ISBN13: 978-0534393397

ISBN10: 053439339X

Cover type:

Edition/Copyright: 5TH 03

Publisher: Brooks/Cole Publishing Co.

Published: 2003

International: No

ISBN10: 053439339X

Cover type:

Edition/Copyright: 5TH 03

Publisher: Brooks/Cole Publishing Co.

Published: 2003

International: No

Stewart's Calculus, FIFTH EDITION has the mathematical precision, accuracy, clarity of exposition and outstanding examples and problem sets that have characterized the first four editions. Stewart retains the focus on problem solving and the pedagogical system that has made the book a favorite of students and instructors in a wide variety of colleges and universities throughout the world. In this Fifth Edition, he has made hundreds of small improvements: new examples, additional steps in existing examples, updating of data in existing examples and exercises, new phrases and margin notes to clarify the exposition, references to other sources and web sites, redrawn art, and references to the TEC CD (Tools for Enriching Calculus). These refinements ensure that students and instructors have the best materials available. The number of pages in the book, however, remains unchanged from the 4th edition. Further support for students and instructors is now available through a vast array of supplementary material.

Benefits:

- NEW! More than 25 percent of the exercises are new. Many of the new exercises make use of current data so students gain a better appreciation for the use of calculus as they learn to solve problems.
- NEW! The text is now supported by BROOKS/COLE ASSESSMENT (BCA). Available online or on CD-ROM, browser-based BCA is fully integrated testing, tutorial, and course management software. With no need for plug-ins or downloads, BCA offers algorithmically-generated problem values and machine-graded free response mathematics.
- NEW! Online homework system that contains guided step wise solutions to problems with context specific feedback.
- NEW! Stewartcalculus.com, an enriching Web site, provides a wealth of additional resources for students and instructors. The renovated site has a collection of exercises, with solutions, that existed in previous editions of the texts; downloadable versions of CalcLab manuals for the TI graphing calculators and Derive; algebra review and tutorials; additional topics; review quizzes, and much more.
- NEW! Instructor's Resource CD-ROM--a world of resources at your fingertips. This CD contains CalcLink 3.0 (a Microsoft®PowerPoint® collection of figures from the text, with animations and narration), BCA 2.0 Testing, the Instructor's Guide, Complete Electronic Solutions, and a Resource Integration Guide that makes it easy to incorporate the extensive supplements package into your teaching.
- NEW! WebTutor for WebCT or Blackboard is available with this edition of CALCULUS.
- NEW! MyCourse 2.0 Ask us about our new FREE online course builder! Whether you want only the easy-o-use tools to build it or the content to furnish it, Brooks/Cole offers you a simple solution for a custom course Web site that allows you to assign, track, and report on student progress; load your syllabus; and more. Contact your Brooks/Cole representative for details.
- Stewart's writing style speaks clearly and directly to the student, guiding them through key ideas, theorems, and problem solving steps. He encourages students to think as they read and learn calculus.
- Every concept is supported by thoughtfully worked examples - many with step-by-step explanations - and carefully chosen exercises. The quality of this pedagogical system is what sets Stewart's texts above others.
- NEW! New writing, laboratory, applied, and discovery projects foster greater understanding of concepts and encourage students to apply their problem solving skills to practical situations.
- A clean, user-friendly design provides a clear presentation of calculus. The art program and its functional and consistent use of color helps students identify and review mathematical concepts more easily.
- The topic of Differential Equations is unified by the theme of modeling. Qualitative, numerical, and analytic approaches are given equal consideration.
- 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. Many of these detailed examples display solutions that are presented graphically, analytically, and/or numerically to provide further insight into mathematical concepts. Margin notes expand on and clarify the steps of the solution.
- 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.
- Stewart's text has an extensive collection of more than 8,000 quality exercises. Each exercise set is carefully graded, progressing from skill-development problems to more challenging problems involving applications and proofs. The wide variety of types of exercises includes many technology-oriented, thought-provoking, real, and engaging problems.
- Conceptual exercises encourage the development of communication skills by explicitly requesting descriptions, conjectures, and explanations. These exercises stimulate critical thinking and reinforce the concepts of calculus.
- 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.
- 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).
- Many exercises in the text can be solved using technology--icons identify exercises where a graphing utility or a computer algebra system are recommended.
- NEW! Stewart has made literally hundreds of small improvements: new examples, additional steps in existing examples, new phrases and margin notes to clarify the exposition, references to other sources and web sites, and redrawn art.
- 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 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" are collections of more challenging exercises, found at the end of every chapter. These 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.
- Historical and biographical margin notes enliven the course and show students that mathematics was developed to help explain and represent natural phenomena.
- NEW! The review of inverse trigonometric functions has been moved from an appendix to Section 1.6.
- NEW! Sections 10.2 and 10.3 have been combined into a single section called "Calculus with Parametric Curves."
- NEW! In addition to the already expansive set of ancillary materials, there are many new supplements for the Fifth Edition. New package items include an Instructor's Resource CD-ROM, videotapes, and BCA Testing and Tutorials, and much more. See the supplements section for a complete and descriptive list. Technology oriented supplements were developed with guidance from a "Teaching Calculus with Technology" focus group. All ancillaries are developed under the direction of Jim Stewart.
- NEW! A free tutorial CD-ROM "Tools for Enriching Calculus (TEC)," is bound into each new copy of the text. References to TEC are indicated throughout the text with a marginal icon. These icons direct students to a specific interactive JAVA applet that helps students visualize the concept being learned. In addition, problems numbered in red correspond with "Homework Hints" on the CD-ROM. These hints guide students through the problem solving process, allowing students to find their own solution. TEC is also a useful classroom presentation tool for instructors.
- NEW! Interactive Video Skillbuilder CD-ROM, is packaged FREE with every new copy of this text.

