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by Arnold Ostebee and Paul Zorn

Edition: 97Copyright: 1997

Publisher: Saunders College Division

Published: 1997

International: No

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Unlike traditional calculus texts that emphasize only an algebraic (symbolic) approach to learning the concepts, Ostebee/Zorn balances the symbolic approach with numerical and graphical ones. These three viewpoints give students a richer understanding of the fundamental concepts. Because important theorems and proofs are included, this text is appropriate for math and physical science majors. Technology (graphing calculators or computers) has a supporting role as an exploratory tool, rather than as an end in itself. Among the text's other distinctive features are the unusual variety of exercises, many which are graphical in nature; the informal, reader-friendly exposition; the attention to careful definitions and theorem statements; and the seamless integration of text and graphics in the exposition.

Volume 1 contains Chapters 1 through 6 and the Appendixes.

Volume 2 contains Chapters 6 through 14 and selections from Chapters 3 and 4. Most chapters end with a Chapter Summary.

1. Functions in Calculus

Functions, calculus Style

Graphs

Machine Graphics

What is a Function?

A Field Guide to Elementary Functions

New Functions from Old

Modeling with Elementary Functions

2. The Derivative

Amount of Functions and Rate Functions: The Idea of the Derivative

Estimating Derivatives: A Closer Look

The Geometry of Derivatives

The Geometry of Higher-Order Derivatives

Average and Instantaneous Rates: Defining the Derivative

Limits and Continuity

Limits Involving Infinity; New Limits from Old

3. Derivatives of Elementary Functions

Derivatives of Power Functions and Polynomials

Using Derivative and Antiderivative Formulas

Derivatives of Exponential and Logarithmic Functions

Derivatives of Trigonometric Functions

New Derivatives From Old: The Product and Quotient Rules

New Derivatives Form Old: The Chain Rule

Implicit Differentiation

Inverse Trigonometric Functions and Their Derivatives

4. Applications of the Derivative

Differential Equations and Their Solutions

More Differential Equations: Modeling Growth

Linear and Quadratic Approximation; Taylor Polynomials

Newton's Method: Finding Roots

Splines: Connecting the Dots

Optimization

Calculus for Money: Derivatives in Economics

Related Rates

Parametric Equations, Parametric Curves

Why Continuity Matters

Why Differentiability Matters; The Mean Value Theorem

5. The Integral

Areas And Integrals

The Area Function

The Fundamental Theorem of Calculus

Approximating Sums: The Integral as a Limit

Approximating Sums: Interpretations and Applications

6. Finding Antiderivatives

Antiderivatives: The Idea

Antidifferentiation by Substitution

Integral Aids: Tables and Computers

7. Numerical Integration

The Idea of Approximation

More on Error: Left and Right Sums and the First Derivative

Trapezoid Sums, Midpoint Sums, and the Second Derivative

Simpson's Rule

8. Using the Definite Integral

Introduction

Finding Volumes by Integration

Arclength

Work

Present Value

Fourier Polynomials

9. More Antidifferentiation Techniques

Integration by Parts

Partial Fractions

Trigonometric Antiderivatives

Miscellaneous Exercises

10. Improper Integrals

When Is an Integral Improper?

Detecting Convergence, Estimating Limits

Improper Integrals and Probability

l'Hôpital's Rule: Comparing Rates

11. Infinite Series

Sequences and Their Limits

Infinite Series, Convergence, and Divergence

Testing for Convergence; Estimating Limits

Absolute Convergence; Alternating Series

Power Series

Power Series as Functions

Maclaurin and Taylor Series

12. Differential Equations

Differential Equations: The Basics

Slope Fields: Solving DE's Graphically

Euler's Method: Solving DE's Numerically

Separating Variables: Solving DE's Symbolically

13. Polar Coordinates

Polar Coordinates and Polar Curves

Calculus in Polar Coordinates

14. Multivariable Calculus: A First Look

Three-Dimensional Space

Functions of Several Variables

Partial Derivatives

Optimization and Partial Derivatives: A First Look

Multiple Integrals and Approximating Sums

Calculating Integrals by Iteration

Double Integrals in Polar Coordinates

Appendices:

