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Calculus: Concepts and Contexts, 4th Edition

  • James Stewart McMaster University
  • ISBN-10: 0495557420  |  ISBN-13: 9780495557425
  • 1152 Pages
  • Previous Editions: 2007, 2005, 2001
  • © 2010 | Published
  • List Price = $ 340.95
  • For quantity discounts, Contact your Representative
  • For single copy purchases, visit CengageBrain.com

About

Overview

Stewart's CALCULUS: CONCEPTS AND CONTEXTS, FOURTH EDITION offers a streamlined approach to teaching calculus, focusing on major concepts and supporting those with precise definitions, patient explanations, and carefully graded problems. CALCULUS: CONCEPTS AND CONTEXTS is highly regarded because this text offers a balance of theory and conceptual work to satisfy more progressive programs as well as those who are more comfortable teaching in a more traditional fashion. Each title is just one component in a comprehensive calculus course program that carefully integrates and coordinates print, media, and technology products for successful teaching and learning.

Features and Benefits

  • Conceptual Exercises; The most important way to foster conceptual understanding is through assigned problems. Stewart Concepts offers various types of problems, including explanations/mathematical writing problems, use of graphs and tables, Concept Checks, and True/False quizzes in the review sections.
  • Graded Homework Exercises Each exercise set is carefully graded, progressing from basic conceptual exercises and skill-development problems to more challenging problems involving applications and proofs.
  • Real World Data Interesting real-world data gathered from a variety of contemporary sources introduces, motivates, and illustrates the concepts of calculus.
  • Instructor Resource Guide w/Solutions—The instructor's resource contains an abundance of resources keyed to the textbook by chapter and section, including diagnostic tests, chapter summaries, teaching strategies, chapter tests, final exams, and more.
  • Solutions Builder is an innovative online tool which allows professors to select the problems and solutions they wish to use, post them on their class website, or print them out for reference. This powerful online tool reduces the bulk of the solutions manual, and offers a personalized, flexible instructional supplement that suits everyone's needs.

Table of Contents

Preface.
To the Student.
Diagnostic Tests.
A Preview of Calculus.
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. Parametric Curves. Laboratory Project: Running Circles around Circles. 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. Continuity. Limits Involving Infinity. Derivatives and Rates of Change. Writing Project: Early Methods for Finding Tangents. The Derivative as a Function. What Does f  Say about f ? Review. Focus on Problem Solving.
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. Laboratory Project: Bézier Curves. Applied Project: Where Should a Pilot Start Descent? Implicit Differentiation. Inverse Trigonometric Functions and their Derivatives. Derivatives of Logarithmic Functions. Discovery Project: Hyperbolic Functions. Rates of Change in the Natural and Social Sciences. Linear Approximations and Differentials. Laboratory Project: Taylor Polynomials. Review. Focus on Problem Solving.
4. APPLICATIONS OF DIFFERENTIATION.
Related Rates. Maximum and Minimum Values. Applied Project: The Calculus of Rainbows. Derivatives and the Shapes of Curves. Graphing with Calculus and Calculators. Indeterminate Forms and l''Hospital''s Rule. Writing Project: The Origins of l''Hospital''s Rule. Optimization Problems. Applied Project: The Shape of a Can. Newton''s Method. Antiderivatives. Review. Focus on Problem Solving.
5. INTEGRALS.
Areas and Distances. The Definite Integral. Evaluating Definite Integrals. Discovery Project: Area Functions. The Fundamental Theorem of Calculus. Writing Project: Newton, Leibniz, and the Invention of Calculus. The Substitution Rule. Integration by Parts. Additional Techniques of Integration. Integration Using Tables and Computer Algebra Systems. Discovery Project: Patterns in Integrals. Approximate Integration. Improper Integrals. Review. Focus on Problem Solving.
6. APPLICATIONS OF INTEGRATION.
More about Areas. Volumes. Discovery Project: Rotating on a Slant. Volumes by Cylindrical Shells. Arc Length. Discovery Project: Arc Length Contest. Average Value of a Function. Applied Project: Where To Sit at the Movies. Applications to Physics and Engineering. Discovery Project: Complementary Coffee Cups. Applications to Economics and Biology. Probability. Review. Focus on Problem Solving.
7. 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. Predator-Prey Systems. Review. Focus on Problem Solving.
8. INFINTE SEQUENCES AND SERIES.
Sequences. Laboratory Project: Logistic Sequences. Series. The Integral and Comparison Tests; Estimating Sums. Other Convergence Tests. Power Series. Representations of Functions as Power Series. Taylor and Maclaurin Series. Laboratory Project: An Elusive Limit. Writing Project: How Newton Discovered the Binomial Series. Applications of Taylor Polynomials. Applied Project: Radiation from the Stars. Review. Focus on Problem Solving.
9. 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. Laboratory Project: Putting 3D in Perspective. Functions and Surfaces. Cylindrical and Spherical Coordinates. Laboratory Project: Families of Surfaces. Review. Focus on Problem Solving.
10. 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. Parametric Surfaces. Review. Focus on Problem Solving.
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. Applied Project: Designing a Dumpster. Discovery Project: Quadratic Approximations and Critical Points. Lagrange Multipliers. Applied Project: Rocket Science. Applied Project: Hydro-Turbine Optimization. Review. Focus on Problem Solving.
12. 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. Focus on Problem Solving.
13. VECTOR CALCULUS.
Vector Fields. Line Integrals. The Fundamental Theorem for Line Integrals. Green''s Theorem. Curl and Divergence. Surface Integrals. Stokes'' Theorem. Writing Project: Three Men and Two Theorems. The Divergence Theorem. Summary. Review. Focus on Problem Solving.
APPENDIXES.
A. Intervals, Inequalities, and Absolute Values.
B. Coordinate Geometry.
C. Trigonometry.
D. Precise Definitions of Limits.
E. A Few Proofs.
F. Sigma Notation.
G. Integration of Rational Functions by Partial Fractions.
H. Polar Coordinates.
I. Complex Numbers.
J. Answers to Odd-Numbered Exercises.

