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by C. Henry Edwards and David E. Penney

Cover type: HardbackEdition: 6TH 02

Copyright: 2002

Publisher: Pearson Custom

Published: 2002

International: No

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For three-semester undergraduate-level courses in Calculus.

This text combines traditional mainstream calculus with the most flexible approach to new ideas and calculator/computer technology. It contains superb problem sets and a fresh conceptual emphasis flavored by new technological possibilities. The Calculus II portion now has a new focus on differential equations.

**Features :**

- NEW-CD Shows animations of nearly all the text examples. It also has the entire book in Maple notebooks.
- NEW-An entire chapter devoted to calculus of transcendental functions-Combines parts of two previous chapters into the new Ch. 7.
- Provides students with a clearer explanation of this subject within one solid, unified, and fully rewritten chapter.
- NEW-Expanded treatment of differential equations (New Chapter 9).
- Introduces students to both direction fields and Euler's method together with the more symbolic elementary methods and applications for both first- and second-order equations.
- NEW-1040 new True/False Questions-Available on the CD. They focus on theory and push the student to read.
- NEW-Reorganized content-Covers applied max-min problems in Ch.3 and defers related rates to Ch.4.
- Offers students the opportunities to focus on and study these challenging topics in separate chapters-and test their knowledge of them in separate unit tests.
- Approximately 7000 total problems and interesting applications-Covers all ranges of difficulty, highly theoretical and computationally oriented problems.
- Encourages students to learn by doing.
- Technology projects-Features icons that take users to Maple/ Mathematica/MATLAB/Calculator resources on the CD-ROM.
- Gives students the opportunity to apply conceptually based technology following key sections of the text.
- 320 Section-ending Concepts: Questions & Discussion.
- Serves students with a basis for either writing assignments or class discussion.
- Small optional section of matrix terminology and notation in the multivariable portion of the text.
- A lively and accessible writing style.
- Helps students feel comfortable with the topics covered, and their ability to master them.
- Most visual text on the market.
- Highlights are hundreds of Mathematica and MATLAB generated figures.

**1. Functions, Graphs, and Models**

Functions and Mathematical Modeling

Graphs of Equations and Functions

Polynomials and Algebraic Functions

Transcendental Functions

Preview: What Is Calculus?