Real Numbers and The Coordinate Plane

Lines and Linear Functions

Polynomial Algebra: A Brisk Review

Real-World Calculus: From Words to Mathematics

Linear, Polynomial, and Rational Functions

Algebra of Exponentials

Algebra of Logarithms

Trigonometric Functions

Selected Proofs

A Graphical Glossary of Functions

Index

Summary

Unlike traditional calculus texts that emphasize only an algebraic (symbolic) approach to learning the concepts, Ostebee/Zorn balances the symbolic approach with numerical and graphical ones. These three viewpoints give students a richer understanding of the fundamental concepts. Because important theorems and proofs are included, this text is appropriate for math and physical science majors. Technology (graphing calculators or computers) has a supporting role as an exploratory tool, rather than as an end in itself. Among the text's other distinctive features are the unusual variety of exercises, many which are graphical in nature; the informal, reader-friendly exposition; the attention to careful definitions and theorem statements; and the seamless integration of text and graphics in the exposition.

Table of Contents

Volume 1 contains Chapters 1 through 6 and the Appendixes.

Volume 2 contains Chapters 6 through 14 and selections from Chapters 3 and 4. Most chapters end with a Chapter Summary.

1. Functions in Calculus

Functions, calculus Style

Graphs

Machine Graphics

What is a Function?

A Field Guide to Elementary Functions

New Functions from Old

Modeling with Elementary Functions

2. The Derivative

Amount of Functions and Rate Functions: The Idea of the Derivative

Estimating Derivatives: A Closer Look

The Geometry of Derivatives

The Geometry of Higher-Order Derivatives

Average and Instantaneous Rates: Defining the Derivative

Limits and Continuity

Limits Involving Infinity; New Limits from Old

3. Derivatives of Elementary Functions

Derivatives of Power Functions and Polynomials

Using Derivative and Antiderivative Formulas

Derivatives of Exponential and Logarithmic Functions

Derivatives of Trigonometric Functions

New Derivatives From Old: The Product and Quotient Rules

New Derivatives Form Old: The Chain Rule

Implicit Differentiation

Inverse Trigonometric Functions and Their Derivatives

4. Applications of the Derivative

Differential Equations and Their Solutions

More Differential Equations: Modeling Growth

Linear and Quadratic Approximation; Taylor Polynomials

Newton's Method: Finding Roots

Splines: Connecting the Dots

Optimization

Calculus for Money: Derivatives in Economics

Related Rates

Parametric Equations, Parametric Curves

Why Continuity Matters

Why Differentiability Matters; The Mean Value Theorem

5. The Integral

Areas And Integrals

The Area Function

The Fundamental Theorem of Calculus

Approximating Sums: The Integral as a Limit

Approximating Sums: Interpretations and Applications

6. Finding Antiderivatives

Antiderivatives: The Idea

Antidifferentiation by Substitution

Integral Aids: Tables and Computers

7. Numerical Integration

The Idea of Approximation

More on Error: Left and Right Sums and the First Derivative

Trapezoid Sums, Midpoint Sums, and the Second Derivative

Simpson's Rule

8. Using the Definite Integral

Introduction

Finding Volumes by Integration

Arclength

Work

Present Value

Fourier Polynomials

9. More Antidifferentiation Techniques

Integration by Parts

Partial Fractions

Trigonometric Antiderivatives

Miscellaneous Exercises

10. Improper Integrals

When Is an Integral Improper?

Detecting Convergence, Estimating Limits

Improper Integrals and Probability

l'Hôpital's Rule: Comparing Rates

11. Infinite Series

Sequences and Their Limits

Infinite Series, Convergence, and Divergence

Testing for Convergence; Estimating Limits

Absolute Convergence; Alternating Series

Power Series

Power Series as Functions

Maclaurin and Taylor Series

12. Differential Equations

Differential Equations: The Basics

Slope Fields: Solving DE's Graphically

Euler's Method: Solving DE's Numerically

Separating Variables: Solving DE's Symbolically

13. Polar Coordinates

Polar Coordinates and Polar Curves

Calculus in Polar Coordinates

14. Multivariable Calculus: A First Look

Three-Dimensional Space

Functions of Several Variables

Partial Derivatives

Optimization and Partial Derivatives: A First Look

Multiple Integrals and Approximating Sums

Calculating Integrals by Iteration

Double Integrals in Polar Coordinates

Appendices:

Real Numbers and The Coordinate Plane

Lines and Linear Functions

Polynomial Algebra: A Brisk Review

Real-World Calculus: From Words to Mathematics

Linear, Polynomial, and Rational Functions

Algebra of Exponentials

Algebra of Logarithms

Trigonometric Functions

Selected Proofs

A Graphical Glossary of Functions

Index

Publisher Info

Publisher: Saunders College Division

Published: 1997

International: No

Published: 1997

International: No

Volume 1 contains Chapters 1 through 6 and the Appendixes.