What's New

  • Four diagnostic tests have been inserted in the beginning of the book for Basic Algebra, Analytic Geometry, Functions, and Trigonometry. Answers are given and students who don't do well are referred to where they should seek help.
  • Some material has been rewritten for greater clarity or for better motivation. See, for instance, the introduction to maximum and minimum values on pages 262-263 and the introduction to series on page 565.
  • Examples are now titled for easier reference, some new examples have been added. In some cases, solutions given have been amplified, and data has been thoroughly revised and reviewed to reflect current values.
  • In response to user feedback, specific areas of content have either been condensed, moved, or expanded upon, including: the material motivating the derivative is briefer and has been combined into a single section called Derivatives and Rates of Change. Rates of Change in the Natural and Social Sciences has been moved later in Chapter 3 in order to incorporate more differentiation rules. Coverage of inverse trigonometric functions has been consolidated in a single dedicated section (3.6). The former sections 4.6 and 4.7 have been merged into a single section, with a briefer treatment of optimization problems in business and economics. There is now a full section on volumes by cylindrical shells (6.3).

Learning Resource Bundles

Choose the textbook packaged with the resources that best meet your course and student needs. Contact your Learning Consultant for more information.

Bundle: Text + Enhanced WebAssign Homework Printed Access Card for Multi Term Math and Science

ISBN-10: 1428251413  | ISBN-13: 9781428251410

List Price = $360.95


Bundle: Text + Enhanced WebAssign Printed Access Card for Calculus, Multi-Term Courses

ISBN-10:  0538796855  | ISBN-13:  9780538796859

List Price = $367.95


Bundle: Text + Enhanced WebAssign Homework and eBook Printed Access Card for Single Term of Multi Course

ISBN-10:  1111115605  | ISBN-13:  9781111115609

List Price = $340.95


Bundle: Text + Student Solutions Manual, MV + Student Solutions Manual, SV

ISBN-10:  0495780634  | ISBN-13:  9780495780632

List Price = $600.95  | CengageBrain Price = $600.95


Bundle: Text (Calc) + CalcLabs with Mathematica (SV) + CalcLabs with Mathematica (MV)

ISBN-10:  0538771704  | ISBN-13:  9780538771702

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Bundle: Text + Study Guide, MV + Study Guide, SV

ISBN-10:  0495780650  | ISBN-13:  9780495780656

List Price = $554.95  | CengageBrain Price = $554.95


Bundle: Text + Maple Student Version 14.0

ISBN-10:  111149892X  | ISBN-13:  9781111498924

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Bundle: Text + Enhanced WebAssign Homework and eBook Printed Access Card for Multi Term Math and Science

ISBN-10:  0538783583  | ISBN-13:  9780538783583

List Price = $367.95  | CengageBrain Price = $367.95


Printed Text + Enhanced WebAssign Instant Access for Calculus, Multi-Term Courses

ISBN-10:  1305603338 | ISBN-13:  9781305603332

List Price = $367.95  | CengageBrain Price = $367.95


Supplements

All supplements have been updated in coordination with the main title. Select the main title's "About" tab, then select "What's New" for updates specific to title's edition.