**2. Prelude to Calculus**

Tangent Lines and Slope Predictors

The Limit Concept

More about Limits

The Concept of Continuity

**3. The Derivative**

The Derivative and Rates of Change

Basic Differentiation Rules

The Chain Rule

Derivatives of Algebraic Functions

Maxima and Minima of Functions on Closed Intervals

Applied Optimization Problems

Derivatives of Trigonometric Functions

Successive Approximations and Newton's Method

**4. Additional Applications of the Derivative**

Implicit Differentiation and Related Rates

Increments, Differentials, and Linear Approximation

Increasing and Decreasing Functions and the Mean Value Theorem

The First Derivative Test and Applications

Simple Curve Sketching

Higher Derivatives and Concavity

Curve Sketching and Asymptotes

**5. The Integral**

Introduction

Antiderivatives and Initial Value Problems

Elementary Area Computations

Riemann Sums and the Integral

Evaluation of Integrals

The Fundamental Theorem of Calculus

Integration by Substitution

Areas of Plane Regions

Numerical Integration

**6. Applications of the Integral**

Riemann Sum Approximations

Volumes by the Method of Cross Sections

Volumes by the Method of Cylindrical Shells

Arc Length and Surface Area of Revolution

Force and Work

Centroids of Plane Regions and Curves

**7. Calculus of Transcendental Functions**

Exponential and Logarithmic Functions

Indeterminate Forms and L'Hopîtal's Rule

More Indeterminate Forms

The Logarithm as an Integral

Inverse Trigonometric Functions

Hyperbolic Functions

**8. Techniques of Integration**

Introduction

Integral Tables and Simple Substitutions

Integration by Parts

Trigonometric Integrals

Rational Functions and Partial Fractions

Trigonometric Substitutions

Integrals Involving Quadratic Polynomials

Improper Integrals

**9. Differential Equations**

Simple Equations and Models

Slope Fields and Euler's Method

Separable Equations and Applications

Linear Equations and Applications

Population Models

Linear Second-Order Equations

Mechanical Vibrations

**10. Polar Coordinates and Parametric Curves**

Analytic Geometry and the Conic Sections

Polar Coordinates

Area Computations in Polar Coordinates

Parametric Curves

Integral Computations with Parametric Curves

Conic Sections and Applications

**11. Infinite Series**

Introduction

Infinite Sequences

Infinite Series and Convergence

Taylor Series and Taylor Polynomials

The Integral Test

Comparison Tests for Positive-Term Series

Alternating Series and Absolute Convergence

Power Series

Power Series Computations

Series Solutions of Differential Equations

**12. Vectors, Curves, and Surfaces in Space**

Vectors in the Plane

Rectangular Coordinates and Three-Dimensional Vectors

The Cross Product of Vectors

Lines and Planes in Space

Curves and Motions in Space

Curvature and Acceleration

Cylinders and Quadric Surfaces

Cylindrical and Spherical Coordinates

**13. Partial Differentiation**

Introduction

Functions of Several Variables

Limits and Continuity

Partial Derivatives

Multivariable Maxima and Minima

Increments and Linear Approximation

The Multivariable Chain Rule

Directional Derivatives and Gradient Vectors

Lagrange Multipliers and Constrained Optimization

Critical Points of Multivariable Functions

**14. Multiple Integrals**

Double Integrals

Double Integrals over More General Regions

Area and Volume by Double Integration

Double Integrals in Polar Coordinates

Applications of Double Integrals

Triple Integrals

Integration in Cylindrical and Spherical Coordinates

Surface Area

Change of Variables in Multiple Integrals

**15. Vector Calculus**

Vector Fields

Line Integrals

The Fundamental Theorem and Independence of Path

Green's Theorem

Surface Integrals

The Divergence Theorem

Stokes' Theorem

Appendices

Answers

Index

Summary

For three-semester undergraduate-level courses in Calculus.

This text combines traditional mainstream calculus with the most flexible approach to new ideas and calculator/computer technology. It contains superb problem sets and a fresh conceptual emphasis flavored by new technological possibilities. The Calculus II portion now has a new focus on differential equations.

**Features :**

- NEW-CD Shows animations of nearly all the text examples. It also has the entire book in Maple notebooks.
- NEW-An entire chapter devoted to calculus of transcendental functions-Combines parts of two previous chapters into the new Ch. 7.
- Provides students with a clearer explanation of this subject within one solid, unified, and fully rewritten chapter.
- NEW-Expanded treatment of differential equations (New Chapter 9).
- Introduces students to both direction fields and Euler's method together with the more symbolic elementary methods and applications for both first- and second-order equations.
- NEW-1040 new True/False Questions-Available on the CD. They focus on theory and push the student to read.
- NEW-Reorganized content-Covers applied max-min problems in Ch.3 and defers related rates to Ch.4.
- Offers students the opportunities to focus on and study these challenging topics in separate chapters-and test their knowledge of them in separate unit tests.
- Approximately 7000 total problems and interesting applications-Covers all ranges of difficulty, highly theoretical and computationally oriented problems.
- Encourages students to learn by doing.
- Technology projects-Features icons that take users to Maple/ Mathematica/MATLAB/Calculator resources on the CD-ROM.
- Gives students the opportunity to apply conceptually based technology following key sections of the text.
- 320 Section-ending Concepts: Questions & Discussion.
- Serves students with a basis for either writing assignments or class discussion.
- Small optional section of matrix terminology and notation in the multivariable portion of the text.
- A lively and accessible writing style.
- Helps students feel comfortable with the topics covered, and their ability to master them.
- Most visual text on the market.
- Highlights are hundreds of Mathematica and MATLAB generated figures.

Table of Contents

**1. Functions, Graphs, and Models**

Functions and Mathematical Modeling

Graphs of Equations and Functions

Polynomials and Algebraic Functions

Transcendental Functions

Preview: What Is Calculus?

