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Cover type: Hardback

Edition: 4TH 99

Copyright: 1999

Publisher: Brooks/Cole Publishing Co.

Published: 1999

International: No

Edition: 4TH 99

Copyright: 1999

Publisher: Brooks/Cole Publishing Co.

Published: 1999

International: No

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This is the most successful calculus textbook in the world. The proof of this success is the text's use in such a wide variety of colleges and universities. The new edition of this best-selling text has been carefully and thoroughly revised by enhancing the features that make it such a powerful teaching and learning tool for calculus: integrity, meticulous accuracy, precision, a clear exposition and patient explanations, character, and attention to detail. It continues to embrace the best aspects of reform (many were incorporated in the previous edition) by combining the traditional theoretical aspects of calculus with creative teaching and learning techniques. This is accomplished by a focus on conceptual understanding, the use of real world data and real-life applications, projects, and the use of technology (where appropriate).

Everyone agrees that the main goal of calculus instruction is for the student to understand the basic ideas. The goal of this book is to support this while motivating students through the use real-world applications, building the essential mathematical reasoning skills, and helping them develop an appreciation and enthusiasm for calculus.

*Features:*

*'A Preview of Calculus'*is located at the beginning of the book and gives an overview of the subject. It ends with a list of questions to motivate further study.- Examples are not only models for problem-solving or a means of demonstrating techniques--they also encourage students to develop an analytic view of the subject.
- Use of technology is optional--appropriate use is recommended as a powerful stimulus to enhance mathematical discovery. Students are encouraged to use a graphing utility or computer algebra system as a tool for exploration, discovery, and problem-solving. Many opportunities to execute complicated computations, and to verify the results of other solution methods using technology are presented.
- In addition to describing the benefits of using technology, the text also pays special attention to its possible misuse or misinterpretation. Notable section: Graphing with Calculus and Calculators (Section 4.6).
- Comprehensive review sections follow each chapter. A
*'Concept Check'*and*'True/False Quiz*' allow the student to prepare for upcoming tests through ideas and skill-building. These are included to further support the idea of conceptual understanding. *'Strategies'*sections (based on George Polya's problem-solving methodology) help students select what techniques they'll need to solve problems in situations where the choice is not obvious. These sections also help them develop true problem-solving skills and intuition.*'Problems Plus'*exercises reinforce concepts by requiring students to apply techniques from more than one chapter of the text.*'Problems Plus'*sections patiently show students how to approach a challenging problem and encourage them to discover the concepts on their own, making them more likely to remember the results. Previously found at the end of every even chapter, they are now at the end.- Stewart draws on physics, engineering, chemistry, biology, medicine, and social science to motivate students and demonstrate the power of calculus as a problem-solving tool.
- A clean, user-friendly design provides a clear presentation of accuracy, clarity, and realism. The art program and its functional use of color will help students visualize mathematical concepts more easily.
- Historical and biographical margin notes enliven the course and show students that mathematics was created by living, breathing human beings.
*The Rule of Four*is incorporated where appropriate and stresses numerical, visual, algebraic, and verbal interpretations.- More than 30% of the exercises are new. Some new exercises encourage the development of communication skills by explicitly requesting descriptions, conjectures, and explanations. The addition of conceptual exercises is designed to stimulate critical thinking and reinforce the concepts of calculus.
- New projects include
*'Writing Projects'*that ask students to compare present-day methods with those of the founders of calculus;*'Laboratory Projects'*featuring content that engages student interest;*'Applied Projects'*that capture students' imagination and demonstrate the real-world use of mathematics; and*'Discovery Projects'*that anticipate results to be discussed later. - A new optional chapter with an introduction to Differential Equations is unified by the theme of modeling. Qualitative, numerical, and analytic approaches are given equal consideration. This is included in the second semester.
- References to
*'Journey through Calculus'*are indicated throughout the text by the use of a marginal icon. These icons direct students to a specific activity in 'Journey through Calculus' that either leads to or expands on the concept being learned. This interactive CD-ROM shows what technology can do as a medium for teaching calculus. *The Stewart Calculus Resource Center*provides additional information on the book as well as a discussion of activities and extra problems.

**Stewart, James : McMaster University **

James Stewart, McMaster University; Ph.D., University of Toronto

**1. FUNCTIONS AND MODELS. **

Four Ways to Represent a Function.

Mathematical Models.

