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Cover type: Paperback

Edition: 2ND 02

Copyright: 2002

Publisher: Harcourt Brace or Harcourt Press

Published: 2002

International: No

Edition: 2ND 02

Copyright: 2002

Publisher: Harcourt Brace or Harcourt Press

Published: 2002

International: No

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Ostebee and Zorn provide concrete strategies that help students understand and master concepts in calculus. This user-friendly text continues to help students interact with the main calculus objects (functions, derivatives, integrals, etc.) not only symbolically but also, where appropriate, graphically and numerically. Ostebee/Zorn strikes an appropriate balance among these points of view, without overemphasizing any of them. New exercises, examples, and much more have added tremendously to this great book.

NAVIGATING CALCULUS, a new CD-ROM, is being released along with the second edition. The CD contains a variety of useful tools, and resources, including a powerful graphing calculator utility, a glossary with examples, and many live activities that deepen students' encounters with calculus ideas. The CD is keyed closely to the book's table of contents.

Any treatment of calculus involves many choices among competing alternatives: how and when to treat limits, which applications to include, what to prove, etc. To explain the authors' views on such matters, they've established an FAQ site at: http://www.stolaf.edu/people/zorn/ozcalc/faq/.

1. FUNCTIONS AND DERIVATIVES: THE GRAPHICAL VIEW

Functions, Calculus Style

Graphs

A Field Guide to Elementary Functions

Amount Functions and Rate Functions: The Idea of the Derivative

Estimating Derivatives: A Closer Look

The Geometry of Derivatives

The Geometry of Higher-Order Derivatives

Chapter Summary

Interlude: Zooming in on Differences

2. FUNCTIONS AND DERIVATIVES: THE SYMBOLIC VIEW

Defining the Derivative

Derivatives of Power Functions ad Polynomials

Limits

Derivatives, Antiderivatives, and Their Uses

Differential Equations; Modeling Motion

Derivatives of Exponential and Logarithm Functions; Modeling Growth

Derivatives of Trigonometric Functions; Modeling Oscillation

Chapter Summary

Interlude: Tangent Lines in History

Interlude: Limit--the Formal Definition

3. NEW DERIVATIVES FROM OLD

Algebraic Combinations: The Product and Quotient Rules

Composition and the Chain Rule

Implicit Functions and Implicit Differentiation

Inverse Functions and their Derivatives; Inverse Trigonometric Functions

Miscellaneous Derivatives and Antiderivatives

Chapter Summary

Interlude: Vibrations--Simple and Damped

Interlude: Hyperbolic Functions

4. USING THE DERIVATIVE

Direction Fields; More on Growth and Motion

Limits Involving Infinity; l'Hôspital's Rule: Comparing Rates

More on Optimization

Parametric Equations

Related Rates

Newton's Method

Linear Approximation and Taylor Polynomials

Continuity

The Mean Value Theorem

Chapter Summary

Interlude: Growth with Interest

Interlude: Logistic Growth

Interlude: Digging Deeper for Roots (More on Newton's Method)

5. THE INTEGRAL

Areas and Integrals

The Area Function

The Fundamental Theorem of Calculus

Finding Antiderivatives by Substitution

Finding Antiderivatives Using Tables and Computers

Approximating Sums: The Integral as a Limit

Working with Approximating Sums

Chapter Summary

Interlude: Mean Value Theorems and Integrals

Summary

Ostebee and Zorn provide concrete strategies that help students understand and master concepts in calculus. This user-friendly text continues to help students interact with the main calculus objects (functions, derivatives, integrals, etc.) not only symbolically but also, where appropriate, graphically and numerically. Ostebee/Zorn strikes an appropriate balance among these points of view, without overemphasizing any of them. New exercises, examples, and much more have added tremendously to this great book.

NAVIGATING CALCULUS, a new CD-ROM, is being released along with the second edition. The CD contains a variety of useful tools, and resources, including a powerful graphing calculator utility, a glossary with examples, and many live activities that deepen students' encounters with calculus ideas. The CD is keyed closely to the book's table of contents.

Any treatment of calculus involves many choices among competing alternatives: how and when to treat limits, which applications to include, what to prove, etc. To explain the authors' views on such matters, they've established an FAQ site at: http://www.stolaf.edu/people/zorn/ozcalc/faq/.

