/33-39 odd, 47-51 odd  and p.290-291/1-6

11/14  Average Value and the Mean Value Theorem for Integrals (5.3)

           HW p.291-292/7-10, 14-18, 37-42, 47

11/17  The Fundamental Theorem of Calculus and Antiderivatives (5.3, 5.4)

           HW p.291-292/19-35 odd, 49, 51 and p.303/27-43 odd

11/18  Derivatives of Integrals with the Chain Rule (5.4)

           HW p.302-303/3-24 by 3's, 45-54

11/20  More problems to practice (5.4 though the CW problems are from another book)

           HW p.303-305/55-64, 68-71, 73, 75-79

11/21  Trapezoidal Rule (5.5)

           HW p.312-314/1, 3, 5-7, 9-11, 20, 21, 27, 30, 39

11/24  Simpson's Rule (5.5)

           HW finish handout
11/25  Review and Extension (handout with answer key)

11/26  Half-day A C F H

11/27  Thanksgiving

11/28  Black Friday

12/01  Parent Conferences

12/02  Ch 5 Test of the Definite Integral

Applications of the Derivative (Chapter 4)

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.

10/16  Post-Ch3 Test HW: download and do handout on Curve Analysis

10/17  4.1  Extreme Values of Functions

                 HW p.194-195/15-30 by 3's, 31-43 odd, 44, 51, 53, 55

10/20  4.2  Mean Value Theorem and Antiderivatives (proof of the MVT)

                 HW p.202-204/3-27 by 3's, 30-35, 41-49 odd, 59, 60

10/21  4.3  Curve Sketching from f ' and f ''

                 HW p.215-218/2, 4, 5, 7, 11-33 odd, 44-47, 51, 53, 61, 63

10/23  4.4  Optimization (using derivatives to find min/max)

                  HW p.226-229/1, 5-7, 12, 15-17, 19, 20-26 even, 27, 29, 31-34, 36

10/24  4.4  More Optimization

                  HW p.229-232/39-41, 45, 47, 48, 50, 58-61, 63

10/27  4.5  AP Problem Quiz, Linear Approximation (using a different book)

                  HW handout/1-12 18-20, 24, 25

10/28  4.5  Using the Approximation

                  HW handout/21-23, 26, 27  and book p.244-245/46, 48, 50, 51, 53-56, 66, 71

10/30  8.2  L'Hopital's Rule (using derivatives to find limits)

                  HW p.450-452/13-47 odd, 53, 55, 58, 68, 70-72

10/31  4.6  Related Rates (everything depends on t) (end of Term 1)

                  HW p.251-254/3-39 by 3's

11/03  4.6  More Related Rates (because everything depends on t)

                  HW p.251-254/5, 7, 10, 17, 19, 20, 22, 26, 31, 32, 42-46

11/04  Professional Development Day - no school
11/06  Review and extra problems (links: review, its answer key, a practice test, that answer key)

11/07  Chapter 4 Test

11/11  Veterans' Day - no school

The rest of Chapter 3

We finish up Chapter 3 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.

10/02  Chain Rule (3.6)  CW p.153/1-27 odd

           HW p.153-155/30-48 by 3's, 53-55, 59, 61, 62, 67-69, 76-79

10/03  Implicit Differentiation (3.7)

           HW p.162-164/3-42 by 3's, 43, 45, 48-53, 56, 65

10/06  Derivatives of Inverse Trig Functions (3.8)

           HW p.170-171/3-27 by 3's, 28, 29, 31-34, 47-49

10/07  Derivatives of Exponential and Logarithmic Functions (3.9)

           HW p.178-180/3-42 by 3's, 49-51, 53, 64, 65

10/09  Log Differentiation (3.9) and Parametric Differentiation (3.6)

           HW p.179/43-48, 52, 54-56  and  p.153-155/41-49 odd, 50-52, 63, 66

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

10/10  Proof of Power Rule for Rational exponents, Review and Extra Problems

10/13  Columbus Day - no school
10/14  Suggested Review Problems from the book: p.181-184/1-53 odd, 66, 67, 71, 73-75, 77, 78

10/16  Chapter 3 Test

           HW download and do handout on Curve Analysis

The first half of Chapter 3...

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

9/12  Introduction to Differentiation HW do p.105/1-12

9/15  3.1 Finish up the intro HW p.106-108/19, 20, 22-24, 26, 27, 32-34, 42, 44 plus nDeriv Worksheet

9/16  3.2 Continuity, Local Linearity, etc. HW p.114-115/4-12 by 4's, 13, 14, 31-33, 35-37, 39 plus Smoothness Worksheet

9/18  3.3 Rules of Differentiation  HW p.124/3-21 by 3's, 13, 14, 23, 27-35 odd

9/19  3.3 Proofs of Rules  HW p.124-125/37-41 odd, 42-46, 49, 50

9/22  3.4 Rates of Change  CW p.138,140/31,32,35,49  HW p.135-140/1,3,5,8-13,18-20,21,24-29

9/23  3.5 Trig Differentiation  CW p.146-147/24-26,50,51  HW p.146-148/1-9 odd,17-23 odd,27-31,33,36,37,39-42
9/25  Rosh Hashanah - no school
9/26  Extra practice (I am out) CW/HW p.124-126/47, 48, 51-59 and p.139-140/46-48, 50

9/29  Review of 3.1-3.5 (all questions answered) (Review Worksheet with Answer Key)

9/30  Test of 3.1-3.5
         HW read 3.6, do p.153/1-27 odd

Upcoming "events"
10/02 Back to School Night
10/13 Columbus Day

Topics for Chapter 2

The list of topics is downloadable here.

Don't forget the suggested list of problems: p.95-97/3-15 by 3's, 16-24, 30, 33, 39-42, 45, 47, 48, 52

Beginning with Chapter 2

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.  Things may change so check back if you are not sure. 

8/28  Introduction to Calculus: slope of curves, area under curves

9/01  Labor Day - no school

9/02  Limits Handout to remember: what they are, notation, rules for operations, ways of finding limits
              HW Worksheet of limit problems and a Sandwich Thrm Proof

9/04  2.1 Limit of Composed Functions, substitution
              HW finish worksheet and p.68/59-62, read section 2.2         
9/05  2.2 Horizontal & Vertical Asymptotes, End Behavior
               HW p.76-77/1, 3, 5, 9-12, 15-55 odd, 65, 67, 69, 70

9/08  2.3 Continuity and 4 Kinds of Discontinuities

               HW p.84-86/1, 5, 9, 11, 14, 15, 17-29 odd, 38-44, 47, 50-52, 60-62

9/09  2.4 Rate of Change and Tangent lines
               HW p.92-94/3-21 by 3's, 43, 44, 47-49

9/11  2.4 and Review  (Answer Key for Extra Rate-of-Change Problems)  Half Day C B A G
               HW (suggested) p.95-97/3-15 by 3's, 16-24, 30, 33, 39-42, 45, 47, 48, 52

9/12  Ch 2 Test

               HW read section 3.1, do p.105/1-12