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Get the calculus textbook specifically designed for science or engineering majors. ESSENTIAL CALCULUS: EARLY TRANSCENDENTALS takes what you need to know about calculus and presents it in simple and concise terms. And each chapter comes with a thorough review to make sure you've mastered the material. Get ready for upper level science or engineering equations with ESSENTIAL CALCULUS: EARLY TRANSCENDENTALS.
Author Bio
James Stewart
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 LIMITS.
Functions and Their Representations. A Catalog of Essential Functions. The Limit of a Function. Calculating Limits. Continuity. Limits Involving Infinity. Review.
2. DERIVATIVES.
Derivatives and Rates of Change. The Derivative as a Function. Basic Differentiation Formulas. The Product and Quotient Rules. The Chain Rule. Implicit Differentiation. Related Rates. Linear Approximations and Differentials. Review.
3. INVERSE FUNCTIONS: EXPONENTIAL, LOGARITHMIC, AND INVERSE TRIGONOMETRIC FUNCTIONS.
Exponential Functions. Inverse Functions and Logarithms. Derivatives of Logarithmic and Exponential Functions. Exponential Growth and Decay. Inverse Trigonometric Functions. Hyperbolic Functions. Indeterminate Forms and l'Hospital's Rule. Review.
4. APPLICATIONS OF DIFFERENTIATION.
Maximum and Minimum Values. The Mean Value Theorem. Derivatives and the Shapes of Graphs. Curve Sketching. Optimization Problems. Newton's Method. Antiderivatives. Review.
5. INTEGRALS.
Areas and Distances. The Definite Integral. Evaluating Definite Integrals. The Fundamental Theorem of Calculus. The Substitution Rule. Review.
6. TECHNIQUES OF INTEGRATION.
Integration by Parts. Trigonometric Integrals and Substitutions. Partial Fractions. Integration with Tables and Computer Algebra Systems. Approximate Integration. Improper Integrals. Review.
7. APPLICATIONS OF INTEGRATION.
Areas between Curves. Volumes. Volumes by Cylindrical Shells. Arc Length. Applications to Physics and Engineering. Differential Equations. Review.
8. SERIES.
Sequences. Series. The Integral and Comparison Tests. Other Convergence Tests. Power Series. Representing Functions as Power Series. Taylor and Maclaurin Series. Applications of Taylor Polynomials. Review.
9. PARAMETRIC EQUATIONS AND POLAR COORDINATES .
Parametric Curves. Calculus with Parametric Curves. Polar Coordinates. Areas and Lengths in Polar Coordinates. Conic Sections in Polar Coordinates. Review.
10. VECTORS AND THE GEOMETRY OF SPACE.
Three-Dimensional Coordinate Systems. Vectors. The Dot Product. The Cross Product. Equations of Lines and Planes. Cylinders and Quadric Surfaces. Vector Functions and Space Curves. Arc Length and Curvature. Motion in Space: Velocity and Acceleration. Review.
11. 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. Lagrange Multipliers. Review.
12. MULTIPLE INTEGRALS.
Double Integrals over Rectangles. Double Integrals over General Regions. Double Integrals in Polar Coordinates. Applications of Double Integrals. Triple Integrals. Triple Integrals in Cylindrical Coordinates. Triple Integrals in Spherical Coordinates. Change of Variables in Multiple Integrals. Review.
13. 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. Review.
Appendix A: Trigonometry.
Appendix B: Proofs.
Appendix C: Sigma Notation.
Appendix D: The Logarithm Defined as an Integral.
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Get the calculus textbook specifically designed for science or engineering majors. ESSENTIAL CALCULUS: EARLY TRANSCENDENTALS takes what you need to know about calculus and presents it in simple and concise terms. And each chapter comes with a thorough review to make sure you've mastered the material. Get ready for upper level science or engineering equations with ESSENTIAL CALCULUS: EARLY TRANSCENDENTALS.
Author Bio
James Stewart
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 LIMITS.
Functions and Their Representations. A Catalog of Essential Functions. The Limit of a Function. Calculating Limits. Continuity. Limits Involving Infinity. Review.
2. DERIVATIVES.
Derivatives and Rates of Change. The Derivative as a Function. Basic Differentiation Formulas. The Product and Quotient Rules. The Chain Rule. Implicit Differentiation. Related Rates. Linear Approximations and Differentials. Review.
3. INVERSE FUNCTIONS: EXPONENTIAL, LOGARITHMIC, AND INVERSE TRIGONOMETRIC FUNCTIONS.
Exponential Functions. Inverse Functions and Logarithms. Derivatives of Logarithmic and Exponential Functions. Exponential Growth and Decay. Inverse Trigonometric Functions. Hyperbolic Functions. Indeterminate Forms and l'Hospital's Rule. Review.
4. APPLICATIONS OF DIFFERENTIATION.
Maximum and Minimum Values. The Mean Value Theorem. Derivatives and the Shapes of Graphs. Curve Sketching. Optimization Problems. Newton's Method. Antiderivatives. Review.
5. INTEGRALS.
Areas and Distances. The Definite Integral. Evaluating Definite Integrals. The Fundamental Theorem of Calculus. The Substitution Rule. Review.
6. TECHNIQUES OF INTEGRATION.
Integration by Parts. Trigonometric Integrals and Substitutions. Partial Fractions. Integration with Tables and Computer Algebra Systems. Approximate Integration. Improper Integrals. Review.
7. APPLICATIONS OF INTEGRATION.
Areas between Curves. Volumes. Volumes by Cylindrical Shells. Arc Length. Applications to Physics and Engineering. Differential Equations. Review.
8. SERIES.
Sequences. Series. The Integral and Comparison Tests. Other Convergence Tests. Power Series. Representing Functions as Power Series. Taylor and Maclaurin Series. Applications of Taylor Polynomials. Review.
9. PARAMETRIC EQUATIONS AND POLAR COORDINATES .
Parametric Curves. Calculus with Parametric Curves. Polar Coordinates. Areas and Lengths in Polar Coordinates. Conic Sections in Polar Coordinates. Review.
10. VECTORS AND THE GEOMETRY OF SPACE.
Three-Dimensional Coordinate Systems. Vectors. The Dot Product. The Cross Product. Equations of Lines and Planes. Cylinders and Quadric Surfaces. Vector Functions and Space Curves. Arc Length and Curvature. Motion in Space: Velocity and Acceleration. Review.
11. 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. Lagrange Multipliers. Review.
12. MULTIPLE INTEGRALS.
Double Integrals over Rectangles. Double Integrals over General Regions. Double Integrals in Polar Coordinates. Applications of Double Integrals. Triple Integrals. Triple Integrals in Cylindrical Coordinates. Triple Integrals in Spherical Coordinates. Change of Variables in Multiple Integrals. Review.
13. 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. Review.
Appendix A: Trigonometry.
Appendix B: Proofs.
Appendix C: Sigma Notation.
Appendix D: The Logarithm Defined as an Integral.
Digital Rights
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.
Download Requirements: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.
User Help:
Click Here to access the VitalSource Bookshelf FAQ
Digital Rights Management (DRM) Key
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."
Expires - Books that have no expiration (the date upon which you will no longer be able to access your eBook) will read "No Expiration." Otherwise it will state the number of days from activation (the first time you actually read it).
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.