Workshop Calculus with Graphing Calculators, Vol. 1 » (1st Edition)

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.

Preface: To the Instructor
Preface: To the Student
------Task P-1: Why Are You Taking This Course?
------Task P-2: Continuous Motion or "Jumps"?
------Task P-3: Getting Started with Your calculator

Unit 1: Functions
--Section 1: Modeling Situations
------Task 1-1: Relating Position and Time
------Task 1-2: Describing a Process for Finding Positions at a Given Time
------Task 1-3: Using the Concept of Function to Buy Pizza
--Section 2: Analyzing Linear Functions
------Task 1-4: Creating Linear Functions
------Task 1-5: Examining Piecewise-Linear Functions
--Section 3: Analyzing Smooth Curves
------Task 1-6: Developing an Intuitive Understanding of a Tangent Line to a Curve
------Task 1-7: Investigating the Behavior of the Tangent Line Near a Turning Point
------Task 1-8: Contemplating Concavity
------Task 1-9: Interpreting Sign Charts

Unit 2: Function Construction
--Section 1: Representing Functions
------Task 2-1: Getting Started with Your Calculator
------Task 2-2: Implementing Functions Using Expressions
------Task 2-3: Representing Functions by Graphs
------Task 2-4: Constructing Discrete Functions
--Section 2: Combining Functions
------Task 2-5: Evaluating Combinations of Functions
------Task 2-6: Combining Functions
------Task 2-7: Composing Functions
--Section 3: Reflecting Functions
------Task 2-8: Sketching Reflections
------Task 2-9: Representing Reflections by Expressions
------Task 2-10: Investigating Inverse Functions

Unit 3: Function Classes
--Section 1: Polynomial and Rational Functions
------Task 3-1: Examining Polynomial Functions
------Task 3-2: Analyzing Rational Functions
------Task 3-3: Using Your Calculator to Investigate the Behavior of Polynomial and Rational Functions
--Section 2: Trigonometric Functions
------Task 3-4: Measuring Angles
------Task 3-5: Graphing Basic Trigonometric Functions
------Task 3-6: Stretching and Shrinking the Sine Function
------Task 3-7: Shifting the Sine Function
--Section 3: Exponential and Logarithmic Functions
------Task 3-8: Modeling Situations Using Exponential Functions
------Task 3-9: Comparing Exponential Functions
------Task 3-10: Investigating the Relationship Between Exponential and Trigonometric Functions
--Section 4: Fitting Curves to Discrete Functions
------Task 3-12: Modeling Data

Unit 4: Limits
--Section 1: Limiting Behavior of Functions
------Task 4-1: Constructing Sequences of Numbers
------Task 4-2: Analyzing the Limiting Behavior of Functions
------Task 4-3: Approximating Limits Using a Graphing Calculator
------Task 4-4: Examining Situations Where the Limit Does Not Exist
--Section 2: Continuity, Limits, and Substitution
------Task 4-5: Inspecting Points of Discontinuity
------Task 4-6: Identifying Continuous Functions
------Task 4-7: Calculating Limits Using Substitution
--Section 3: More Limits
------Task 4-8: Using Limits to Investigate Functions
------Task 4-9: Using Limits to Locate Horizontal Asymptotes

Unit 5: Derivatives and Integrals: First Pass
--Section 1: The Derivative
------Task 5-1: Examining an Example
------Task 5-2: Discovering a Definition for the Derivative
------Task 5-3: Representing a Derivative by an Expression
------Task 5-4: Inspecting the Domain of a Derivative
------Task 5-5: Investigating the Relationship Between a Function and its Derivative
------Task 5-6: Gleaning Information About the Graph of a Function from its Derivative
--Section 2: The Definite Integral
------Task 5-7: Finding Some Areas
------Task 5-8: Describing Some Possible Approaches
------Task 5-9: Applying a Rectangular Approach
------Task 5-10: Considering the General Situation
------Task 5-11: Calculating Riemann Sums
------Task 5-12: Interpreting Definite Integrals
------Task 5-13: Checking the Connection Between Derivatives and Definite Integrals