Author Bio

**Stewart, James : McMaster University **

1. FUNCTIONS AND MODELS.

Four Ways to Represent a Function. Mathematical Models: A Catalog of Essential Functions. 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, Writing Project: Early Methods for Finding Tangents.

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, Applied Project: Where Should a Pilot Start Descent?, Applied Project: Building a Better Roller Coaster. Related Rates.

Linear Approximations and Differentials, Laboratory Project: Taylor Polynomials.

Review.

Problems Plus.

4. APPLICATIONS OF DIFFERENTIATION.

Maximum and Minimum Values, Applied Project: The Calculus of Rainbows.

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, Applied Project: The Shape of a Can.

Applications to Business and Economics.

Newton's Method.

Antiderivatives.

Review.

Problems Plus.

5. INTEGRALS.

Areas and Distances.

The Definite Integral, Discovery Project: Area Functions.

The Fundamental Theorem of Calculus.

Indefinite Integrals and the Net Change Theorem, Writing Project: Newton, Leibniz, and the Invention of Calculus.

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: EXPONENTIAL, LOGARITHMIC, AND INVERSE TRIGONOMETRIC FUNCTIONS.

Inverse Functions, Instructors may cover either Sections 7.2-7.4 or Sections 7.2*-7.4*, See the Preface. 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, Applied Project: Where to Sit at the Movie.

Hyperbolic Functions. Indeterminate Forms and L'Hospital's Rule, Writing Project: The Origins of 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, Discovery Project: Patterns in Integrals.

Approximate Integration.

Improper Integrals.

Review.

Problems Plus.

9. FURTHER APPLICATIONS OF INTEGRATION.

Arc Length, Discovery Project: Arc Length Contest.

Area of a Surface of Revolution, Discovery Project: rotating on a Slant.

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, Applied Project: How Fast Does a Tank Drain?, Applied Project: Which is Faster, Going Up or Coming Down?

Exponential Growth and Decay, Applied Project: Calculus and Baseball.

The Logistic Equation.

Linear Equations.

Predator-Prey Systems.

Review.