New Functions from Old Functions.

Graphing Calculators and Computers.

Review.

Principles of Problem Solving.

**2. LIMITS AND RATES OF CHANGE. **

The Tangent and Velocity Problems.

The Limit of a Function.

Calculating Limits Using the Limit Laws.

The Precise Definition of a Limit.

Continuity.

Tangents, Velocities, and Other Rates of Change.

Review.

Problems Plus.

**3. DERIVATIVES. **

Derivatives.

The Derivative as a Function.

Differentiation Formulas.

Rates of Change in the Natural and Social Sciences.

Derivatives of Trigonometric Functions.

The Chain Rule.

Implicit Differentiation.

Higher Derivatives.

Related Rates.

Linear Approximations and Differentials.

Review.

Problems Plus.

**4. APPLICATIONS OF DIFFERENTIATION. **

Maximum and Minimum Values.

The Mean Value Theorem.

How Derivatives Affect the Shape of a Graph.

Limits at Infinity; Horizontal Asymptotes.

Summary of Curve Sketching.

Graphing with Calculus and Calculators.

Optimization Problems.

Applications to Economics.

Newton's Method.

Antiderivatives.

Review.

Problems Plus.

**5. INTEGRALS. **

Areas and Distances.

The Definite Integral.

The Fundamental Theorem of Calculus.

Indefinite Integrals and the Total Change Theorem.

The Substitution Rule.

Review.

Problems Plus.

**6. APPLICATIONS OF INTEGRATION. **

Areas Between Curves.

Volume.

Volumes by Cylindrical Shells.

Work.

Average Value of a Function.

Review.

Problems Plus.

**7. INVERSE FUNCTIONS. **

Inverse Functions.

Exponential Functions and Their Derivatives.

Logarithmic Functions.

Derivatives of Logarithmic Functions.

The Natural Logarithmic Function.

The Natural Exponential Function.

General Logarithmic and Exponential Functions.

Inverse Trigonometric Functions.

Hyperbolic Functions.

Indeterminate Forms and l'Hospital's Rule.

Review.

Problems Plus.

**8. TECHNIQUES OF INTEGRATION. **

Integration by Parts.

Trigonometric Integrals.

Trigonometric Substitution.

Integration of Rational Functions by Partial Fractions.

Strategy for Integration.

Integration Using Tables and Computer Algebra Systems.

Approximate Integration.

Improper Integrals.

Review.

Problems Plus.

**9. FURTHER APPLICATIONS OF INTEGRATION. **

Arc Length.

Area of a Surface of Revolution.

Applications to Physics and Engineering.

Applications to Economics and Biology.

Probability.

Review.

Problems Plus.

**10. DIFFERENTIAL EQUATIONS. **

Modeling with Differential Equations.

Direction Fields and Euler's Method.

Separable Equations.

Exponential Growth and Decay.

The Logistic Equation.

Linear Equations.

Predator-Prey Systems.

Review.

Problems Plus.

**11. PARAMETRIC EQUATIONS AND POLAR COORDINATES. **

Curves Defined by Parametric Equations.

Tangents and Areas.

Arc Length and Surface Area.

Polar Coordinates.

Areas and Lengths in Polar Coordinates.

Conic Sections.

Conic Sections in Polar Coordinates.

Review.

Problems Plus.

**12. INFINITE SEQUENCES AND SERIES. **

Sequences. Series.

The Integral Test and Estimates of Sums.

The Comparison Tests.

Alternating Series.

Absolute Convergence and the Ratio and Root Tests.

Strategy for Testing Series.

Power Series.

Representation of Functions as Power Series.

Taylor and Maclaurin Series.

The Binomial Series.

Applications of Taylor Polynomials.

Review. Problems Plus.

**13. VECTORS AND THE GEOMETRY OF SPACE. **

Three-Dimensional Coordinate Systems.

Vectors.

The Dot Product.

The Cross Product.

Equations of Lines and Planes.

Cylinders and Quadratic Surfaces.

Cylindrical and Spherical Coordinates.

Review.

Problems Plus.

**14. VECTOR FUNCTIONS. **

Vector Functions and Space Curves.

Derivatives and Integrals of Vector Functions.

Arc Length and Curvature.

Motion in Space: Velocity and Acceleration.

Review.

Problems Plus.

**15. PARTIAL DERIVATIVES. **

Functions of Several Variables.

