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by Arnold Ostebee and Paul Zorn

Cover type: PaperbackEdition: 2ND 02

Copyright: 2002

Publisher: Brooks/Cole Publishing Co.

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/.

Benefits:

- The basic principles of the first edition remain unchanged. Conceptual understanding is still the main goal, and combining various viewpoints is still the main strategy for achieving it. The text still has an emphasis on concepts and sense making; complementing symbolic with graphical and numerical points of view; exercises of varied nature and difficulty; and a narrative aimed at student readers.
- NEW! Content changes include a new brief chapter on function approximation, centering on Taylor polynomial approximation, but also including basic discussion of Fourier polynomials.
- NEW! Many users found the previous edition short on routine exercises, so many more have been added to second edition.
- NEW! More exercises that point to specific issues and examples in the narrative have been added.
- NEW! The text now provides answers (not solutions) to odd-numbered exercises in the back of the book, in response to many user requests (from instructors, not just from students).
- NEW! To help students read the text more successfully, more examples have been added to many sections, parts of the narrative have been rewritten, and more detail and brief commentary has been included on many calculations.
- Most chapters end with one or more Interludes. These brief, project-oriented expositions with exercises are designed for independent student work and address topics or questions that are optional or out of the chapter's main stream of development.
- NEW! To make the text easier to use, changes have been made in narrative, exercises, content, emphasis, and order of presentation, based on suggestions from both teachers and students.
- NEW! The precalculus material has been compressed in order to get to the derivative idea faster. Chapter 1 now includes essentially complete coverage of the graphical point of view; derivatives now appear first in Section 1.4.
- NEW! Chapter 2 introduces and interprets the symbolic point of view, and Chapter 3 presents the combinatorial rules for calculating derivatives (e.g., the product and quotient rules).
- NEW! Differential equations provide a natural approach to scientific and engineering applications. DEs now appear earlier and appear repeatedly in subsequent sections and in exercises.
- NEW! Although DEs are emphasized more strongly, this is not a calculus/DE text. It does not cover, or even catalog, the huge variety of DEs and solution techniques. Instead, we sometimes use DEs to motivate new techniques and concepts as they develop naturally over the course.
- NEW! Slope fields now appear in Chapter 4 (they previously appeared in Chapter 12).
- NEW! Euler's method now appears in Chapter 6 (along with numerical integration methods), and separation of variables appear in Chapter 7 as an application of symbolic anti-differentiation.

**Ostebee, Arnold : St. Olaf College **

Zorn, Paul : St. Olaf College

7. USING THE INTEGRAL

Interpretations of the Integral

Areas and Volumes

Motion; Work

Probability

Separable Differential Equations

8. SYMBOLIC ANTIDIFFERENTIATION TECHNIQUES

Integration by Parts

Partial Fractions

Trigonometric Antiderivatives

Miscellaneous Antidifferentiation Exercises

9. FUNCTION APPROXIMATION

Taylor Polynomials

Taylor's Theorem

Fourier Polynomials

10. IMPROPER INTEGRALS

When Is an Integral Improper? Detecting Convergence; Estimating Limits

11. INFINITE SERIES

Sequences and Their Limits; Infinite Series, Convergence, and Divergence

Testing for Convergence; Estimating Limits

Absolute Convergence; Alternating Series

Power Series; Taylor Series

Algebra and Calculus with Power Series

12. CURVES AND VECTORS

Three-Dimensional Space

Curves and Parametric Equations

Vectors

Vector-Valued Functions, Derivatives, and Integrals

Derivatives, Antiderivatives, and Motion

The Dot Product

Lines and Planes in Three Dimensions

The Cross Product

13. DERIVATIVES

Functions of Several Variables

Partial Derivatives

Partial Derivatives and Linear Approximation

The Gradient and Directional Derivatives

Local Linearity: Theory of the Derivative

Higher Order Derivatives and Quadratic Approximation

Maxima, Minima, and Quadratic Approximation

The Chain Rule

14. INTEGRALS

Multiple Integrals and Approximating Sums

Calculating Integrals by Iteration

Double Integrals in Polar Coordinates

More on Triple Integrals; Cylindrical and Spherical Coordinates

Multiple Integrals Overviewed; Change of Variables

15. OTHER TOPICS

Linear, Circular, and Combined Motion

Using the Dot Product: More on Curves

Curvature

Lagrange Multipliers and Constrained Optimization

16. VECTOR CALCULUS

Line Integrals

More on Line Integrals; A Fundamental Theorem

Relating Line and Area Integrals: Green's Theorem

Surfaces and Their Parametrizations

Surface Integrals

Derivatives and Integrals of Vector Fields

Back to Fundamentals: Stokes' Theorem and the Divergence Theorem

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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/.