**2. Prelude to Calculus**

Tangent Lines and Slope Predictors

The Limit Concept

More about Limits

The Concept of Continuity

**3. The Derivative**

The Derivative and Rates of Change

Basic Differentiation Rules

The Chain Rule

Derivatives of Algebraic Functions

Maxima and Minima of Functions on Closed Intervals

Applied Optimization Problems

Derivatives of Trigonometric Functions

Successive Approximations and Newton's Method

**4. Additional Applications of the Derivative**

Implicit Differentiation and Related Rates

Increments, Differentials, and Linear Approximation

Increasing and Decreasing Functions and the Mean Value Theorem

The First Derivative Test and Applications

Simple Curve Sketching

Higher Derivatives and Concavity

Curve Sketching and Asymptotes

**5. The Integral**

Introduction

Antiderivatives and Initial Value Problems

Elementary Area Computations

Riemann Sums and the Integral

Evaluation of Integrals

The Fundamental Theorem of Calculus

Integration by Substitution

Areas of Plane Regions

Numerical Integration

**6. Applications of the Integral**

Riemann Sum Approximations

Volumes by the Method of Cross Sections

Volumes by the Method of Cylindrical Shells

Arc Length and Surface Area of Revolution

Force and Work

Centroids of Plane Regions and Curves

**7. Calculus of Transcendental Functions**

Exponential and Logarithmic Functions

Indeterminate Forms and L'Hopîtal's Rule

More Indeterminate Forms

The Logarithm as an Integral

Inverse Trigonometric Functions

Hyperbolic Functions

**8. Techniques of Integration**

Introduction

Integral Tables and Simple Substitutions

Integration by Parts

Trigonometric Integrals

Rational Functions and Partial Fractions

Trigonometric Substitutions

Integrals Involving Quadratic Polynomials

Improper Integrals

**9. Differential Equations**

Simple Equations and Models

Slope Fields and Euler's Method

Separable Equations and Applications

Linear Equations and Applications

Population Models

Linear Second-Order Equations

Mechanical Vibrations

**10. Polar Coordinates and Parametric Curves**

Analytic Geometry and the Conic Sections

Polar Coordinates

Area Computations in Polar Coordinates

Parametric Curves

Integral Computations with Parametric Curves

Conic Sections and Applications

**11. Infinite Series**

Introduction

Infinite Sequences

Infinite Series and Convergence

Taylor Series and Taylor Polynomials

The Integral Test

Comparison Tests for Positive-Term Series

Alternating Series and Absolute Convergence

Power Series

Power Series Computations

Series Solutions of Differential Equations

**12. Vectors, Curves, and Surfaces in Space**

Vectors in the Plane

Rectangular Coordinates and Three-Dimensional Vectors

The Cross Product of Vectors

Lines and Planes in Space

Curves and Motions in Space

Curvature and Acceleration

Cylinders and Quadric Surfaces

Cylindrical and Spherical Coordinates

**13. Partial Differentiation**

Introduction

Functions of Several Variables

Limits and Continuity

Partial Derivatives

Multivariable Maxima and Minima

Increments and Linear Approximation

The Multivariable Chain Rule

Directional Derivatives and Gradient Vectors

Lagrange Multipliers and Constrained Optimization

Critical Points of Multivariable Functions

**14. Multiple Integrals**

Double Integrals

Double Integrals over More General Regions

Area and Volume by Double Integration

Double Integrals in Polar Coordinates

Applications of Double Integrals

Triple Integrals

Integration in Cylindrical and Spherical Coordinates

Surface Area

Change of Variables in Multiple Integrals

**15. Vector Calculus**

Vector Fields

Line Integrals

The Fundamental Theorem and Independence of Path

Green's Theorem

Surface Integrals

The Divergence Theorem

Stokes' Theorem

Appendices

Answers

Index

Publisher Info

Publisher: Pearson Custom

Published: 2002

International: No

Published: 2002

International: No

For three-semester undergraduate-level courses in Calculus.

This text combines traditional mainstream calculus with the most flexible approach to new ideas and calculator/computer technology. It contains superb problem sets and a fresh conceptual emphasis flavored by new technological possibilities. The Calculus II portion now has a new focus on differential equations.

**Features :**

- NEW-CD Shows animations of nearly all the text examples. It also has the entire book in Maple notebooks.
- NEW-An entire chapter devoted to calculus of transcendental functions-Combines parts of two previous chapters into the new Ch. 7.
- Provides students with a clearer explanation of this subject within one solid, unified, and fully rewritten chapter.
- NEW-Expanded treatment of differential equations (New Chapter 9).
- Introduces students to both direction fields and Euler's method together with the more symbolic elementary methods and applications for both first- and second-order equations.
- NEW-1040 new True/False Questions-Available on the CD. They focus on theory and push the student to read.
- NEW-Reorganized content-Covers applied max-min problems in Ch.3 and defers related rates to Ch.4.
- Offers students the opportunities to focus on and study these challenging topics in separate chapters-and test their knowledge of them in separate unit tests.
- Approximately 7000 total problems and interesting applications-Covers all ranges of difficulty, highly theoretical and computationally oriented problems.
- Encourages students to learn by doing.
- Technology projects-Features icons that take users to Maple/ Mathematica/MATLAB/Calculator resources on the CD-ROM.
- Gives students the opportunity to apply conceptually based technology following key sections of the text.
- 320 Section-ending Concepts: Questions & Discussion.
- Serves students with a basis for either writing assignments or class discussion.
- Small optional section of matrix terminology and notation in the multivariable portion of the text.
- A lively and accessible writing style.
- Helps students feel comfortable with the topics covered, and their ability to master them.
- Most visual text on the market.
- Highlights are hundreds of Mathematica and MATLAB generated figures.

