Essential Calculus: Early Transcendentals

Author : James Stewart

9781133112280

960 Pages Hardcover

2nd Edition | Previous Editions: 2007

£ 82.99 Price

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This book is for instructors who think that most calculus textbooks are too long. In writing the book, James Stewart asked himself: What is essential for a three-semester calculus course for scientists and engineers? ESSENTIAL CALCULUS: EARLY TRANSCENDENTALS, Second Edition, offers a concise approac... more

Features

The text presents a concise approach to calculus for instructors who want to focus on essential principles and who feel no need for frills.

Brevity is achieved through condensed exposition, fewer examples in some sections, fewer technology and conceptual problems, and fewer appendixes. Problems Plu... more

Features

The text presents a concise approach to calculus for instructors who want to focus on essential principles and who feel no need for frills.

Brevity is achieved through condensed exposition, fewer examples in some sections, fewer technology and conceptual problems, and fewer appendixes. Problems Plus and Projects have been moved to the author's website at www.stewartcalculus.com.

Certain topics, for example, the treatment of the integral and the remainder term in Taylor Series, are presented in a manner that is more traditional than in Stewart's other books.

This version of the text presents exponential, logarithmic, and inverse trigonometric functions in Chapter Three. Those who wish to cover such functions later, with the logarithm defined as an integral, should consider the book entitled simply, ESSENTIAL CALCULUS.

Each chapter ends with a comprehensive review that includes a true/false quiz, Concept Check Questions, and exercises for every topic covered in the chapter.

Tools for Enriching Calculus--a free, online, interactive resource that allows Calculus students to work with animations that deepen their understanding by helping them visualize the concepts they are learning--has been updated with new problems and a new Flash design that is more visually appealing and engaging. Written and narrated by James Stewart, these assignable animations are also integrated into Cengage YouBook, and many are available directly to students at www.stewartcalculus.com.

For the convenience of instructors who wish to cover additional material, the www.stewartcalculus.com website contains: Review of Algebra, Trigonometry, Analytic Geometry, and Conic Sections; Additional Examples; Projects; Archived Problems (drill exercises from Stewart's other books) with solutions; Challenge Problems; Lies My Calculator and Computer Told Me, and more.

Additional topics (with exercises) available at www.stewartcalculus.com include Principles of Problem Solving, Strategy for Integration, Strategy for Testing Series, Fourier Series, Area of a Surface of Revolution, Linear Differential Equations, Second Order Linear Differential Equations, Nonhomogeneous Linear Equations, Applications of Second Order Differential Equations, Using Series to Solve Differential Equations, Complex Numbers, and Rotation of Axes. Links to outside web resources and the History of Mathematics, with links to historical websites, are also available at the site.

New to this Edition

The book begins with four diagnostic tests in Basic Algebra, Analytic Geometry, Functions, and Trigonometry. These tests address the gaps in many students' prerequisite skills--and help them start the course with confidence--by giving them opportunities to get up to speed or brush up.

Some material... more

Author

James Stewart

James Stewart received the M.S. degree from Stanford University and the Ph.D. from the University of Toronto. After two years as a postdoctoral fellow at the University of London, he became Professor of Mathematics at McMaster University. His research has been in harmonic analysis and functional analysis. Stewart’s books include a series of high school textbooks as well as a best-selling series of calculus textbooks published by Cengage Learning. He is also co-author, with Lothar Redlin and Saleem Watson, of a series of college algebra and precalculus textbooks. Translations of his books include those into Spanish, Portuguese, French, Italian, Korean, Chinese, Greek, Indonesian and Japanese. A talented violinist, Stewart was concertmaster of the McMaster Symphony Orchestra for many years and played professionally in the Hamilton Philharmonic Orchestra. He has given more than 20 talks worldwide on mathematics and music. Stewart was named a Fellow of the Fields Institute in 2002 and was awarded an honorary D.Sc. in 2003 by McMaster University. The library of the Fields Institute is named after him. The James Stewart Mathematics Centre was opened in October, 2003, at McMaster University.

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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.
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.
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.
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.
5. INTEGRALS.
Areas and Distances. The Definite Integral. Evaluating Definite Integrals. The Fundamental Theorem of Calculus. The Substitution Rule.
6. TECHNIQUES OF INTEGRATION.
Integration by Parts. Trigonometric Integrals and Substitutions. Partial Fractions. Integration with Tables and Computer Algebra Systems. Approximate Integration. Improper Integrals.
7. APPLICATIONS OF INTEGRATION.
Areas between Curves. Volumes. Volumes by Cylindrical Shells. Arc Length. Area of a Surface of Revolution. Applications to Physics and Engineering. Differential Equations.
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.
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.
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.
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.
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.
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.
Appendix A. Trigonometry.
Appendix B. Proofs.
Appendix C. Sigma Notation.
Appendix D. The Logarithm Defined as an Integral

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