Workshop Calculus With Graphing Calculators

by Hastings, Nancy Baxter; Reynolds, Barbara E.; Laws, P. (CON); Callahan, K. (CON); Bottorff, M. (CON)

• ISBN13: 9780387986753
• ISBN10: 0387986758
• Format: Paperback
• Copyright: 1999-06-01
• Publisher: Key Curriculum Pr

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