Limits and Continuity.

Partial Derivatives.

Tangent Planes and Differentials.

The Chain Rule.

Directional Derivatives and the Gradient Vector.

Maximum and Minimum Values.

Lagrange Multipliers.

Review.

Problems Plus.

**16. MULTIPLE INTEGRALS. **

Double Integrals over Rectangles.

Iterated Integrals.

Double Integrals over General Regions.

Double Integrals in Polar Coordinates.

Applications of Double Integrals.

Surface Area.

Triple Integrals.

Triple Integrals in Cylindrical and Spherical Coordinates.

Change of Variables in Multiple Integrals.

Review.

Problems Plus.

**17. VECTOR CALCULUS. **

Vector Fields. Line Integrals.

The Fundamental Theorem for Line Integrals.

Green's Theorem.

Curl and Divergence.

Parametric Surfaces and Their Areas.

Surface Integrals.

Stokes' Theorem.

The Divergence Theorem.

Summary.

Review.

Problems Plus.

**18. SECOND-ORDER DIFFERENTIAL EQUATIONS. **

Second-Order Linear Equations.

Nonhomogeneous Linear Equations.

Applications of Second-Order Differential Equations.

Series Solutions.

Review.

Problems Plus.

APPENDICES.

A. Integers, Inequalities, and Absolute Values.

B. Coordinate Geometry and Lines.

C. Graphs of Second-Degree Equations.

D. Trigonometry.

E. Sigma Notation.

F. Proofs of Theorems.

G. Complex Numbers.

H. Answers to Odd-Numbered Exercises.

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Summary

This is the most successful calculus textbook in the world. The proof of this success is the text's use in such a wide variety of colleges and universities. The new edition of this best-selling text has been carefully and thoroughly revised by enhancing the features that make it such a powerful teaching and learning tool for calculus: integrity, meticulous accuracy, precision, a clear exposition and patient explanations, character, and attention to detail. It continues to embrace the best aspects of reform (many were incorporated in the previous edition) by combining the traditional theoretical aspects of calculus with creative teaching and learning techniques. This is accomplished by a focus on conceptual understanding, the use of real world data and real-life applications, projects, and the use of technology (where appropriate).

Everyone agrees that the main goal of calculus instruction is for the student to understand the basic ideas. The goal of this book is to support this while motivating students through the use real-world applications, building the essential mathematical reasoning skills, and helping them develop an appreciation and enthusiasm for calculus.

*Features:*

*'A Preview of Calculus'*is located at the beginning of the book and gives an overview of the subject. It ends with a list of questions to motivate further study.- Examples are not only models for problem-solving or a means of demonstrating techniques--they also encourage students to develop an analytic view of the subject.
- Use of technology is optional--appropriate use is recommended as a powerful stimulus to enhance mathematical discovery. Students are encouraged to use a graphing utility or computer algebra system as a tool for exploration, discovery, and problem-solving. Many opportunities to execute complicated computations, and to verify the results of other solution methods using technology are presented.
- In addition to describing the benefits of using technology, the text also pays special attention to its possible misuse or misinterpretation. Notable section: Graphing with Calculus and Calculators (Section 4.6).
- Comprehensive review sections follow each chapter. A
*'Concept Check'*and*'True/False Quiz*' allow the student to prepare for upcoming tests through ideas and skill-building. These are included to further support the idea of conceptual understanding. *'Strategies'*sections (based on George Polya's problem-solving methodology) help students select what techniques they'll need to solve problems in situations where the choice is not obvious. These sections also help them develop true problem-solving skills and intuition.*'Problems Plus'*exercises reinforce concepts by requiring students to apply techniques from more than one chapter of the text.*'Problems Plus'*sections patiently show students how to approach a challenging problem and encourage them to discover the concepts on their own, making them more likely to remember the results. Previously found at the end of every even chapter, they are now at the end.- Stewart draws on physics, engineering, chemistry, biology, medicine, and social science to motivate students and demonstrate the power of calculus as a problem-solving tool.
- A clean, user-friendly design provides a clear presentation of accuracy, clarity, and realism. The art program and its functional use of color will help students visualize mathematical concepts more easily.
- Historical and biographical margin notes enliven the course and show students that mathematics was created by living, breathing human beings.
*The Rule of Four*is incorporated where appropriate and stresses numerical, visual, algebraic, and verbal interpretations.- More than 30% of the exercises are new. Some new exercises encourage the development of communication skills by explicitly requesting descriptions, conjectures, and explanations. The addition of conceptual exercises is designed to stimulate critical thinking and reinforce the concepts of calculus.
- New projects include
*'Writing Projects'*that ask students to compare present-day methods with those of the founders of calculus;*'Laboratory Projects'*featuring content that engages student interest;*'Applied Projects'*that capture students' imagination and demonstrate the real-world use of mathematics; and*'Discovery Projects'*that anticipate results to be discussed later. - A new optional chapter with an introduction to Differential Equations is unified by the theme of modeling. Qualitative, numerical, and analytic approaches are given equal consideration. This is included in the second semester.
- References to
*'Journey through Calculus'*are indicated throughout the text by the use of a marginal icon. These icons direct students to a specific activity in 'Journey through Calculus' that either leads to or expands on the concept being learned. This interactive CD-ROM shows what technology can do as a medium for teaching calculus. *The Stewart Calculus Resource Center*provides additional information on the book as well as a discussion of activities and extra problems.

