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by Daniel Anderson, Jeffery A. Cole and Daniel Drucker

Cover type: PaperbackEdition: 6TH 08

Copyright: 2007

Publisher: Brooks/Cole Publishing Co.

Published: 2007

International: No

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Provides completely worked-out solutions to all odd-numbered exercises within the text, giving students a way to check their answers and ensure that they took the correct steps to arrive at an answer.

James Stewart received his M.S. from Stanford University and his Ph.D. from the University of Toronto. He did research at the University of London and was influenced by the famous mathematician George Polya at Stanford University. Stewart is currently Professor of Mathematics at McMaster University, and his research field is harmonic analysis. Stewart is the author of a best-selling calculus textbook series published by Cengage Learning Brooks/Cole, including CALCULUS, CALCULUS: EARLY TRANSCENDENTALS, and CALCULUS: CONCEPTS AND CONTEXTS, as well as a series of precalculus texts.

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. Exponential Functions. Inverse Functions and Logarithms. Principles of Problem Solving.

2. Limits and Derivatives.

The Tangent and Velocity Problems. The Limit of a Function. Calculating Limits Using the Limit Laws. The Precise Definition of a Limit. Continuity. Limits at Infinity; Horizontal Asymptotes. Derivatives and Rates of Change. Writing Project: Early Methods for Finding Tangents. The Derivative as a Function.

3. Differentiation Rules.

Derivatives of Polynomials and Exponential Functions. Applied Project: Building a Better Roller Coaster. The Product and Quotient Rules. Derivatives of Trigonometric Functions. The Chain Rule. Applied Project: Where Should a Pilot Start Descent? Implicit Differentiation. Derivatives of Logarithmic Functions. Rates of Change in the Natural and Social Sciences. Exponential Growth and Decay. Related Rates. Linear Approximations and Differentials. Laboratory Project: Taylor Polynomials. Hyperbolic Functions.

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. Indeterminate Forms and L'Hospital's Rule. Writing Project: The Origins of L'Hospital's Rule. 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.

5. Integrals.

Areas and Distances. The Definite Integral. Discovery Project: Area Functions. The Fundamental Theorem of Calculus. Indefinite Integrals and the Total Change Theorem. Writing Project: Newton, Leibniz, and the Invention of Calculus. The Substitution Rule 6. Applications of Integration.

Areas between Curves. Volume. Volumes by Cylindrical Shells. Work. Average Value of a Function. Applied Project: Where to Sit at the Movies.

7. 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.

8. 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.

9. Differential Equations.

Modeling with Differential Equations. Direction Fields and Euler's Method. Separable Equations. 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.

10. Parametric Equations and Polar Coordinates.

Curves Defined by Parametric Equations. Laboratory Project: Families of Hypocycloids. Tangents and Areas. Laboratory Project: Bezier Curves. Arc Length and Surface Area. Polar Coordinates. Areas and Lengths in Polar Coordinates. Conic Sections. Conic Sections in Polar Coordinates. Applied Project: Transfer Orbits. Review. Problems Plus.

11. 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 The Binomial Series. Writing Project: How Newton Discovered the Binomial Series. Applications of Taylor Polynomials. Applied Project: Radiation from the Stars. Review. Problems Plus.

12. 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. Quadric Surfaces. Cylindrical and Spherical Coordinates. Laboratory Project: Families of Surfaces. Review. Problems Plus.

13. 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.

14. 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. 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.

15. 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.

16. Vector Calculus.

Vector Fields. Line Integrals. The Fundamental Theorem for Line Integrals. Greens Theorem. Curl and Divergence. Parametric Surfaces and Their Areas. Surface Integrals. Writing Project: Three Men and Two Theorems. The Divergence Theorem. Summary. Review. Problems Plus.

17. Second-Order Differential Equations.

Second-Order Linear Equations. Nonhomogeneous Linear Equations. Applications of Second-Order Differential Equations. Series Solutions. Review. Problems Plus.

Appendixes.

A: Numbers, 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: The Logarithm Defined as an Integral. H: Complex Numbers. I: Answers to Odd-Numbered Exercises.

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Summary

Provides completely worked-out solutions to all odd-numbered exercises within the text, giving students a way to check their answers and ensure that they took the correct steps to arrive at an answer.

