Workshop Calculus With Graphing Calculators,9780387986753

Workshop Calculus With Graphing Calculators

by ; ; ; ;
ISBN13: 9780387986753
ISBN10: 0387986758
Format: Paperback
Pub. Date: 1999-06-01
Publisher(s): Key Curriculum Pr
List Price: $54.99

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Summary

This project is based on the use of graphing calculators by students enrolled in calculus. There is enough material in the book to cover precalculus review, as well as first year single variable calculus topics. Intended for use in workshop-centered calculus courses. Developed as part of the well-known NSF-sponsored project, Workshop Mathematics, the text is intended for use with students in a math laboratory, instead of a traditional lecture course. There are student-oriented activities, experiments and graphing calculator exercises found throughout the text. The authors are well-known teachers and innovative thinkers about ways to improve undergraduate mathematics teaching.

Table of Contents

Volume 2
PREFACE: TO THE INSTRUCTOR xi(8)
PREFACE: TO THE STUDENT xix
Unit 5: Derivatives and Integrals: First Pass 3(62)
SECTION 1: THE DERIVATIVE
5(33)
Task 5-1: Examining an Example
5(4)
Task 5-2: Discovering a Definition for the Derivative
9(3)
Task 5-3: Representing a Derivative by an Expression
12(5)
Task 5-4: Inspecting the Domain of a Derivative
17(5)
Task 5-5: Investigating the Relationship Between a Function and Its Derivative
22(4)
Task 5-6: Gleaning Information About the Graph of a Function from Its Derivative
26(12)
SECTION 2: THE DEFINITE INTEGRAL
38(27)
Task 5-7: Finding Some Areas
39(3)
Task 5-8: Describing Some Possible Approaches
42(1)
Task 5-9: Applying a Rectangular Approach
43(3)
Task 5-10: Considering the General Situation
46(4)
Task 5-11: Calculating Riemann Sums
50(4)
Task 5-12: Interpreting Definite Integrals
54(5)
Task 5-13: Checking the Connection Between Derivatives and Definite Integrals
59(6)
Unit 6: Derivatives: The Calculus Approach 65(82)
SECTION 1: DIFFERENTIATING COMBINATIONS OF FUNCTIONS
68(25)
Task 6-1: Examining the Power Rule
70(3)
Task 6-2: Applying the Scalar Multiple Rule
73(2)
Task 6-3: Using the Sum and Difference Rules
75(3)
Task 6-4: Employing the Extended Power Rule
78(2)
Task 6-5: Investigating the Product Rule
80(4)
Task 6-6: Engaging the Quotient Rule
84(2)
Task 6-7: Utilizing the Chain Rule
86(7)
SECTION 2: ANALYZING FUNCTIONAL BEHAVIOR
93(26)
Task 6-8: Contemplating Concavity (Again)
94(4)
Task 6-9: Utilizing Higher-Order Derivatives
98(3)
Task 6-10: Sketching Curves
101(6)
Task 6-11: Locating Absolute Extrema
107(12)
SECTION 3: DIFFERENTIATING TRIGONOMETRIC, EXPONENTIAL, AND LOGARITHMIC FUNCTIONS
119(28)
Task 6-12: Finding the Derivatives of sin(x) and cos(x)
119(3)
Task 6-13: Finding Derivatives of Functions Containing Trigonometric Expressions
122(4)
Task 6-14: Finding the Derivatives of e^(x) and e^f(x)
126(5)
Task 6-15: Finding the Derivatives of In(x) and In(f(x))
131(4)
Task 6-16: Finding the Derivatives of General Exponential and Logarithmic Functions
135(12)
Unit 7: Definite Integrals: The Calculus Approach 147(68)
SECTION 1: APPLYING THE RIEMANN SUM APPROACH TO OTHER SITUATIONS
150(28)
Task 7-1: Finding a Formula for Distance When the Velocity Varies
151(5)
Task 7-2: Integrating Functions Whose Graphs Dip Below the Axis
156(4)
Task 7-3: Interpreting Definite Integrals (Again)
160(3)
Task 7-4: Using Partial Riemann Sums to Approximate Accumulation Functions
163(4)
Task 7-5: Representing the Area Between Two Curves by a Definite Integral
167(11)
SECTION 2: CALCULATING ANTIDERIVATIVES
178(18)
Task 7-6: Examining How Antiderivatives Are Related
179(2)
Task 7-7: Finding Antiderivatives of Basic Functions
181(6)
Task 7-8: Finding Antiderivatives of Linear Combinations
187(3)
Task 7-9: Finding Specific Antiderivatives
190(6)
SECTION 3: FUNDAMENTAL THEOREM OF CALCULUS
196(19)
Task 7-10: Using Your Calculator to Compare Accumulation Functions and Antiderivatives
197(5)
Task 7-11: Testing Part II of the FTC
202(3)
Task 7-12: Applying Part II of the FTC
205(10)
Unit 8: Methods of Integration 215(80)
SECTION 1: INTEGRATING BY SUBSTITUTION
217(31)
Task 8-1: Equating Areas
218(7)
Task 8-2: Examining the Strategy Underlying Substitution
225(6)
Task 8-3: Inspecting Situations Where Substitution Applies
231(7)
Task 8-4: Using Substitution
238(3)
Task 8-5: (Project) Tracking the Human Race
241(7)
SECTION 2: USING INTEGRATION BY PARTS
248(15)
Task 8-6: Examining the Strategy Underlying Integration by Parts
250(3)
Task 8-7: Using Integration by Parts
253(3)
Task 8-8: (Project) Sounding Off
256(7)
SECTION 3: USING INTEGRATION TABLES
263(7)
Task 8-9: Looking Up Integrals
264(2)
Task 8-10: (Project) Finding the Right Water Level
266(4)
SECTION 4: APPROXIMATING DEFINITE INTEGRALS
270(25)
Task 8-11: Finding a Formula for the Trapezoidal Rule
271(3)
Task 8-12: Using the Trapezoidal Rule on a Function Without a Simple Antiderivative
274(2)
Task 8-13: Using the Trapezoidal Rule on a Data Set
276(4)
Task 8-14: (Project) Estimating the National Debt
280(2)
Task 8-15: Fitting a Curve and Using the Model
282(3)
Task 8-16: (Project) Finding an Average Temperature
285(10)
Unit 9: Using Differentiation and Integration 295(74)
SECTION 1: IMPLICIT DIFFERENTIATION AND INVERSE FUNCTIONS
297(20)
Task 9-1: Using Implicit Differentiation
298(2)
Task 9-2: Defining Inverse Trigonometric Functions
300(5)
Task 9-3: Differentiating Inverse Trigonometric Functions
305(4)
Task 9-4: Finding the Derivative of an Inverse Function
309(8)
SECTION 2: EQUATIONS INVOLVING DERIVATIVES
317(27)
Task 9-5: Solving Related Rates Problems
319(4)
Task 9-6: Investigating Differential Equations
323(3)
Task 9-7: Solving Separable Equations
326(5)
Task 9-8: Utilizing Euler's Method
331(13)
SECTION 3: MORE ON INTEGRATION
344(25)
Task 9-9: Evaluating Improper Integrals
345(5)
Task 9-10: Finding the Volume of a Solid of Revolution Using the Disc Approach
350(9)
Task 9-11: Finding the Volume of a Solid of Revolution Using the Washer Approach
359(3)
Task 9-12: (Project) Filling a Nectar Bottle
362(7)
Appendix: Table of Integrals 369(24)
Index 393

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