Workshop Calculus With Graphing Calculators

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

• ISBN13: 9780387986364
• ISBN10: 0387986367
• 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 1
PREFACE: TO THE INSTRUCTOR	xi	(8)
PREFACE: TO THE STUDENT	xix
Unit 1: Functions	3	(60)
SECTION 1: MODELING SITUATIONS	4	(8)
Task 1-1: Relating Position and Time	5	(2)
Task 1-2: Describing a Process for Finding the Position at a Given Time	7	(1)
Task 1-3: Using the Concept of Function to Buy Pizza	8	(4)
SECTION 2: ANALYZING LINEAR FUNCTIONS	12	(19)
Task 1-4: Creating Linear Functions	12	(5)
Task 1-5: Examining Piecewise-Linear Functions	17	(14)
SECTION 3: ANALYZING SMOOTH CURVES	31	(32)
Task 1-6: Developing an Intuitive Understanding of a Tangent Line to a Curve	31	(8)
Task 1-7: Investigating the Behavior of the Tangent Line near a Turning Point	39	(4)
Task 1-8: Contemplating Concavity	43	(7)
Task 1-9: Interpreting Sign Charts	50	(13)
Unit 2: Function Construction	63	(72)
SECTION 1: REPRESENTING FUNCTIONS	65	(25)
Task 2-1: Becoming Familiar with Your Calculator	66	(2)
Task 2-2: Implementing Functions Using Expressions	68	(7)
Task 2-3: Representing Functions by Graphs	75	(4)
Task 2-4: Constructing Discrete Functions	79	(11)
SECTION 2: COMBINING FUNCTIONS	90	(19)
Task 2-5: Evaluating Combinations of Functions	91	(3)
Task 2-6: Combining Functions	94	(8)
Task 2-7: Composing Functions	102	(7)
SECTION 3: REFLECTING FUNCTIONS	109	(26)
Task 2-8: Sketching Reflections	110	(5)
Task 2-9: Representing Reflections by Expressions	115	(8)
Task 2-10: Investigating Inverse Functions	123	(12)
Unit 3: Function Classes	135	(86)
SECTION 1: POLYNOMIAL AND RATIONAL FUNCTIONS	136	(27)
Task 3-1: Examining Polynomial Functions	137	(10)
Task 3-2: Analyzing Rational Functions	147	(7)
Task 3-3: Using Your Calculator to Investigate the Behavior of Polynomial and Rational Functions	154	(9)
SECTION 2: TRIGONOMETRIC FUNCTIONS	163	(22)
Task 3-4: Measuring Angles	165	(4)
Task 3-5: Graphing Basic Trigonometric Functions	169	(5)
Task 3-6: Stretching and Shrinking the Sine Function	174	(4)
Task 3-7: Shifting the Sine Function	178	(7)
SECTION 3: EXPONENTIAL AND LOGARITHMIC FUNCTIONS	185	(25)
Task 3-8: Modeling Situations Using Exponential Functions	185	(5)
Task 3-9: Comparing Exponential Functions	190	(8)
Task 3-10: Investigating the Relationship Between Exponential and Logarithmic Functions	198	(4)
Task 3-11: Evaluating and Graphing Log Functions	202	(8)
SECTION 4: FITTING CURVES TO DISCRETE FUNCTIONS	210	(11)
Task 3-12: Modeling Data	211	(10)
Unit 4: Limits	221	(64)
SECTION 1: LIMITING BEHAVIOR OF FUNCTIONS	222	(24)
Task 4-1: Constructing Sequences of Numbers	222	(6)
Task 4-2: Analyzing the Limiting Behavior of Functions	228	(5)
Task 4-3: Approximating Limits Using a Graphing Calculator	233	(5)
Task 4-4: Examining Situations Where the Limit Does Not Exist	238	(8)
SECTION 2: CONTINUITY, LIMITS, AND SUBSTITUTION	246	(20)
Task 4-5: Inspecting Points of Discontinuity	248	(3)
Task 4-6: Identifying Continuous Functions	251	(6)
Task 4-7: Calculating Limits Using Substitution	257	(9)
SECTION 3: MORE LIMITS	266	(19)
Task 4-8: Using Limits to Investigate Functions	269	(7)
Task 4-9: Using Limits to Locate Horizontal Asymptotes	276	(9)
Unit 5: Derivatives and Integrals: First Pass	285	(62)
SECTION 1: THE DERIVATIVE	287	(33)
Task 5-1: Examining an Example	287	(4)
Task 5-2: Discovering a Definition for the Derivative	291	(3)
Task 5-3: Representing a Derivative by an Expression	294	(5)
Task 5-4: Inspecting the Domain of a Derivative	299	(5)
Task 5-5: Investigating the Relationship Between a Function and Its Derivative	304	(4)
Task 5-6: Gleaning Information About the Graph of a Function from Its Derivative	308	(12)
SECTION 2: THE DEFINITE INTEGRAL	320	(27)
Task 5-7: Finding Some Areas	321	(3)
Task 5-8: Describing Some Possible Approaches	324	(1)
Task 5-9: Applying a Rectangular Approach	325	(3)
Task 5-10: Considering the General Situation	328	(4)
Task 5-11: Calculating Riemann Sums	332	(4)
Task 5-12: Interpreting Definite Integrals	336	(5)
Task 5-13: Checking the Connection Between Derivatives and Definite Integrals	341	(6)
Appendix: Using the TJ-83 Graphing Calculator in Workshop Calculus	347	(66)
Index	413