Benefits:

- The basic principles of the first edition remain unchanged. Conceptual understanding is still the main goal, and combining various viewpoints is still the main strategy for achieving it. The text still has an emphasis on concepts and sense making; complementing symbolic with graphical and numerical points of view; exercises of varied nature and difficulty; and a narrative aimed at student readers.
- NEW! Content changes include a new brief chapter on function approximation, centering on Taylor polynomial approximation, but also including basic discussion of Fourier polynomials.
- NEW! Many users found the previous edition short on routine exercises, so many more have been added to second edition.
- NEW! More exercises that point to specific issues and examples in the narrative have been added.
- NEW! The text now provides answers (not solutions) to odd-numbered exercises in the back of the book, in response to many user requests (from instructors, not just from students).
- NEW! To help students read the text more successfully, more examples have been added to many sections, parts of the narrative have been rewritten, and more detail and brief commentary has been included on many calculations.
- Most chapters end with one or more Interludes. These brief, project-oriented expositions with exercises are designed for independent student work and address topics or questions that are optional or out of the chapter's main stream of development.
- NEW! To make the text easier to use, changes have been made in narrative, exercises, content, emphasis, and order of presentation, based on suggestions from both teachers and students.
- NEW! The precalculus material has been compressed in order to get to the derivative idea faster. Chapter 1 now includes essentially complete coverage of the graphical point of view; derivatives now appear first in Section 1.4.
- NEW! Chapter 2 introduces and interprets the symbolic point of view, and Chapter 3 presents the combinatorial rules for calculating derivatives (e.g., the product and quotient rules).
- NEW! Differential equations provide a natural approach to scientific and engineering applications. DEs now appear earlier and appear repeatedly in subsequent sections and in exercises.
- NEW! Although DEs are emphasized more strongly, this is not a calculus/DE text. It does not cover, or even catalog, the huge variety of DEs and solution techniques. Instead, we sometimes use DEs to motivate new techniques and concepts as they develop naturally over the course.
- NEW! Slope fields now appear in Chapter 4 (they previously appeared in Chapter 12).
- NEW! Euler's method now appears in Chapter 6 (along with numerical integration methods), and separation of variables appear in Chapter 7 as an application of symbolic anti-differentiation.

Author Bio

**Ostebee, Arnold : St. Olaf College **

Zorn, Paul : St. Olaf College

Table of Contents

7. USING THE INTEGRAL

Interpretations of the Integral

Areas and Volumes

Motion; Work

Probability

Separable Differential Equations

8. SYMBOLIC ANTIDIFFERENTIATION TECHNIQUES

Integration by Parts

Partial Fractions

Trigonometric Antiderivatives

Miscellaneous Antidifferentiation Exercises

9. FUNCTION APPROXIMATION

Taylor Polynomials

Taylor's Theorem

Fourier Polynomials

10. IMPROPER INTEGRALS

When Is an Integral Improper? Detecting Convergence; Estimating Limits

11. INFINITE SERIES

Sequences and Their Limits; Infinite Series, Convergence, and Divergence

Testing for Convergence; Estimating Limits

Absolute Convergence; Alternating Series

Power Series; Taylor Series

Algebra and Calculus with Power Series

12. CURVES AND VECTORS

Three-Dimensional Space

Curves and Parametric Equations

Vectors

Vector-Valued Functions, Derivatives, and Integrals

Derivatives, Antiderivatives, and Motion

The Dot Product

Lines and Planes in Three Dimensions

The Cross Product

13. DERIVATIVES

Functions of Several Variables

Partial Derivatives

Partial Derivatives and Linear Approximation

The Gradient and Directional Derivatives

Local Linearity: Theory of the Derivative

Higher Order Derivatives and Quadratic Approximation

Maxima, Minima, and Quadratic Approximation

The Chain Rule

14. INTEGRALS

Multiple Integrals and Approximating Sums

Calculating Integrals by Iteration

Double Integrals in Polar Coordinates

More on Triple Integrals; Cylindrical and Spherical Coordinates

Multiple Integrals Overviewed; Change of Variables

15. OTHER TOPICS

Linear, Circular, and Combined Motion

Using the Dot Product: More on Curves

Curvature

Lagrange Multipliers and Constrained Optimization

16. VECTOR CALCULUS

Line Integrals

More on Line Integrals; A Fundamental Theorem

Relating Line and Area Integrals: Green's Theorem

Surfaces and Their Parametrizations

Surface Integrals

Derivatives and Integrals of Vector Fields

Back to Fundamentals: Stokes' Theorem and the Divergence Theorem

Publisher Info

Publisher: Brooks/Cole Publishing Co.