Author Bio

**Stewart, James : McMaster University **

James Stewart, McMaster University; Ph.D., University of Toronto

Table of Contents

**1. FUNCTIONS AND MODELS. **

Four Ways to Represent a Function.

Mathematical Models.

New Functions from Old Functions.

Graphing Calculators and Computers.

Review.

Principles of Problem Solving.

**2. LIMITS AND RATES OF CHANGE. **

The Tangent and Velocity Problems.

The Limit of a Function.

Calculating Limits Using the Limit Laws.

The Precise Definition of a Limit.

Continuity.

Tangents, Velocities, and Other Rates of Change.

Review.

Problems Plus.

**3. DERIVATIVES. **

Derivatives.

The Derivative as a Function.

Differentiation Formulas.

Rates of Change in the Natural and Social Sciences.

Derivatives of Trigonometric Functions.

The Chain Rule.

Implicit Differentiation.

Higher Derivatives.

Related Rates.

Linear Approximations and Differentials.

Review.

Problems Plus.

**4. APPLICATIONS OF DIFFERENTIATION. **

Maximum and Minimum Values.

The Mean Value Theorem.

How Derivatives Affect the Shape of a Graph.

Limits at Infinity; Horizontal Asymptotes.

Summary of Curve Sketching.

Graphing with Calculus and Calculators.

Optimization Problems.

Applications to Economics.

Newton's Method.

Antiderivatives.

Review.

Problems Plus.

**5. INTEGRALS. **

Areas and Distances.

The Definite Integral.

The Fundamental Theorem of Calculus.

Indefinite Integrals and the Total Change Theorem.

The Substitution Rule.

Review.

Problems Plus.

**6. APPLICATIONS OF INTEGRATION. **

Areas Between Curves.

Volume.

Volumes by Cylindrical Shells.

Work.

Average Value of a Function.

Review.

Problems Plus.

**7. INVERSE FUNCTIONS. **

Inverse Functions.

Exponential Functions and Their Derivatives.

Logarithmic Functions.

Derivatives of Logarithmic Functions.

The Natural Logarithmic Function.

The Natural Exponential Function.

General Logarithmic and Exponential Functions.

Inverse Trigonometric Functions.

Hyperbolic Functions.

Indeterminate Forms and l'Hospital's Rule.

Review.

Problems Plus.

**8. TECHNIQUES OF INTEGRATION. **

Integration by Parts.

Trigonometric Integrals.

Trigonometric Substitution.

Integration of Rational Functions by Partial Fractions.

Strategy for Integration.

Integration Using Tables and Computer Algebra Systems.

Approximate Integration.

Improper Integrals.

Review.

Problems Plus.

**9. FURTHER APPLICATIONS OF INTEGRATION. **

Arc Length.

Area of a Surface of Revolution.

Applications to Physics and Engineering.

Applications to Economics and Biology.

Probability.

Review.

Problems Plus.

**10. DIFFERENTIAL EQUATIONS. **

Modeling with Differential Equations.

Direction Fields and Euler's Method.

Separable Equations.

Exponential Growth and Decay.

The Logistic Equation.

Linear Equations.

Predator-Prey Systems.

Review.

Problems Plus.

