Workshop Calculus With Graphing Calculators,9780387986364

Workshop Calculus With Graphing Calculators

by ; ; ;
ISBN13: 9780387986364
ISBN10: 0387986367
Format: Paperback
Pub. Date: 1999-06-01
Publisher(s): Key Curriculum Pr
List Price: $49.99

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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 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

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