Problems Plus.

11. PARAMETRIC EQUATIONS AND POLAR COORDINATES.

Curves Defined by Parametric Equations, Laboratory Project: Families of Hypocycloids.

Calculus with Parametric Curves, Laboratory Project: Bezier Curves.

Polar Coordinates.

Areas and Lengths in Polar Coordinates.

Conic Sections.

Conic Sections in Polar Coordinates.

Review.

Problems Plus.

12. INFINITE SEQUENCES AND SERIES.

Sequences, Laboratory Project: Logistic 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.

Laboratory Project: An Ellusive Limit.

The Binomial Series, Writing Project: How Newton Discovered the Binomial Series.

Applications of Taylor Polynomials, Applied Project: Radiation from the Stars.

Review.

Problems Plus.

13. VECTORS AND THE GEOMETRY OF SPACE.

Three-Dimensional Coordinate Systems.

Vectors.

The Dot Product.

The Cross Product, Discovery Project: The Geometry of a Tetrahedron.

Equations of Lines and Planes.

Cylinders and Quadric Surfaces.

Cylindrical and Spherical Coordinates, Laboratory Project: Families of Surfaces.

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, Applied Project: Kepler's Laws.

Review.

Problems Plus.

15. PARTIAL DERIVATIVES.

Functions of Several Variables.

Limits and Continuity.

Partial Derivatives.

Tangent Planes and Linear Approximations.

The Chain Rule.

Directional Derivatives and the Gradient Vector.

Maximum and Minimum Values, Applied Project: Designing a Dumpster, Discovery Project: Quadratic Approximations and Critical Points.

Lagrange Multipliers, Applied Project: Rocket Science, Applied Project: Hydro-Turbine Optimization.

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, Discovery Project: Volumes of Hyperspheres.

Triple Integrals in Cylindrical and Spherical Coordinates, Applied Project: Roller Derby, Discovery Project: The Intersection of Three Cylinders.

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, Writing Project: Three Men and Two Theorems.

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.

Appendixes.

Answers to Odd-Numbered Exercises.

Index.

ISBN10: 053439339X

Cover type:

Edition/Copyright: 5TH 03

Publisher: Brooks/Cole Publishing Co.

Published: 2003

International: No

Stewart's Calculus, FIFTH EDITION has the mathematical precision, accuracy, clarity of exposition and outstanding examples and problem sets that have characterized the first four editions. Stewart retains the focus on problem solving and the pedagogical system that has made the book a favorite of students and instructors in a wide variety of colleges and universities throughout the world. In this Fifth Edition, he has made hundreds of small improvements: new examples, additional steps in existing examples, updating of data in existing examples and exercises, new phrases and margin notes to clarify the exposition, references to other sources and web sites, redrawn art, and references to the TEC CD (Tools for Enriching Calculus). These refinements ensure that students and instructors have the best materials available. The number of pages in the book, however, remains unchanged from the 4th edition. Further support for students and instructors is now available through a vast array of supplementary material.

Benefits:

- NEW! More than 25 percent of the exercises are new. Many of the new exercises make use of current data so students gain a better appreciation for the use of calculus as they learn to solve problems.
- NEW! The text is now supported by BROOKS/COLE ASSESSMENT (BCA). Available online or on CD-ROM, browser-based BCA is fully integrated testing, tutorial, and course management software. With no need for plug-ins or downloads, BCA offers algorithmically-generated problem values and machine-graded free response mathematics.
- NEW! Online homework system that contains guided step wise solutions to problems with context specific feedback.
- NEW! Stewartcalculus.com, an enriching Web site, provides a wealth of additional resources for students and instructors. The renovated site has a collection of exercises, with solutions, that existed in previous editions of the texts; downloadable versions of CalcLab manuals for the TI graphing calculators and Derive; algebra review and tutorials; additional topics; review quizzes, and much more.
- NEW! Instructor's Resource CD-ROM--a world of resources at your fingertips. This CD contains CalcLink 3.0 (a Microsoft®PowerPoint® collection of figures from the text, with animations and narration), BCA 2.0 Testing, the Instructor's Guide, Complete Electronic Solutions, and a Resource Integration Guide that makes it easy to incorporate the extensive supplements package into your teaching.
- NEW! WebTutor for WebCT or Blackboard is available with this edition of CALCULUS.
- NEW! MyCourse 2.0 Ask us about our new FREE online course builder! Whether you want only the easy-o-use tools to build it or the content to furnish it, Brooks/Cole offers you a simple solution for a custom course Web site that allows you to assign, track, and report on student progress; load your syllabus; and more. Contact your Brooks/Cole representative for details.
- Stewart's writing style speaks clearly and directly to the student, guiding them through key ideas, theorems, and problem solving steps. He encourages students to think as they read and learn calculus.
- Every concept is supported by thoughtfully worked examples - many with step-by-step explanations - and carefully chosen exercises. The quality of this pedagogical system is what sets Stewart's texts above others.
- NEW! New writing, laboratory, applied, and discovery projects foster greater understanding of concepts and encourage students to apply their problem solving skills to practical situations.
- A clean, user-friendly design provides a clear presentation of calculus. The art program and its functional and consistent use of color helps students identify and review mathematical concepts more easily.
- The topic of Differential Equations is unified by the theme of modeling. Qualitative, numerical, and analytic approaches are given equal consideration.
- 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. Many of these detailed examples display solutions that are presented graphically, analytically, and/or numerically to provide further insight into mathematical concepts. Margin notes expand on and clarify the steps of the solution.
- 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.
- Stewart's text has an extensive collection of more than 8,000 quality exercises. Each exercise set is carefully graded, progressing from skill-development problems to more challenging problems involving applications and proofs. The wide variety of types of exercises includes many technology-oriented, thought-provoking, real, and engaging problems.
- Conceptual exercises encourage the development of communication skills by explicitly requesting descriptions, conjectures, and explanations. These exercises stimulate critical thinking and reinforce the concepts of calculus.
- 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.
- 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).
- Many exercises in the text can be solved using technology--icons identify exercises where a graphing utility or a computer algebra system are recommended.
- NEW! Stewart has made literally hundreds of small improvements: new examples, additional steps in existing examples, new phrases and margin notes to clarify the exposition, references to other sources and web sites, and redrawn art.
- 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 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" are collections of more challenging exercises, found at the end of every chapter. These 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.
- Historical and biographical margin notes enliven the course and show students that mathematics was developed to help explain and represent natural phenomena.
- NEW! The review of inverse trigonometric functions has been moved from an appendix to Section 1.6.
- NEW! Sections 10.2 and 10.3 have been combined into a single section called "Calculus with Parametric Curves."
- NEW! In addition to the already expansive set of ancillary materials, there are many new supplements for the Fifth Edition. New package items include an Instructor's Resource CD-ROM, videotapes, and BCA Testing and Tutorials, and much more. See the supplements section for a complete and descriptive list. Technology oriented supplements were developed with guidance from a "Teaching Calculus with Technology" focus group. All ancillaries are developed under the direction of Jim Stewart.
- NEW! A free tutorial CD-ROM "Tools for Enriching Calculus (TEC)," is bound into each new copy of the text. References to TEC are indicated throughout the text with a marginal icon. These icons direct students to a specific interactive JAVA applet that helps students visualize the concept being learned. In addition, problems numbered in red correspond with "Homework Hints" on the CD-ROM. These hints guide students through the problem solving process, allowing students to find their own solution. TEC is also a useful classroom presentation tool for instructors.
- NEW! Interactive Video Skillbuilder CD-ROM, is packaged FREE with every new copy of this text.

Author Bio

**Stewart, James : McMaster University **

Table of Contents

1. FUNCTIONS AND MODELS.

Four Ways to Represent a Function. Mathematical Models: A Catalog of Essential Functions. 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, Writing Project: Early Methods for Finding Tangents.