Table of Contents

1. FUNCTIONS AND DERIVATIVES: THE GRAPHICAL VIEW

Functions, Calculus Style

Graphs

A Field Guide to Elementary Functions

Amount Functions and Rate Functions: The Idea of the Derivative

Estimating Derivatives: A Closer Look

The Geometry of Derivatives

The Geometry of Higher-Order Derivatives

Chapter Summary

Interlude: Zooming in on Differences

2. FUNCTIONS AND DERIVATIVES: THE SYMBOLIC VIEW

Defining the Derivative

Derivatives of Power Functions ad Polynomials

Limits

Derivatives, Antiderivatives, and Their Uses

Differential Equations; Modeling Motion

Derivatives of Exponential and Logarithm Functions; Modeling Growth

Derivatives of Trigonometric Functions; Modeling Oscillation

Chapter Summary

Interlude: Tangent Lines in History

Interlude: Limit--the Formal Definition

3. NEW DERIVATIVES FROM OLD

Algebraic Combinations: The Product and Quotient Rules

Composition and the Chain Rule

Implicit Functions and Implicit Differentiation

Inverse Functions and their Derivatives; Inverse Trigonometric Functions

Miscellaneous Derivatives and Antiderivatives

Chapter Summary

Interlude: Vibrations--Simple and Damped

Interlude: Hyperbolic Functions

4. USING THE DERIVATIVE

Direction Fields; More on Growth and Motion

Limits Involving Infinity; l'Hôspital's Rule: Comparing Rates

More on Optimization

Parametric Equations

Related Rates

Newton's Method

Linear Approximation and Taylor Polynomials

Continuity

The Mean Value Theorem

Chapter Summary

Interlude: Growth with Interest

Interlude: Logistic Growth

Interlude: Digging Deeper for Roots (More on Newton's Method)

5. THE INTEGRAL

Areas and Integrals

The Area Function

The Fundamental Theorem of Calculus

Finding Antiderivatives by Substitution

Finding Antiderivatives Using Tables and Computers

Approximating Sums: The Integral as a Limit

Working with Approximating Sums

Chapter Summary

Interlude: Mean Value Theorems and Integrals

Publisher Info

Publisher: Harcourt Brace or Harcourt Press

Published: 2002

International: No

Published: 2002

International: No

NAVIGATING CALCULUS, a new CD-ROM, is being released along with the second edition. The CD contains a variety of useful tools, and resources, including a powerful graphing calculator utility, a glossary with examples, and many live activities that deepen students' encounters with calculus ideas. The CD is keyed closely to the book's table of contents.

Any treatment of calculus involves many choices among competing alternatives: how and when to treat limits, which applications to include, what to prove, etc. To explain the authors' views on such matters, they've established an FAQ site at: http://www.stolaf.edu/people/zorn/ozcalc/faq/.

1. FUNCTIONS AND DERIVATIVES: THE GRAPHICAL VIEW

Functions, Calculus Style

Graphs

A Field Guide to Elementary Functions

Amount Functions and Rate Functions: The Idea of the Derivative

Estimating Derivatives: A Closer Look

The Geometry of Derivatives

The Geometry of Higher-Order Derivatives

Chapter Summary

Interlude: Zooming in on Differences

2. FUNCTIONS AND DERIVATIVES: THE SYMBOLIC VIEW

Defining the Derivative

Derivatives of Power Functions ad Polynomials

Limits

Derivatives, Antiderivatives, and Their Uses

Differential Equations; Modeling Motion

Derivatives of Exponential and Logarithm Functions; Modeling Growth

Derivatives of Trigonometric Functions; Modeling Oscillation

Chapter Summary

Interlude: Tangent Lines in History

Interlude: Limit--the Formal Definition

3. NEW DERIVATIVES FROM OLD

Algebraic Combinations: The Product and Quotient Rules

Composition and the Chain Rule

Implicit Functions and Implicit Differentiation

Inverse Functions and their Derivatives; Inverse Trigonometric Functions

Miscellaneous Derivatives and Antiderivatives

Chapter Summary

Interlude: Vibrations--Simple and Damped

Interlude: Hyperbolic Functions

4. USING THE DERIVATIVE

Direction Fields; More on Growth and Motion

Limits Involving Infinity; l'Hôspital's Rule: Comparing Rates

More on Optimization

Parametric Equations

Related Rates

Newton's Method

Linear Approximation and Taylor Polynomials

Continuity

The Mean Value Theorem

Chapter Summary

Interlude: Growth with Interest

Interlude: Logistic Growth

Interlude: Digging Deeper for Roots (More on Newton's Method)

5. THE INTEGRAL

Areas and Integrals

The Area Function

The Fundamental Theorem of Calculus

Finding Antiderivatives by Substitution

Finding Antiderivatives Using Tables and Computers

Approximating Sums: The Integral as a Limit

Working with Approximating Sums

Chapter Summary

Interlude: Mean Value Theorems and Integrals