The Indefinite Integral - Ch 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.

12/07  Intro to Differential Equations (initial value problems)
          HW p.327-330/1-23 odd, 65-70

12/10  Slope Fields (graphical diff. eq) & Euler's Method (numerical diff. eq)
          HW finish handout and p.328-329/41-49 odd, 51-58
12/11  Substitution method undoes chain rule differentiation
          HW p.337-339/1 - 39 odd, 69, 77 (the last one will be turned in - be neat)
12/13  Integration  Quiz 1;  Changing limits of integration
          HW p.338-340/41, 43, 45, 53-67 odd, 68, 79
12/14  Int  Quiz 2;  Integration by Parts undoes the product rule
          HW p.346-347/1-16, 33, 36, 39, 41

12/17  More (Harder) Integration by parts
          HW p.347-348/17-31 odd, 34, 35, 43, 47-56
12/18  Int Quiz 3;  Higher Powers of Trig Functions and Trig Substitution (additional notes)
          HW p.338, 340/47-52, 81-84 and packet problems 1-3,7,13,17,22,27,34,35,38,39
12/20  Differential Equations by Separation of Variables
          HW from Hughes-Hallett handout/3-42 by 3's, 28, 43-47
12/21  Int Quiz 4;  Multiple Choice Questions from Ch 4

12/22-1/2  Christmas vacation (note: Wednesday, January 2th, is Parent Conferences - no school)

01/03  Recap and Exponential Growth and Decay
          HW finish handout and 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)
01/04  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)

01/07  Int Quiz 5;  Logistic Functions
          HW p.369-371/15-35 odd, 36, 37, 44-46
01/08  Laplace Transforms (Day 1 - Intro)
          HW finish proofs in handout
01/10  Int Quiz 6;  Laplace Transforms (Day 2 - Technical Skills) [Half Day B A G F]
          HW finish problems in handout
01/11  Laplace Transforms (Day 3 - Applications)
          HW finish application problems in handout

01/14  Wrap-up of integration techniques and solving differential equations
01/15  Ch 6 Test

01/18  End of Term 2

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.

11/13  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)
11/15  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
11/16  Defining the Definite Integral and looking at Integration Properties (5.2, 5.3)
           HW p.283-284/33-39 odd, 47-51 odd  and p.290-291/1-6

11/19  Average Value and the Mean Value Theorem for Integrals (5.3)
           HW p.291-292/7-10, 14-18, 37-42, 47
11/20  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
11/21  Half-day A C F H
11/22  Thanksgiving
11/23  Black Friday

11/26  Derivatives of Integrals with the Chain Rule (5.4)
           HW p.302-303/3-24 by 3's, 45-54
11/27  More problems to practice (5.4)
           CW/HW p.303-305/55-64, 68-71, 73, 75-79
11/29  Trapezoidal Rule (5.5)
           HW p.312-314/1, 3, 5-7, 9-11, 20, 21, 27, 30, 39
11/30  Simpson's Rule (5.5)
           HW finish handout

12/03  Recap and Review
12/04  Review and Extension
12/06  Ch 5 Test of the Definite Integral

Applications of the Derivative (Ch 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.

10/18  4.1  Extreme Values of Functions
                 HW p.194-195/15-30 by 3's, 31-43 odd, 44, 51, 53, 55
10/19  4.2  Mean Value Theorem and Antiderivatives
                 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
10/26  4.5  Linear Approximation (using a different book)
                  HW handout/1-12 18-20, 24, 25

10/29  Hurricane - no school
10/30  Hurricane damage - no school
11/01  4.5  Using the Approximation
                  HW handout/21-23, 26, 27  and book p.244-245/46, 48, 50, 51, 53-56, 66, 71
11/02  8.2  L'Hopital's Rule (using derivatives to find limits)
                  HW p.450-452/13-47 odd, 53, 55, 58, 68, 70-72

11/05  4.6  Related Rates (everything depends on t)
                  HW p.251-254/3-39 by 3's
11/06  Professional Development Day - no school
11/08  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
11/09  Review and extra problems (DRAFT of answer key)

11/12  Veterans' Day - no school
11/13  Chapter 4 Test

The Derivative, 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
10/05  Implicit Differentiation (3.7)
           HW p.162-164/3-42 by 3's, 43, 45, 48-53, 56, 65

10/08  Columbus Day - no school
10/09  Derivatives of Inverse Trig Functions (3.8)
           HW p.170-171/3-27 by 3's, 28, 29, 31-34, 47-49
10/11  Derivatives of Exponential and Logarithmic Functions (3.9)
           HW p.178-180/3-42 by 3's, 49-51, 53, 64, 65
10/12  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.

10/15  Review and Extra Problems
10/16  Chapter 3 Test
           HW read 4.1 and do p.193-194/1-12

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.

9/14  Introduction to Differentiation HW do p.105/1-12

9/17  Rosh Hashannah
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
9/21  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 p.124-126/42-45, 48, 51, 52, 59 and p.140/50
9/26  Yom Kippur (no school)
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
9/28  3.5 (Trig Differentiation)
         CW 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)
10/2  Test of 3.1-3.5
         HW read 3.6, do p.153/1-27 odd

Upcoming "events"
10/04 Back to School Night
10/08 Columbus Day
11/02 Term 1 ends
11/06 Professional Development Day
11/12 Veterans' Day

Answers to the multiple choice problems

Quiz 2.1-2.2   B  A  D  B  E  D  D  B

Quiz 2.3-2.4   C  E  3:(one possible answer below)  C  A  D  E

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. 

8/30  Introduction to Calculus: slope of curves, area under curves

8/31  no school

9/03  Labor Day
9/04  2.1 Review Limits: what they are, notation, rules for operations, 7 ways of finding limits
              CW Sandwich Thrm Proof,  HW Worksheet of limit problems
9/06  2.1 Limit of Composed Functions, substitution   Half Day C B A G
              HW finish worksheet and p.68/59-62, read section 2.2           
9/07  2.2 Horizontal & Vertical Asymptotes, End Behavior
               HW p.76-77/1, 3, 5, 9-12, 15-55 odd, 65, 67, 69, 70

9/10  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
9/11  2.4 Rate of Change and Tangent lines
               HW p.92-94/3-21 by 3's, 43, 44, 47-49
9/13  2.4 and Review
               HW (suggested) p.95-97/3-15 by 3's, 16-24, 30, 33, 39-42, 45, 47, 48, 52

9/14  Ch 2 Test

               (if possible) HW read section 3.1, do p.105/1-12

9/17  Rosh Hashanah - no school
9/26  Yom Kippur - no school

Welcome!

This blog is intended to provide a syllabus, homework, and any hints or requests that I may have for you.  The course moves quickly (a year of college math in a year of high school) so you want to make sure that you keep up.

The first week of school we only meet once, on Thursday the 30th at 8:40 until 9:50.  With this 70 minute block we will have the chance to get acquainted and then dive right in.  It is an exciting year.  I hope you are looking forward to it as much as I am.