For more information about these supplements, or to obtain them, contact your Learning Consultant.

Instructor Supplements

CalcLabs with Mathematica, SV Calc.  (ISBN-10: 0495560634 | ISBN-13: 9780495560630)

This comprehensive lab manual helps students learn to effectively use the technology tools that are available to them. Each lab contains clearly explained exercises and a variety of lab projects to accompany the text.

List Price = $126.95  | College Bookstore Wholesale Price = $95.75

Study Guide, SV Calc.  (ISBN-10: 0495560642 | ISBN-13: 9780495560647)

Contains key concepts, skills to master, a brief discussion of the ideas of the section, and worked-out examples with tips on how to find the solution.

List Price = $133.95  | CengageBrain Price = $133.95  | College Bookstore Wholesale Price = $101.00

Web Site  (ISBN-10: 0495561223 | ISBN-13: 9780495561224)

The student website contains an abundance of resources for teaching and learning, such as wuiowpeuroiewuroiewuroiewruewoiureoiwur.

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Test Bank  (ISBN-10: 0495561231 | ISBN-13: 9780495561231)

Contains multiple-choice and short-answer test items that key directly to the test.

CalcLabs with Maple for Single Variable Calculus  (ISBN-10: 0495560626 | ISBN-13: 9780495560623)

Maple is a powerful software tool for mathematical computations and visualization. The goal of this manual is to introduce Maple to students who are taking first year calculus. As such, Maple is a tool to solve problems that are too difficult to solve by hand. In addition, students will improve their understanding of the concepts of calculus. The order of the material is organized by computational topic and should be suitable for most texts on Single Variable calculus.

List Price = $122.95  | CengageBrain Price = $122.95  | College Bookstore Wholesale Price = $92.50

Enhanced WebAssign Homework Only Printed Access Card for Math and Science  (ISBN-10: 1305408047 | ISBN-13: 9781305408043)

List Price = $94.00  | CengageBrain Price = $94.00  | College Bookstore Wholesale Price = $70.50

Instructor's Guide  (ISBN-10: 0495560472 | ISBN-13: 9780495560470)

Each section of the main text is discussed from several viewpoints and contains suggested time to allot, points to stress, text discussion topics, core materials for lecture, workshop/discussion suggestions, group work exercises in a form suitable for handout, and suggested homework problems.

PowerLecture  (ISBN-10: 0495560499 | ISBN-13: 9780495560494)

This comprehensive instructor resource contains all the art from the text in both jpeg and PowerPoint formats, key equations and tables from the text, complete pre-built PowerPoint lectures, electronic versions of the Instructor's Guide and Test Bank, and ExamView computerized testing that allows you to create, deliver, and customize tests in minutes with easy-to-use assessment and tutorial software.

Interactive Video Skillbuilder  (ISBN-10: 0495560502 | ISBN-13: 9780495560500)

Think of it as portable office hours! The Interactive Video Skillbuilder contains over eight hours of video instruction. The questions worked out during each video lesson are shown next to the viewing screen so that students can try working them before watching the solution.

List Price = $26.95  | College Bookstore Wholesale Price = $20.00

Instructor's Complete Solutions Manual (Chapters 8-13)  (ISBN-10: 0495560561 | ISBN-13: 9780495560562)

This manual includes worked out solutions to every exercise in Multivariable Calculus: Concepts & Contexts, 4e (Chapters 8-13 of Stewart's Calculus: Concepts & Contexts, 4e).

Study Guide, MV Calc.  (ISBN-10: 049556057X | ISBN-13: 9780495560579)

Contains key concepts, skills to master, a brief discussion of the ideas of the section, and worked-out examples with tips on how to find the solution.

List Price = $79.95  | CengageBrain Price = $79.95  | College Bookstore Wholesale Price = $59.75

CalcLabs with Maple for Multivariable Calculus  (ISBN-10: 0495560588 | ISBN-13: 9780495560586)

List Price = $74.95  | College Bookstore Wholesale Price = $56.50

Enhanced WebAssign Instant Access for Calculus, Multi-Term Courses  (ISBN-10: 1285858255 | ISBN-13: 9781285858258)

IMPORTANT: When purchasing this instant access code for Calculus, ensure that you are using it in a Calculus course. Use with a different course may cause complications with access. Exclusively from Cengage Learning, Enhanced WebAssign combines exceptional mathematics content with the most powerful online homework solution, WebAssign. Enhanced WebAssign engages students with immediate feedback, rich tutorial content, and an interactive, fully customizable eBook, Cengage YouBook helping students to develop a deeper conceptual understanding of their subject matter. This access code includes access to Enhanced WebAssign and life-of-edition access to the eBook for the registered edition of that text. If you need to retake the course and your instructor is using the same book AND edition then you will not need to buy a new code. This instant access code will be delivered via email when purchased. If you are not certain this is the correct access code for your course, please contact your instructor.