Author Bio

James Stewart received his M.S. from Stanford University and his Ph.D. from the University of Toronto. He did research at the University of London and was influenced by the famous mathematician George Polya at Stanford University. Stewart is currently Professor of Mathematics at McMaster University, and his research field is harmonic analysis. Stewart is the author of a best-selling calculus textbook series published by Cengage Learning Brooks/Cole, including CALCULUS, CALCULUS: EARLY TRANSCENDENTALS, and CALCULUS: CONCEPTS AND CONTEXTS, as well as a series of precalculus texts.

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. Exponential Functions. Inverse Functions and Logarithms. Principles of Problem Solving.

2. Limits and Derivatives.

The Tangent and Velocity Problems. The Limit of a Function. Calculating Limits Using the Limit Laws. The Precise Definition of a Limit. Continuity. Limits at Infinity; Horizontal Asymptotes. Derivatives and Rates of Change. Writing Project: Early Methods for Finding Tangents. The Derivative as a Function.

3. Differentiation Rules.

Derivatives of Polynomials and Exponential Functions. Applied Project: Building a Better Roller Coaster. The Product and Quotient Rules. Derivatives of Trigonometric Functions. The Chain Rule. Applied Project: Where Should a Pilot Start Descent? Implicit Differentiation. Derivatives of Logarithmic Functions. Rates of Change in the Natural and Social Sciences. Exponential Growth and Decay. Related Rates. Linear Approximations and Differentials. Laboratory Project: Taylor Polynomials. Hyperbolic Functions.

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. Indeterminate Forms and L'Hospital's Rule. Writing Project: The Origins of L'Hospital's Rule. 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.

5. Integrals.

Areas and Distances. The Definite Integral. Discovery Project: Area Functions. The Fundamental Theorem of Calculus. Indefinite Integrals and the Total Change Theorem. Writing Project: Newton, Leibniz, and the Invention of Calculus. The Substitution Rule 6. Applications of Integration.

Areas between Curves. Volume. Volumes by Cylindrical Shells. Work. Average Value of a Function. Applied Project: Where to Sit at the Movies.

7. 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.

8. 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.

9. Differential Equations.

Modeling with Differential Equations. Direction Fields and Euler's Method. Separable Equations. 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.

10. Parametric Equations and Polar Coordinates.

Curves Defined by Parametric Equations. Laboratory Project: Families of Hypocycloids. Tangents and Areas. Laboratory Project: Bezier Curves. Arc Length and Surface Area. Polar Coordinates. Areas and Lengths in Polar Coordinates. Conic Sections. Conic Sections in Polar Coordinates. Applied Project: Transfer Orbits. Review. Problems Plus.

11. 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 The Binomial Series. Writing Project: How Newton Discovered the Binomial Series. Applications of Taylor Polynomials. Applied Project: Radiation from the Stars. Review. Problems Plus.

12. 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. Quadric Surfaces. Cylindrical and Spherical Coordinates. Laboratory Project: Families of Surfaces. Review. Problems Plus.

13. 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.

14. 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. 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.

15. 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.

16. Vector Calculus.

Vector Fields. Line Integrals. The Fundamental Theorem for Line Integrals. Greens Theorem. Curl and Divergence. Parametric Surfaces and Their Areas. Surface Integrals. Writing Project: Three Men and Two Theorems. The Divergence Theorem. Summary. Review. Problems Plus.

17. Second-Order Differential Equations.

Second-Order Linear Equations. Nonhomogeneous Linear Equations. Applications of Second-Order Differential Equations. Series Solutions. Review. Problems Plus.

Appendixes.

A: Numbers, 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: The Logarithm Defined as an Integral. H: Complex Numbers. I: Answers to Odd-Numbered Exercises.

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Being online is not required for reading an eTextbook after successfully downloading it. You must only be connected to the Internet during the download process.

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Publisher Info

Publisher: Brooks/Cole Publishing Co.

Published: 2007

International: No

Published: 2007

International: No

Four Ways to Represent a Function. Mathematical Models: A Catalog of Essential Functions. New Functions from Old Functions. Graphing Calculators and Computers. Exponential Functions. Inverse Functions and Logarithms. Principles of Problem Solving.

2. Limits and Derivatives.

The Tangent and Velocity Problems. The Limit of a Function. Calculating Limits Using the Limit Laws. The Precise Definition of a Limit. Continuity. Limits at Infinity; Horizontal Asymptotes. Derivatives and Rates of Change. Writing Project: Early Methods for Finding Tangents. The Derivative as a Function.

