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Calculus : Mathematics and Modeling, Updated Preliminary Edition

Calculus : Mathematics and Modeling, Updated Preliminary Edition - 99 edition

ISBN13: 978-0201338607

Cover of Calculus : Mathematics and Modeling, Updated Preliminary Edition 99 (ISBN 978-0201338607)
ISBN13: 978-0201338607
ISBN10: 0201338602
Cover type:
Edition/Copyright: 99
Publisher: Addison-Wesley Longman, Inc.
Published: 1999
International: No

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Calculus : Mathematics and Modeling, Updated Preliminary Edition - 99 edition

ISBN13: 978-0201338607

Wade Ellis, Bill Bauldry and Joe Fiedler

ISBN13: 978-0201338607
ISBN10: 0201338602
Cover type:
Edition/Copyright: 99
Publisher: Addison-Wesley Longman, Inc.

Published: 1999
International: No
Summary

The first generation of calculus reformers exploited emerging technologies and the theme of multiple representations of functions. These pioneers also demonstrated effective, innovative teaching techniques, including collaborative learning, writing, discovery, and extended problem solving. Calculus: Mathematics and Modeling introduces a second generation of calculus reform, combining the lessons of the first generation with advances in differential equations through the use of discrete dynamical systems. This teaching philosophy requires a computational environment in which students can move smoothly between symbolic, numeric, graphic, and textual contexts. The text requires use of a computer algebra-capable graphing calculator.

  • This text represents the second generation of calculus reform, combining first-generation calculus reform philosophy with advances in differential equations, through the use of discrete dynamical systems.
  • A rigorous approach to the content requires the use of a computer algebra capable graphing calculator.
  • Concepts are applied to science, engineering, economics, and math.
  • A full 50 percent of the exercises require written interpretation of results.
  • Applied problems and exercises are used to introduce the development of topics.
  • Group problems (for in-class use) and exercises (for out of class use) are used as examples.
  • Discovery Activities, using trial and error; conjecturing solutions from tables; graphs; and symbols, are used within the exercise sets.
  • One or two Extended Projects are included in each chapter.
  • "Interludes," covering non-essential theoretical, technical, and historical topics, are included.
  • Chapter Summary remarks contain a statement of what was learned, and why it was included.

Table of Contents

Part I: The Calculus of Change

Modeling Change

Drugs in the Body
Patterns of Accumulation
A Model for Natural Growth
Modeling Motion
Linear Functions as Models
Solving Equations

Measuring Change

Measuring Change: Regular Data
Analyzing a Discrete Function
From Discrete to Continuous Functions
Measuring Change: Irregular Data
Rate of Change
From Average Rate of Change to Instantaneous Rate of Change
Rate of Change as a Function

The Derivative: A Tool for Measuring Change

The Derivative at a Point and the Idea of a Limit
The Derivative as a Function
Rules, Rules, and More Rules
Finding Features of a Continuous Function
Optimization: Finding Global Extrema
Implicit and Parametric Differentiation
Partial Derivatives

The Definite Integral: Accumulating Change

Rate and Distance
Sums of Products
Error Bounds for the Left and Right Endpoint Methods
The Definite Integral
Other Methods and Their Error Bounds
Applications
The Truth About Limits

The Fundamental Theorem of Calculus and its Uses

Rate and Accumulation
The Antiderivative Concept and The Fundamental Theorem of Calculus, Part I
The Fundamental Theorem of Calculus, Part II
Applications
Using the Chain Rule in Finding Antiderivatives
Techniques of Integration
Further Techniques of Integration

Part II: Modeling with Calculus

Models and Derivatives

One Day in the Life of a Modeler
Population Modeling
Euler's Method
Slope Fields

Symbolic and Numeric Solutions

Integration and Separation of Variables
Linear Differential Equations
Errors in the Model Construction
Errors in Model Analysis: Euler's Method
Advanced Numeric Techniques
Existence and Uniqueness Theorems
Uniqueness
Existence
The General Existence and Uniqueness Theorem

Modeling With Systems

Spirals of Change: You Are What You Eat
Modeling
Numerical Solutions: Iteration and Euler's Method
Symbolic Solutions of Systems of Differential Equations
Bungee Jumping

Power Series: Approximating Functions with Functions

Polynomial Approximation of Functions
Using Polynomial Approximations
How Good Is a Good Polynomial Approximation?
Convergence of Series
Power Series Solutions of Differential Equations

Optimization of Functions of Two Variables

Optimization with Two Variables
Vectors, Lines, and Planes
Tangent Vectors and Tangent Lines in Three Dimensions
Tangent Planes
The Gradient Search

Appendix: Handheld Computer Algebra System Tutorial
The Computer Algebra System Tutorial
Troubleshooting: Things that Go Bump in the Night

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