**1. Functions, Graphs, and Models**

Functions and Mathematical Modeling

Graphs of Equations and Functions

Polynomials and Algebraic Functions

Transcendental Functions

Preview: What Is Calculus?

**2. Prelude to Calculus**

Tangent Lines and Slope Predictors

The Limit Concept

More about Limits

The Concept of Continuity

**3. The Derivative**

The Derivative and Rates of Change

Basic Differentiation Rules

The Chain Rule

Derivatives of Algebraic Functions

Maxima and Minima of Functions on Closed Intervals

Applied Optimization Problems

Derivatives of Trigonometric Functions

Successive Approximations and Newton's Method

**4. Additional Applications of the Derivative**

Implicit Differentiation and Related Rates

Increments, Differentials, and Linear Approximation

Increasing and Decreasing Functions and the Mean Value Theorem

The First Derivative Test and Applications

Simple Curve Sketching

Higher Derivatives and Concavity

Curve Sketching and Asymptotes

**5. The Integral**

Introduction

Antiderivatives and Initial Value Problems

Elementary Area Computations

Riemann Sums and the Integral

Evaluation of Integrals

The Fundamental Theorem of Calculus

Integration by Substitution

Areas of Plane Regions

Numerical Integration

**6. Applications of the Integral**

Riemann Sum Approximations

Volumes by the Method of Cross Sections

Volumes by the Method of Cylindrical Shells

Arc Length and Surface Area of Revolution

Force and Work

Centroids of Plane Regions and Curves

**7. Calculus of Transcendental Functions**

Exponential and Logarithmic Functions

Indeterminate Forms and L'Hopîtal's Rule

More Indeterminate Forms

The Logarithm as an Integral

Inverse Trigonometric Functions

Hyperbolic Functions

**8. Techniques of Integration**

Introduction

Integral Tables and Simple Substitutions

Integration by Parts

Trigonometric Integrals

Rational Functions and Partial Fractions

Trigonometric Substitutions

Integrals Involving Quadratic Polynomials

Improper Integrals

**9. Differential Equations**

Simple Equations and Models

Slope Fields and Euler's Method

Separable Equations and Applications

Linear Equations and Applications

Population Models

Linear Second-Order Equations

Mechanical Vibrations

**10. Polar Coordinates and Parametric Curves**

Analytic Geometry and the Conic Sections

Polar Coordinates

Area Computations in Polar Coordinates

Parametric Curves

Integral Computations with Parametric Curves

Conic Sections and Applications

**11. Infinite Series**

Introduction

Infinite Sequences

Infinite Series and Convergence

Taylor Series and Taylor Polynomials

The Integral Test

Comparison Tests for Positive-Term Series

Alternating Series and Absolute Convergence

Power Series

Power Series Computations

Series Solutions of Differential Equations

**12. Vectors, Curves, and Surfaces in Space**

Vectors in the Plane

Rectangular Coordinates and Three-Dimensional Vectors

The Cross Product of Vectors

Lines and Planes in Space

Curves and Motions in Space

Curvature and Acceleration

Cylinders and Quadric Surfaces

Cylindrical and Spherical Coordinates

**13. Partial Differentiation**

Introduction

Functions of Several Variables

Limits and Continuity

Partial Derivatives

Multivariable Maxima and Minima

Increments and Linear Approximation

The Multivariable Chain Rule

Directional Derivatives and Gradient Vectors

Lagrange Multipliers and Constrained Optimization

Critical Points of Multivariable Functions

**14. Multiple Integrals**

Double Integrals

Double Integrals over More General Regions

Area and Volume by Double Integration

Double Integrals in Polar Coordinates

Applications of Double Integrals

Triple Integrals

Integration in Cylindrical and Spherical Coordinates

Surface Area

Change of Variables in Multiple Integrals

**15. Vector Calculus**

Vector Fields

Line Integrals

The Fundamental Theorem and Independence of Path

Green's Theorem

Surface Integrals

The Divergence Theorem

Stokes' Theorem

Appendices

Answers

Index