3. Differentiation Rules.

Derivatives of Polynomials and Exponential Functions. Applied Project: Building a Better Roller Coaster. The Product and Quotient Rules. Derivatives of Trigonometric Functions. The Chain Rule. Applied Project: Where Should a Pilot Start Descent? Implicit Differentiation. Derivatives of Logarithmic Functions. Rates of Change in the Natural and Social Sciences. Exponential Growth and Decay. Related Rates. Linear Approximations and Differentials. Laboratory Project: Taylor Polynomials. Hyperbolic Functions.

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. Indeterminate Forms and L'Hospital's Rule. Writing Project: The Origins of L'Hospital's Rule. 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.

5. Integrals.

Areas and Distances. The Definite Integral. Discovery Project: Area Functions. The Fundamental Theorem of Calculus. Indefinite Integrals and the Total Change Theorem. Writing Project: Newton, Leibniz, and the Invention of Calculus. The Substitution Rule 6. Applications of Integration.

Areas between Curves. Volume. Volumes by Cylindrical Shells. Work. Average Value of a Function. Applied Project: Where to Sit at the Movies.

7. 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.

8. 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.

9. Differential Equations.

Modeling with Differential Equations. Direction Fields and Euler's Method. Separable Equations. 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.

10. Parametric Equations and Polar Coordinates.

Curves Defined by Parametric Equations. Laboratory Project: Families of Hypocycloids. Tangents and Areas. Laboratory Project: Bezier Curves. Arc Length and Surface Area. Polar Coordinates. Areas and Lengths in Polar Coordinates. Conic Sections. Conic Sections in Polar Coordinates. Applied Project: Transfer Orbits. Review. Problems Plus.

11. 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 The Binomial Series. Writing Project: How Newton Discovered the Binomial Series. Applications of Taylor Polynomials. Applied Project: Radiation from the Stars. Review. Problems Plus.

12. 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. Quadric Surfaces. Cylindrical and Spherical Coordinates. Laboratory Project: Families of Surfaces. Review. Problems Plus.

13. 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.

14. 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. 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.

15. 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.

16. Vector Calculus.

Vector Fields. Line Integrals. The Fundamental Theorem for Line Integrals. Greens Theorem. Curl and Divergence. Parametric Surfaces and Their Areas. Surface Integrals. Writing Project: Three Men and Two Theorems. The Divergence Theorem. Summary. Review. Problems Plus.

17. Second-Order Differential Equations.

Second-Order Linear Equations. Nonhomogeneous Linear Equations. Applications of Second-Order Differential Equations. Series Solutions. Review. Problems Plus.

Appendixes.

A: Numbers, 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: The Logarithm Defined as an Integral. H: Complex Numbers. I: Answers to Odd-Numbered Exercises.

- Windows 7/8, or Mac OS X 10.6 or above

eTextbooks and eChapters can be viewed by using the free reader listed below.

Be sure to check the format of the eTextbook/eChapter you purchase to know which reader you will need. After purchasing your eTextbook or eChapter, you will be emailed instructions on where and how to download your free reader.

Due to the size of eTextbooks, a high-speed Internet connection (cable modem, DSL, LAN) is required for download stability and speed. Your connection can be wired or wireless.

Being online is not required for reading an eTextbook after successfully downloading it. You must only be connected to the Internet during the download process.

Click Here to access the VitalSource Bookshelf FAQ

VitalSource

**Copying:** Allowed, 10 selections may be copied every 365 days

**Printing:** Allowed, 10 prints for 365 days

**Expires:** Yes, may be used for 365 days after activation

**Reading Aloud:** Allowed

**Sharing:** Not Allowed

**Min. Software Version:** Online: No additional software required

Offline: VitalSource Bookshelf

**Suitable Devices:** PCs, Tablet PCs, Macs, Laptops

**Copying** - Books that cannot be copied will show "Not Allowed." Otherwise, this will detail the number of times it can be copied, or "Allowed with no limits."

Offline: VitalSource Bookshelf

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**Printing** - Books that cannot be printed will show "Not Allowed." Otherwise, this will detail the number of times it can be printed, or "Allowed with no limits."

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**Reading Aloud** - Books enabled with the "text-to-speech" feature so that they can be read aloud will show "Allowed."

**Sharing** - Books that cannot be shared with other computers will show "Not Allowed."

**Min. Software Version** - This is the minimum software version needed to read this book.

**Suitable Devices** - Hardware known to be compatible with this book. Note: Reader software still needs to be installed.