Workshop Calculus with Graphing Calculators (Paperback)

Nancy Baxter Hastings

ISBN 10: 0387986367 / ISBN 13: 9780387986364

Editore: Springer-Verlag New York Inc., New York, NY, 1999

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Paperback. 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. Based on the use of graphing calculators by students enrolled in calculus, this text covers precalculus review, as well as first-year single variable calculus topics. Shipping may be from multiple locations in the US or from the UK, depending on stock availability.

Codice articolo 9780387986364

Dati bibliografici

• Titolo: Workshop Calculus with Graphing Calculators (Paperback)
• Editore: Springer-Verlag New York Inc., New York, NY
• Data di pubblicazione: 1999
• Lingua: Inglese
• ISBN 10: 0387986367
• ISBN 13: 9780387986364
• Rilegatura: Paperback
• Condizione: new

Descrizione articolo

Riassunto

TO THE INSTRUCTOR I hear, I forget. I see, I remember. I do, I understand. Anonymous OBJECTIVES OF WORKSHOP CALCULUS 1. Impel students to be active learners. 2. Help students to develop confidence about their ability to think about and do mathematics. 3. Encourage students to read, write, and discuss mathematical ideas. 4. Enhance students’ understanding of the fundamental concepts under- ing the calculus. 5. Prepare students to use calculus in other disciplines. 6. Inspire students to continue their study of mathematics. 7. Provide an environment where students enjoy learning and doing ma- ematics. xi xii To the Instructor THE WORKSHOP APPROACH Workshop Calculus with Graphing Calculators: Guided Exploration with Review provides students with a gateway into the study of calculus. The two-volume series integrates a review of basic precalculus ideas with the study of c- cepts traditionally encountered in beginning calculus: functions, limits, - rivatives, integrals, and an introduction to integration techniques and d- ferential equations. It seeks to help students develop the confidence, understanding, and skills necessary for using calculus in the natural and - cial sciences, and for continuing their study of mathematics.

Contenuti

Functions.- Relating Position and Time.- Describing a Process for Finding the Position at a Given Time.- Using the Concept of Function to Buy Pizza.- Creating Linear Functions.- Examining Piecewise-Linear Functions.- Developing an Intuitive Understanding of a Tangent Line to a Curve.- Investigating the Behavior of the Tangent Line near a Turning Point.- Contemplating Concavity.- Interpreting Sign Charts.- Function Construction.- Becoming Familiar with Your Calculator.- Implementing Functions Using Expressions.- Representing Functions by Graphs.- Constructing Discrete Functions.- Evaluating Combinations of Functions.- Combining Functions.- Composing Functions.- Sketching Reflections.- Representing Reflections by Expression.- Investigating Inverse Functions.- Function Classes.- Examining Polynomial Functions.- Analyzing Rational Functions.- Using Your Calculator to Investigate the Behavior of Polynomial and Rational Functions.- Measuring Angles.- Graphing Basic Trigonometric Functions.- Stretching and Shrinking the Sine Function.- Shifting the Sine Function.- Modeling Situations Using Exponential Functions.- Comparing Exponential Functions.- Investigating the Relationship Between Exponential and Logarithmic Functions.- Evaluating and Graphing Log Functions.- Modeling Data.- Limits.- Constructing Sequences of Numbers.- Analyzing the Limiting Behavior of Functions.- Approximating Limits Using a Graphing Calculator.- Examining Situations Where the Limit Does Not Exist.- Inspecting Points of Discontinuity.- Identifying Continuous Functions.- Calculating Limits Using Substitution.- Using Limits to Investigate Functions.- Using Limits to Locate Horizontal Asymptotes.- Derivatives and Integrals: First Pass.- Examining an Example.- Discovering a Definition for the Derivative.- Representing a Derivative by an Expression.- Inspecting the Domain of a Derivative.- Investigating the Relationship Between a Function and Its Derivative.- Gleaning Information About the Graph of a Function from Its Derivative.- Finding Some Areas.- Describing Some Possible Approaches.- Applying a Rectangular Approach.- Considering the General Situation.- Calculating Riemann Sums.- Interpreting Definite Integrals.- Checking the Connection Between Derivatives and Definite Integrals.