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Stewart's CALCULUS: EARLY TRANSCENDENTALS, 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. The structure of CALCULUS: EARLY TRANSCENDENTALS, FIFTH EDITION, remains largely unchanged, the sole exception being that the review of inverse trigonometric functions has been moved from an appendix to Section 1.6. Stewart 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 using this text are using the best resource available. The number of pages in the book, however, remains unchanged from the 4th edition. This edition is complemented with and expanded array of supplementary material for both students and instructors. These best-selling texts differ from CALCULUS, FIFTH EDITION in that the exponential and logarithmic functions are covered earlier. In the Fifth Edition of CALCULUS, EARLY TRANSCENDENTALS these functions are introduced in the first chapter and their limits and derivatives are found in Chapters 2 and 3 at the same time as polynomials and other elementary functions.
Author Bio
Stewart, James : McMaster University
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. Stewart is currently a Professor of Mathematics at McMaster University. His research field is harmonic analysis. James Stewart is the author of a best-selling calculus textbook series published by Brooks/Cole, including CALCULUS, 5th Edition, CALCULUS: EARLY TRANSCENDENTALS, 5th Edition, and CALCULUS: CONCEPTS AND CONTEXTS, 2nd Edition, 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.
Review.
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.
Tangents, Velocities, and Other Rates of Change.
Derivatives.
Writing Project: Early Methods for Finding Tangents.
The Derivative as a Function.
Review.
Problems Plus.
3. DIFFERENTIATION RULES.
Derivatives of Polynomials and Exponential Functions.
The Product and Quotient Rules.
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.
Derivatives of Logarithmic Functions.
Hyperbolic Functions.
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.
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.
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.
The Logarithm Defined as an Integral.
Review.
Problems Plus.
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 Movie.
Review.
Problems Plus.
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: 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.
10. 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.
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.
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.
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.
Cylinders and 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 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.
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.
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.
17. 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.
Stewart's CALCULUS: EARLY TRANSCENDENTALS, 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. The structure of CALCULUS: EARLY TRANSCENDENTALS, FIFTH EDITION, remains largely unchanged, the sole exception being that the review of inverse trigonometric functions has been moved from an appendix to Section 1.6. Stewart 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 using this text are using the best resource available. The number of pages in the book, however, remains unchanged from the 4th edition. This edition is complemented with and expanded array of supplementary material for both students and instructors. These best-selling texts differ from CALCULUS, FIFTH EDITION in that the exponential and logarithmic functions are covered earlier. In the Fifth Edition of CALCULUS, EARLY TRANSCENDENTALS these functions are introduced in the first chapter and their limits and derivatives are found in Chapters 2 and 3 at the same time as polynomials and other elementary functions.
Author Bio
Stewart, James : McMaster University
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. Stewart is currently a Professor of Mathematics at McMaster University. His research field is harmonic analysis. James Stewart is the author of a best-selling calculus textbook series published by Brooks/Cole, including CALCULUS, 5th Edition, CALCULUS: EARLY TRANSCENDENTALS, 5th Edition, and CALCULUS: CONCEPTS AND CONTEXTS, 2nd Edition, 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.
Review.
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.
Tangents, Velocities, and Other Rates of Change.
Derivatives.
Writing Project: Early Methods for Finding Tangents.
The Derivative as a Function.
Review.
Problems Plus.
3. DIFFERENTIATION RULES.
Derivatives of Polynomials and Exponential Functions.
The Product and Quotient Rules.
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.
Derivatives of Logarithmic Functions.
Hyperbolic Functions.
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.
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.
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.
The Logarithm Defined as an Integral.
Review.
Problems Plus.
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 Movie.
Review.
Problems Plus.
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: 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.
10. 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.
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.
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.
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.
Cylinders and 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 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.
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.
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.
17. 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.