Ch 6 - The Indefinite Integral

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.

12/02  Intro to Differential Equations (initial value problems)
          HW p.327-330/1-23 odd, 65-70

12/03  Math Department Professional Development - no class

12/04  Slope Fields (graphical diff. eq) & Euler's Method (numerical diff. eq)
          HW finish handout and p.328-329/41-49 odd, 51-58
12/06  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

12/10  Int  Quiz 2;  Integration by Parts undoes the product rule
          HW p.346-347/1-16, 33, 36, 39, 41

12/11  More (Harder) Integration by parts
          HW p.347-348/17-31 odd, 34, 35, 43, 47-56

12/13  Int Quiz 3;  Higher Powers of Trig Functions and Trig Substitution (additional notes)

          HW p.338, 340/47-52, 81-84 and packet problems 1-10

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

12/17  Int Quiz 4; Exponential Growth and Decay

          HW p.357-361/8, 11, 13, 19, 29, 31, 33, 36, 39, 41-44, 53, 54, 58

12/18  Int Quiz 5;  Partial Fraction Decomposition
          HW handout problems 7-31 odd, 41, 43, 45, 47-50 (see book p.369-371/1-14, 47, 48 for more practice)
12/20  Longterm HW Mixed Integrals Worksheet (finish by January 10th)

12/21-1/2  Christmas vacation 

01/03  Snow Day

01/06  Recap and Logistic Functions

          HW p.369-371/15-35 odd, 36, 37, 44-46
01/07  Int Quiz 6; Laplace Transforms (Day 1 - Intro)

          HW finish proofs in handout

01/08  Laplace Transforms (Day 2 - Technical Skills)

          HW finish problems in handout
01/09  Half Day B A G F

01/10  Laplace Transforms (Day 3 - Applications)

          HW finish application problems in handout

01/13  Wrap-up of integration techniques and solving differential equations
01/14  Ch 6 Test
           HW 7.1  Integration as Net Change p. 386/1-11 odd, 12-16, 17-21 odd

01/17  End of Term 2

Chapter 5 - The Definite Integral

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.

11/06  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)

11/08  Area and Rectangular Approximation Methods (5.1)

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

11/11  Veterans' Day - no school

11/12  Riemann Sums and Defining the Definite Integral (5.2)

           HW p.282-284/9-27 by 3's, 33-39 odd, 47-51 odd

11/13  Integration Properties, Average Value and the Mean Value Theorem for Integrals (5.3)

           HW p.290-292/1-10, 14-18, 37-42, 47

11/15  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

11/19  More problems to practice (5.4)

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

11/20  Trapezoidal Rule (5.5)

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

11/21  Professional Development - no school

11/22  Review and Extension

11/25  Simpson's Rule (5.5)

           HW finish handout

11/26  Ch 5 Test of the Definite Integral

11/27  Half-day A C F H

11/28  Thanksgiving

11/29  Black Friday

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  4.1  Post-Test HW handout on Curve Analysis

10/18  4.1  Extreme Values of Functions

                 HW p.194-195/6-30 by 3's, 31-43 odd, 44, 51, 53, 55

10/21  4.2  Mean Value Theorem and Antiderivatives (proof of MVT)

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

10/22  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

10/25  4.4  AP Problem Quiz, more Optimization

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

10/28  4.5  Linear Approximation (using a different book)

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

10/29  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

11/01  4.6  Related Rates (everything depends on t)

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

11/04  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

11/05  Review and extra problems (Answer Key)

11/06  Chapter 4 Test (practice test and solutions)

11/12  Veterans' Day - no school

11/21  Professional Development Day - no school

11/27  Half-Day before Thanksgiving  A  C  F   H

Derivatives, part 2

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  Post test (3.6) HW p.153/1-27 odd

10/04  More Chain Rule (3.6)

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

10/07  Implicit Differentiation (3.7)

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

10/08  Derivatives of Inverse Trig Functions (3.8)

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

10/09  Derivatives of Exponential and Logarithmic Functions (3.9)

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

10/11  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.

10/14  Columbus Day - no school

10/15  Review and Extra Problems

10/16  Chapter 3 Test

           HW do handout on Curve Analysis

Chapter 3 - The Derivative, part 1

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

9/17  Introduction to Differentiation HW do p.105/1-12

9/18  3.1 Finish up the intro HW p.106-108/19, 20, 22-24, 26, 27, 32-34, 42, 44 plus nDeriv Worksheet

9/20  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

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

9/24  3.3 Proofs of Rules  HW p.124-125/33-41 odd, 46, 49, 50

9/25  3.3 CW/HW p.124-126/42-45, 48, 51, 52, 59 and p.140/50
9/27  3.4 Rates of Change  CW p.138/31,32,35,49  HW p.135-140/1,3,5,8-13,18-20,21,24-29,47,48

9/30  3.5 Trig Differentiation  CW p.146-147/24-26,50  HW p.147-148/1-9 odd,17-23 odd,27-31,33,36,37,39-42,51

10/1  Review of 3.1-3.5 (all questions answered) (Review Worksheet with Answer Key)
10/2  Test of 3.1-3.5
         HW read 3.6, do p.153/1-27 odd

Upcoming "events"
10/02 Back to School Night
10/14 Columbus Day

Beginning with Chapter 2 (and a schedule in chaos)

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. 

9/04  Introduction to Calculus: slope of curves, area under curves

9/05  Rosh Hashanah - no school

9/06  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

9/09  2.1 Limit of Composed Functions, substitution
              HW finish worksheet and p.68/59-62, read section 2.2         
9/10  2.2 Horizontal & Vertical Asymptotes, End Behavior
               HW p.76-77/1, 3, 5, 9-12, 15-55 odd, 65, 67, 69, 70

9/11  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

9/12  Half Day C B A G
9/13  2.4 Rate of Change and Tangent lines
               HW p.92-94/3-21 by 3's, 43, 44, 47-49

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

9/17  Ch 2 Test

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