List Price = $125.00  | CengageBrain Price = $125.00  | College Bookstore Wholesale Price = $125.00

Enhanced WebAssign Printed Access Card for Calculus, Multi-Term Courses, Life of Edition  (ISBN-10: 1285858263 | ISBN-13: 9781285858265)

IMPORTANT: When purchasing this printed access card for Calculus, ensure that you are using it in a Calculus course. Use with a different course may cause complications with access. Exclusively from Cengage Learning, Enhanced WebAssign combines exceptional mathematics content with the most powerful online homework solution, WebAssign. Enhanced WebAssign engages students with immediate feedback, rich tutorial content, and an interactive, fully customizable eBook, Cengage YouBook helping students to develop a deeper conceptual understanding of their subject matter. This access code includes access to Enhanced WebAssign and life-of-edition access to the eBook for the registered edition of that text. If you need to retake the course and your instructor is using the same book AND edition then you will not need to buy a new code. If you are not certain this is the correct access code for your course, please contact your instructor.

List Price = $125.00  | College Bookstore Wholesale Price = $93.75

Complete Solutions Manual (Chapters 1-8)  (ISBN-10: 049556060X | ISBN-13: 9780495560609)

This manual includes worked out solutions to every exercise in Single Variable Calculus: Concepts & Contexts, 4e (Chapters 1-8 of Stewart's Calculus: Concepts & Contexts, 4e).

Student Solutions Manual (Chapters 1-8)  (ISBN-10: 0495560618 | ISBN-13: 9780495560616)

This manual includes worked out solutions to every odd-numbered exercise in Single Variable Calculus: Concepts & Contexts, 4e (Chapters 1-8 of Stewart's Calculus: Concepts & Contexts, 4e).

List Price = $157.95  | CengageBrain Price = $157.95  | College Bookstore Wholesale Price = $118.50

Student Solutions Manual (Chapters 8-13)  (ISBN-10: 0495560553 | ISBN-13: 9780495560555)

This manual includes worked out solutions to every odd-numbered exercise in Multivariable Calculus: Concepts & Contexts, 4e (Chapters 8-13 of Stewart's Calculus: Concepts & Contexts, 4e).

List Price = $101.95  | CengageBrain Price = $101.95  | College Bookstore Wholesale Price = $76.50

Student Supplements

CalcLabs with Mathematica, SV Calc.  (ISBN-10: 0495560634 | ISBN-13: 9780495560630)

This comprehensive lab manual helps students learn to effectively use the technology tools that are available to them. Each lab contains clearly explained exercises and a variety of lab projects to accompany the text.

List Price = $126.95  | College Bookstore Wholesale Price = $95.75

Study Guide, SV Calc.  (ISBN-10: 0495560642 | ISBN-13: 9780495560647)

Contains key concepts, skills to master, a brief discussion of the ideas of the section, and worked-out examples with tips on how to find the solution.

List Price = $133.95  | CengageBrain Price = $133.95  | College Bookstore Wholesale Price = $101.00

Web Site  (ISBN-10: 0495561223 | ISBN-13: 9780495561224)

The student website contains an abundance of resources for teaching and learning, such as wuiowpeuroiewuroiewuroiewruewoiureoiwur.

List Price = $.00  | College Bookstore Wholesale Price = $.00

CalcLabs with Maple for Single Variable Calculus  (ISBN-10: 0495560626 | ISBN-13: 9780495560623)

Maple is a powerful software tool for mathematical computations and visualization. The goal of this manual is to introduce Maple to students who are taking first year calculus. As such, Maple is a tool to solve problems that are too difficult to solve by hand. In addition, students will improve their understanding of the concepts of calculus. The order of the material is organized by computational topic and should be suitable for most texts on Single Variable calculus.

List Price = $122.95  | CengageBrain Price = $122.95  | College Bookstore Wholesale Price = $92.50

Enhanced WebAssign Homework Only Printed Access Card for Math and Science  (ISBN-10: 1305408047 | ISBN-13: 9781305408043)

List Price = $94.00  | CengageBrain Price = $94.00  | College Bookstore Wholesale Price = $70.50

Interactive Video Skillbuilder  (ISBN-10: 0495560502 | ISBN-13: 9780495560500)

Think of it as portable office hours! The Interactive Video Skillbuilder contains over eight hours of video instruction. The questions worked out during each video lesson are shown next to the viewing screen so that students can try working them before watching the solution.