Published: 2002

International: No

Published: 2002

International: No

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/.

Benefits:

- The basic principles of the first edition remain unchanged. Conceptual understanding is still the main goal, and combining various viewpoints is still the main strategy for achieving it. The text still has an emphasis on concepts and sense making; complementing symbolic with graphical and numerical points of view; exercises of varied nature and difficulty; and a narrative aimed at student readers.
- NEW! Content changes include a new brief chapter on function approximation, centering on Taylor polynomial approximation, but also including basic discussion of Fourier polynomials.
- NEW! Many users found the previous edition short on routine exercises, so many more have been added to second edition.
- NEW! More exercises that point to specific issues and examples in the narrative have been added.
- NEW! The text now provides answers (not solutions) to odd-numbered exercises in the back of the book, in response to many user requests (from instructors, not just from students).
- NEW! To help students read the text more successfully, more examples have been added to many sections, parts of the narrative have been rewritten, and more detail and brief commentary has been included on many calculations.
- Most chapters end with one or more Interludes. These brief, project-oriented expositions with exercises are designed for independent student work and address topics or questions that are optional or out of the chapter's main stream of development.
- NEW! To make the text easier to use, changes have been made in narrative, exercises, content, emphasis, and order of presentation, based on suggestions from both teachers and students.
- NEW! The precalculus material has been compressed in order to get to the derivative idea faster. Chapter 1 now includes essentially complete coverage of the graphical point of view; derivatives now appear first in Section 1.4.
- NEW! Chapter 2 introduces and interprets the symbolic point of view, and Chapter 3 presents the combinatorial rules for calculating derivatives (e.g., the product and quotient rules).
- NEW! Differential equations provide a natural approach to scientific and engineering applications. DEs now appear earlier and appear repeatedly in subsequent sections and in exercises.
- NEW! Although DEs are emphasized more strongly, this is not a calculus/DE text. It does not cover, or even catalog, the huge variety of DEs and solution techniques. Instead, we sometimes use DEs to motivate new techniques and concepts as they develop naturally over the course.
- NEW! Slope fields now appear in Chapter 4 (they previously appeared in Chapter 12).
- NEW! Euler's method now appears in Chapter 6 (along with numerical integration methods), and separation of variables appear in Chapter 7 as an application of symbolic anti-differentiation.

**Ostebee, Arnold : St. Olaf College **

Zorn, Paul : St. Olaf College

7. USING THE INTEGRAL

Interpretations of the Integral

Areas and Volumes

Motion; Work

Probability

Separable Differential Equations

8. SYMBOLIC ANTIDIFFERENTIATION TECHNIQUES

Integration by Parts

Partial Fractions

Trigonometric Antiderivatives

Miscellaneous Antidifferentiation Exercises

9. FUNCTION APPROXIMATION

Taylor Polynomials

Taylor's Theorem

Fourier Polynomials

10. IMPROPER INTEGRALS

When Is an Integral Improper? Detecting Convergence; Estimating Limits

11. INFINITE SERIES

Sequences and Their Limits; Infinite Series, Convergence, and Divergence

Testing for Convergence; Estimating Limits

Absolute Convergence; Alternating Series

Power Series; Taylor Series

Algebra and Calculus with Power Series

12. CURVES AND VECTORS

Three-Dimensional Space

Curves and Parametric Equations

Vectors

Vector-Valued Functions, Derivatives, and Integrals

Derivatives, Antiderivatives, and Motion

The Dot Product

Lines and Planes in Three Dimensions

The Cross Product

13. DERIVATIVES

Functions of Several Variables

Partial Derivatives

Partial Derivatives and Linear Approximation

The Gradient and Directional Derivatives

Local Linearity: Theory of the Derivative

Higher Order Derivatives and Quadratic Approximation

Maxima, Minima, and Quadratic Approximation

The Chain Rule

14. INTEGRALS

Multiple Integrals and Approximating Sums

Calculating Integrals by Iteration

Double Integrals in Polar Coordinates

More on Triple Integrals; Cylindrical and Spherical Coordinates

Multiple Integrals Overviewed; Change of Variables

15. OTHER TOPICS

Linear, Circular, and Combined Motion

Using the Dot Product: More on Curves

Curvature

Lagrange Multipliers and Constrained Optimization

16. VECTOR CALCULUS

Line Integrals

More on Line Integrals; A Fundamental Theorem

Relating Line and Area Integrals: Green's Theorem

Surfaces and Their Parametrizations

Surface Integrals

Derivatives and Integrals of Vector Fields

Back to Fundamentals: Stokes' Theorem and the Divergence Theorem