**11. PARAMETRIC EQUATIONS AND POLAR COORDINATES. **

Curves Defined by Parametric Equations.

Tangents and Areas.

Arc Length and Surface Area.

Polar Coordinates.

Areas and Lengths in Polar Coordinates.

Conic Sections.

Conic Sections in Polar Coordinates.

Review.

Problems Plus.

**12. INFINITE SEQUENCES AND SERIES. **

Sequences. Series.

The Integral Test and Estimates of Sums.

The Comparison Tests.

Alternating Series.

Absolute Convergence and the Ratio and Root Tests.

Strategy for Testing Series.

Power Series.

Representation of Functions as Power Series.

Taylor and Maclaurin Series.

The Binomial Series.

Applications of Taylor Polynomials.

Review. Problems Plus.

**13. VECTORS AND THE GEOMETRY OF SPACE. **

Three-Dimensional Coordinate Systems.

Vectors.

The Dot Product.

The Cross Product.

Equations of Lines and Planes.

Cylinders and Quadratic Surfaces.

Cylindrical and Spherical Coordinates.

Review.

Problems Plus.

**14. VECTOR FUNCTIONS. **

Vector Functions and Space Curves.

Derivatives and Integrals of Vector Functions.

Arc Length and Curvature.

Motion in Space: Velocity and Acceleration.

Review.

Problems Plus.

**15. PARTIAL DERIVATIVES. **

Functions of Several Variables.

Limits and Continuity.

Partial Derivatives.

Tangent Planes and Differentials.

The Chain Rule.

Directional Derivatives and the Gradient Vector.

Maximum and Minimum Values.

Lagrange Multipliers.

Review.

Problems Plus.

**16. MULTIPLE INTEGRALS. **

Double Integrals over Rectangles.

Iterated Integrals.

Double Integrals over General Regions.

Double Integrals in Polar Coordinates.

Applications of Double Integrals.

Surface Area.

Triple Integrals.

Triple Integrals in Cylindrical and Spherical Coordinates.

Change of Variables in Multiple Integrals.

Review.

Problems Plus.

**17. VECTOR CALCULUS. **

Vector Fields. Line Integrals.

The Fundamental Theorem for Line Integrals.

Green's Theorem.

Curl and Divergence.

Parametric Surfaces and Their Areas.

Surface Integrals.

Stokes' Theorem.

The Divergence Theorem.

Summary.

Review.

Problems Plus.

**18. SECOND-ORDER DIFFERENTIAL EQUATIONS. **

Second-Order Linear Equations.

Nonhomogeneous Linear Equations.

Applications of Second-Order Differential Equations.

Series Solutions.

Review.

Problems Plus.

APPENDICES.

A. Integers, Inequalities, and Absolute Values.

B. Coordinate Geometry and Lines.

C. Graphs of Second-Degree Equations.

D. Trigonometry.

E. Sigma Notation.

F. Proofs of Theorems.

G. Complex Numbers.

H. Answers to Odd-Numbered Exercises.

Publisher Info

Publisher: Brooks/Cole Publishing Co.

Published: 1999

International: No

Published: 1999

International: No

This is the most successful calculus textbook in the world. The proof of this success is the text's use in such a wide variety of colleges and universities. The new edition of this best-selling text has been carefully and thoroughly revised by enhancing the features that make it such a powerful teaching and learning tool for calculus: integrity, meticulous accuracy, precision, a clear exposition and patient explanations, character, and attention to detail. It continues to embrace the best aspects of reform (many were incorporated in the previous edition) by combining the traditional theoretical aspects of calculus with creative teaching and learning techniques. This is accomplished by a focus on conceptual understanding, the use of real world data and real-life applications, projects, and the use of technology (where appropriate).

Everyone agrees that the main goal of calculus instruction is for the student to understand the basic ideas. The goal of this book is to support this while motivating students through the use real-world applications, building the essential mathematical reasoning skills, and helping them develop an appreciation and enthusiasm for calculus.