Volume 2 contains Chapters 6 through 14 and selections from Chapters 3 and 4. Most chapters end with a Chapter Summary.

1. Functions in Calculus

Functions, calculus Style

Graphs

Machine Graphics

What is a Function?

A Field Guide to Elementary Functions

New Functions from Old

Modeling with Elementary Functions

2. The Derivative

Amount of Functions and Rate Functions: The Idea of the Derivative

Estimating Derivatives: A Closer Look

The Geometry of Derivatives

The Geometry of Higher-Order Derivatives

Average and Instantaneous Rates: Defining the Derivative

Limits and Continuity

Limits Involving Infinity; New Limits from Old

3. Derivatives of Elementary Functions

Derivatives of Power Functions and Polynomials

Using Derivative and Antiderivative Formulas

Derivatives of Exponential and Logarithmic Functions

Derivatives of Trigonometric Functions

New Derivatives From Old: The Product and Quotient Rules

New Derivatives Form Old: The Chain Rule

Implicit Differentiation

Inverse Trigonometric Functions and Their Derivatives

4. Applications of the Derivative

Differential Equations and Their Solutions

More Differential Equations: Modeling Growth

Linear and Quadratic Approximation; Taylor Polynomials

Newton's Method: Finding Roots

Splines: Connecting the Dots

Optimization

Calculus for Money: Derivatives in Economics

Related Rates

Parametric Equations, Parametric Curves

Why Continuity Matters

Why Differentiability Matters; The Mean Value Theorem

5. The Integral

Areas And Integrals

The Area Function

The Fundamental Theorem of Calculus

Approximating Sums: The Integral as a Limit

Approximating Sums: Interpretations and Applications

6. Finding Antiderivatives

Antiderivatives: The Idea

Antidifferentiation by Substitution

Integral Aids: Tables and Computers

7. Numerical Integration

The Idea of Approximation

More on Error: Left and Right Sums and the First Derivative

Trapezoid Sums, Midpoint Sums, and the Second Derivative

Simpson's Rule

8. Using the Definite Integral

Introduction

Finding Volumes by Integration

Arclength

Work

Present Value

Fourier Polynomials

9. More Antidifferentiation Techniques

Integration by Parts

Partial Fractions

Trigonometric Antiderivatives

Miscellaneous Exercises

10. Improper Integrals

When Is an Integral Improper?

Detecting Convergence, Estimating Limits

Improper Integrals and Probability

l'Hôpital's Rule: Comparing Rates

11. Infinite Series

Sequences and Their Limits

Infinite Series, Convergence, and Divergence

Testing for Convergence; Estimating Limits

Absolute Convergence; Alternating Series

Power Series

Power Series as Functions

Maclaurin and Taylor Series

12. Differential Equations

Differential Equations: The Basics

Slope Fields: Solving DE's Graphically

Euler's Method: Solving DE's Numerically

Separating Variables: Solving DE's Symbolically

13. Polar Coordinates

Polar Coordinates and Polar Curves

Calculus in Polar Coordinates

14. Multivariable Calculus: A First Look

Three-Dimensional Space

Functions of Several Variables

Partial Derivatives

Optimization and Partial Derivatives: A First Look

Multiple Integrals and Approximating Sums

Calculating Integrals by Iteration

Double Integrals in Polar Coordinates

Appendices:

Real Numbers and The Coordinate Plane

Lines and Linear Functions

Polynomial Algebra: A Brisk Review

Real-World Calculus: From Words to Mathematics

Linear, Polynomial, and Rational Functions

Algebra of Exponentials

Algebra of Logarithms

Trigonometric Functions

Selected Proofs

A Graphical Glossary of Functions

Index