List Price = $26.95  | College Bookstore Wholesale Price = $20.00

Study Guide, MV Calc.  (ISBN-10: 049556057X | ISBN-13: 9780495560579)

Contains key concepts, skills to master, a brief discussion of the ideas of the section, and worked-out examples with tips on how to find the solution.

List Price = $79.95  | CengageBrain Price = $79.95  | College Bookstore Wholesale Price = $59.75

CalcLabs with Maple for Multivariable Calculus  (ISBN-10: 0495560588 | ISBN-13: 9780495560586)

List Price = $74.95  | College Bookstore Wholesale Price = $56.50

Enhanced WebAssign Instant Access for Calculus, Multi-Term Courses  (ISBN-10: 1285858255 | ISBN-13: 9781285858258)

IMPORTANT: When purchasing this instant access code for Calculus, ensure that you are using it in a Calculus course. Use with a different course may cause complications with access. Exclusively from Cengage Learning, Enhanced WebAssign combines exceptional mathematics content with the most powerful online homework solution, WebAssign. Enhanced WebAssign engages students with immediate feedback, rich tutorial content, and an interactive, fully customizable eBook, Cengage YouBook helping students to develop a deeper conceptual understanding of their subject matter. This access code includes access to Enhanced WebAssign and life-of-edition access to the eBook for the registered edition of that text. If you need to retake the course and your instructor is using the same book AND edition then you will not need to buy a new code. This instant access code will be delivered via email when purchased. If you are not certain this is the correct access code for your course, please contact your instructor.

List Price = $125.00  | CengageBrain Price = $125.00  | College Bookstore Wholesale Price = $125.00

Enhanced WebAssign Printed Access Card for Calculus, Multi-Term Courses, Life of Edition  (ISBN-10: 1285858263 | ISBN-13: 9781285858265)

IMPORTANT: When purchasing this printed access card for Calculus, ensure that you are using it in a Calculus course. Use with a different course may cause complications with access. Exclusively from Cengage Learning, Enhanced WebAssign combines exceptional mathematics content with the most powerful online homework solution, WebAssign. Enhanced WebAssign engages students with immediate feedback, rich tutorial content, and an interactive, fully customizable eBook, Cengage YouBook helping students to develop a deeper conceptual understanding of their subject matter. This access code includes access to Enhanced WebAssign and life-of-edition access to the eBook for the registered edition of that text. If you need to retake the course and your instructor is using the same book AND edition then you will not need to buy a new code. If you are not certain this is the correct access code for your course, please contact your instructor.

List Price = $125.00  | College Bookstore Wholesale Price = $93.75

Student Solutions Manual (Chapters 1-8)  (ISBN-10: 0495560618 | ISBN-13: 9780495560616)

This manual includes worked out solutions to every odd-numbered exercise in Single Variable Calculus: Concepts & Contexts, 4e (Chapters 1-8 of Stewart's Calculus: Concepts & Contexts, 4e).

List Price = $157.95  | CengageBrain Price = $157.95  | College Bookstore Wholesale Price = $118.50

Student Solutions Manual (Chapters 8-13)  (ISBN-10: 0495560553 | ISBN-13: 9780495560555)

This manual includes worked out solutions to every odd-numbered exercise in Multivariable Calculus: Concepts & Contexts, 4e (Chapters 8-13 of Stewart's Calculus: Concepts & Contexts, 4e).

List Price = $101.95  | CengageBrain Price = $101.95  | College Bookstore Wholesale Price = $76.50

CourseMate Instant Access  (ISBN-10: 1133599710 | ISBN-13: 9781133599715)

Cengage Learning's CourseMate brings course concepts to life with interactive learning, study, and exam preparation tools that support the printed textbook. Maximize your course success with the integrated eBook and chapter-specific learning tools that include flashcards, quizzes, videos, and more in your CourseMate. Key Features: Interactive eBook, Engagement Tracker, Learning Objectives, Tutorial Quizzes, Glossary and Flashcards, and Web Links and References.

List Price = $272.00  | CengageBrain Price = $272.00  | College Bookstore Wholesale Price = $272.00

Meet the Author

Author Bio

James Stewart

The late 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 was most recently Professor of Mathematics at McMaster University, and his research field was harmonic analysis. Stewart was the author of a best-selling calculus textbook series published by Cengage Learning, including CALCULUS, CALCULUS: EARLY TRANSCENDENTALS, and CALCULUS: CONCEPTS AND CONTEXTS, as well as a series of precalculus texts.