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, Applied Project: Where Should a Pilot Start Descent?, Applied Project: Building a Better Roller Coaster. Related Rates.

Linear Approximations and Differentials, Laboratory Project: Taylor Polynomials.

Review.

Problems Plus.

4. APPLICATIONS OF DIFFERENTIATION.

Maximum and Minimum Values, Applied Project: The Calculus of Rainbows.

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, Applied Project: The Shape of a Can.

Applications to Business and Economics.

Newton's Method.

Antiderivatives.

Review.

Problems Plus.

5. INTEGRALS.

Areas and Distances.

The Definite Integral, Discovery Project: Area Functions.

The Fundamental Theorem of Calculus.

Indefinite Integrals and the Net Change Theorem, Writing Project: Newton, Leibniz, and the Invention of Calculus.

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: EXPONENTIAL, LOGARITHMIC, AND INVERSE TRIGONOMETRIC FUNCTIONS.

Inverse Functions, Instructors may cover either Sections 7.2-7.4 or Sections 7.2*-7.4*, See the Preface. 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, Applied Project: Where to Sit at the Movie.

Hyperbolic Functions. Indeterminate Forms and L'Hospital's Rule, Writing Project: The Origins of 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, Discovery Project: Patterns in Integrals.

Approximate Integration.

Improper Integrals.

Review.

Problems Plus.

9. FURTHER APPLICATIONS OF INTEGRATION.

Arc Length, Discovery Project: Arc Length Contest.

Area of a Surface of Revolution, Discovery Project: rotating on a Slant.

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, Applied Project: How Fast Does a Tank Drain?, Applied Project: Which is Faster, Going Up or Coming Down?

Exponential Growth and Decay, Applied Project: Calculus and Baseball.

The Logistic Equation.

Linear Equations.

Predator-Prey Systems.

Review.

Problems Plus.

11. PARAMETRIC EQUATIONS AND POLAR COORDINATES.

Curves Defined by Parametric Equations, Laboratory Project: Families of Hypocycloids.

Calculus with Parametric Curves, Laboratory Project: Bezier Curves.

Polar Coordinates.

Areas and Lengths in Polar Coordinates.

Conic Sections.

Conic Sections in Polar Coordinates.

Review.

Problems Plus.

12. INFINITE SEQUENCES AND SERIES.

Sequences, Laboratory Project: Logistic 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.

Laboratory Project: An Ellusive Limit.

The Binomial Series, Writing Project: How Newton Discovered the Binomial Series.

Applications of Taylor Polynomials, Applied Project: Radiation from the Stars.

Review.

Problems Plus.

13. VECTORS AND THE GEOMETRY OF SPACE.

Three-Dimensional Coordinate Systems.

Vectors.

The Dot Product.

The Cross Product, Discovery Project: The Geometry of a Tetrahedron.

Equations of Lines and Planes.

Cylinders and Quadric Surfaces.

Cylindrical and Spherical Coordinates, Laboratory Project: Families of Surfaces.

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, Applied Project: Kepler's Laws.

Review.

Problems Plus.

15. PARTIAL DERIVATIVES.

Functions of Several Variables.

Limits and Continuity.

Partial Derivatives.

Tangent Planes and Linear Approximations.

The Chain Rule.

Directional Derivatives and the Gradient Vector.

Maximum and Minimum Values, Applied Project: Designing a Dumpster, Discovery Project: Quadratic Approximations and Critical Points.

Lagrange Multipliers, Applied Project: Rocket Science, Applied Project: Hydro-Turbine Optimization.

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, Discovery Project: Volumes of Hyperspheres.

Triple Integrals in Cylindrical and Spherical Coordinates, Applied Project: Roller Derby, Discovery Project: The Intersection of Three Cylinders.

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, Writing Project: Three Men and Two Theorems.

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.

Appendixes.

Answers to Odd-Numbered Exercises.

Index.

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