*Features:*

*'A Preview of Calculus'*is located at the beginning of the book and gives an overview of the subject. It ends with a list of questions to motivate further study.- Examples are not only models for problem-solving or a means of demonstrating techniques--they also encourage students to develop an analytic view of the subject.
- Use of technology is optional--appropriate use is recommended as a powerful stimulus to enhance mathematical discovery. Students are encouraged to use a graphing utility or computer algebra system as a tool for exploration, discovery, and problem-solving. Many opportunities to execute complicated computations, and to verify the results of other solution methods using technology are presented.
- In addition to describing the benefits of using technology, the text also pays special attention to its possible misuse or misinterpretation. Notable section: Graphing with Calculus and Calculators (Section 4.6).
- Comprehensive review sections follow each chapter. A
*'Concept Check'*and*'True/False Quiz*' allow the student to prepare for upcoming tests through ideas and skill-building. These are included to further support the idea of conceptual understanding. *'Strategies'*sections (based on George Polya's problem-solving methodology) help students select what techniques they'll need to solve problems in situations where the choice is not obvious. These sections also help them develop true problem-solving skills and intuition.*'Problems Plus'*exercises reinforce concepts by requiring students to apply techniques from more than one chapter of the text.*'Problems Plus'*sections patiently show students how to approach a challenging problem and encourage them to discover the concepts on their own, making them more likely to remember the results. Previously found at the end of every even chapter, they are now at the end.- Stewart draws on physics, engineering, chemistry, biology, medicine, and social science to motivate students and demonstrate the power of calculus as a problem-solving tool.
- A clean, user-friendly design provides a clear presentation of accuracy, clarity, and realism. The art program and its functional use of color will help students visualize mathematical concepts more easily.
- Historical and biographical margin notes enliven the course and show students that mathematics was created by living, breathing human beings.
*The Rule of Four*is incorporated where appropriate and stresses numerical, visual, algebraic, and verbal interpretations.- More than 30% of the exercises are new. Some new exercises encourage the development of communication skills by explicitly requesting descriptions, conjectures, and explanations. The addition of conceptual exercises is designed to stimulate critical thinking and reinforce the concepts of calculus.
- New projects include
*'Writing Projects'*that ask students to compare present-day methods with those of the founders of calculus;*'Laboratory Projects'*featuring content that engages student interest;*'Applied Projects'*that capture students' imagination and demonstrate the real-world use of mathematics; and*'Discovery Projects'*that anticipate results to be discussed later. - A new optional chapter with an introduction to Differential Equations is unified by the theme of modeling. Qualitative, numerical, and analytic approaches are given equal consideration. This is included in the second semester.
- References to
*'Journey through Calculus'*are indicated throughout the text by the use of a marginal icon. These icons direct students to a specific activity in 'Journey through Calculus' that either leads to or expands on the concept being learned. This interactive CD-ROM shows what technology can do as a medium for teaching calculus. *The Stewart Calculus Resource Center*provides additional information on the book as well as a discussion of activities and extra problems.

**Stewart, James : McMaster University **

James Stewart, McMaster University; Ph.D., University of Toronto

**1. FUNCTIONS AND MODELS. **

Four Ways to Represent a Function.

Mathematical Models.

New Functions from Old Functions.

Graphing Calculators and Computers.

Review.

Principles of Problem Solving.

**2. LIMITS AND RATES OF CHANGE. **

The Tangent and Velocity Problems.

The Limit of a Function.

Calculating Limits Using the Limit Laws.

The Precise Definition of a Limit.

Continuity.

Tangents, Velocities, and Other Rates of Change.

Review.

Problems Plus.

**3. DERIVATIVES. **

Derivatives.

The Derivative as a Function.

Differentiation Formulas.

Rates of Change in the Natural and Social Sciences.

Derivatives of Trigonometric Functions.

The Chain Rule.

Implicit Differentiation.

Higher Derivatives.

Related Rates.

Linear Approximations and Differentials.

Review.

Problems Plus.

**4. APPLICATIONS OF DIFFERENTIATION. **

Maximum and Minimum Values.

The Mean Value Theorem.

How Derivatives Affect the Shape of a Graph.

Limits at Infinity; Horizontal Asymptotes.

Summary of Curve Sketching.

Graphing with Calculus and Calculators.

Optimization Problems.

Applications to Economics.

Newton's Method.

Antiderivatives.

Review.

Problems Plus.

**5. INTEGRALS. **

Areas and Distances.

The Definite Integral.

The Fundamental Theorem of Calculus.

Indefinite Integrals and the Total Change Theorem.

The Substitution Rule.

Review.

Problems Plus.

**6. APPLICATIONS OF INTEGRATION. **

Areas Between Curves.

Volume.

Volumes by Cylindrical Shells.

Work.

Average Value of a Function.

Review.

Problems Plus.

**7. INVERSE FUNCTIONS. **

Inverse Functions.

Exponential Functions and Their Derivatives.

Logarithmic Functions.

Derivatives of Logarithmic Functions.

The Natural Logarithmic Function.

The Natural Exponential Function.

General Logarithmic and Exponential Functions.

Inverse Trigonometric Functions.

Hyperbolic Functions.

Indeterminate Forms and l'Hospital's Rule.

Review.

Problems Plus.

**8. TECHNIQUES OF INTEGRATION. **

Integration by Parts.

Trigonometric Integrals.

Trigonometric Substitution.

Integration of Rational Functions by Partial Fractions.

Strategy for Integration.

Integration Using Tables and Computer Algebra Systems.

Approximate Integration.

Improper Integrals.

Review.

Problems Plus.

**9. FURTHER APPLICATIONS OF INTEGRATION. **

Arc Length.

Area of a Surface of Revolution.

Applications to Physics and Engineering.

Applications to Economics and Biology.

Probability.

Review.

Problems Plus.

**10. DIFFERENTIAL EQUATIONS. **

Modeling with Differential Equations.

Direction Fields and Euler's Method.

Separable Equations.

Exponential Growth and Decay.

The Logistic Equation.

Linear Equations.

Predator-Prey Systems.

Review.

Problems Plus.

**11. PARAMETRIC EQUATIONS AND POLAR COORDINATES. **

Curves Defined by Parametric Equations.

Tangents and Areas.

Arc Length and Surface Area.

Polar Coordinates.

Areas and Lengths in Polar Coordinates.

Conic Sections.

Conic Sections in Polar Coordinates.

Review.

Problems Plus.

**12. INFINITE SEQUENCES AND SERIES. **

Sequences. Series.

The Integral Test and Estimates of Sums.

The Comparison Tests.

Alternating Series.

Absolute Convergence and the Ratio and Root Tests.

Strategy for Testing Series.

Power Series.

Representation of Functions as Power Series.

Taylor and Maclaurin Series.

The Binomial Series.

Applications of Taylor Polynomials.

Review. Problems Plus.

**13. VECTORS AND THE GEOMETRY OF SPACE. **

Three-Dimensional Coordinate Systems.

Vectors.

The Dot Product.

The Cross Product.

Equations of Lines and Planes.

Cylinders and Quadratic Surfaces.

Cylindrical and Spherical Coordinates.

Review.

Problems Plus.

**14. VECTOR FUNCTIONS. **

Vector Functions and Space Curves.

Derivatives and Integrals of Vector Functions.

Arc Length and Curvature.

Motion in Space: Velocity and Acceleration.

Review.

Problems Plus.

**15. PARTIAL DERIVATIVES. **

Functions of Several Variables.

Limits and Continuity.

Partial Derivatives.

Tangent Planes and Differentials.

The Chain Rule.

Directional Derivatives and the Gradient Vector.

Maximum and Minimum Values.

Lagrange Multipliers.

Review.

Problems Plus.

**16. MULTIPLE INTEGRALS. **

Double Integrals over Rectangles.

Iterated Integrals.

Double Integrals over General Regions.

Double Integrals in Polar Coordinates.

Applications of Double Integrals.

Surface Area.

Triple Integrals.

Triple Integrals in Cylindrical and Spherical Coordinates.

Change of Variables in Multiple Integrals.

Review.

Problems Plus.

**17. VECTOR CALCULUS. **

Vector Fields. Line Integrals.

The Fundamental Theorem for Line Integrals.

Green's Theorem.

Curl and Divergence.

Parametric Surfaces and Their Areas.

Surface Integrals.

Stokes' Theorem.

The Divergence Theorem.

Summary.

Review.

Problems Plus.

**18. SECOND-ORDER DIFFERENTIAL EQUATIONS. **

Second-Order Linear Equations.

Nonhomogeneous Linear Equations.

Applications of Second-Order Differential Equations.

Series Solutions.

Review.

Problems Plus.

APPENDICES.

A. Integers, Inequalities, and Absolute Values.

B. Coordinate Geometry and Lines.

C. Graphs of Second-Degree Equations.

D. Trigonometry.

E. Sigma Notation.

F. Proofs of Theorems.

G. Complex Numbers.

H. Answers to Odd-Numbered Exercises.