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## 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.

- 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).

- 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.

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.

Cengage provides a range of supplements that are updated in coordination with the main title selection. For more information about these supplements, contact your Learning Consultant.

### FOR INSTRUCTORS

#### Web Site

ISBN: 9780495561224

These websites encompass the interactive online products and services integrated with Cengage Learning/Brooks Cole mathematics programs. Students and instructors have access to the content directly through text-specific student and instructor websites and via online learning platforms including WebAssign, Blackboard®, WebCT®, and other course management systems.

#### Test Bank

ISBN: 9780495561231

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

#### Instructor's Guide

ISBN: 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: 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.

#### Complete Solutions Manual (Chapters 9-13)

ISBN: 9780495560562

This manual includes worked-out solutions to every exercise in Multivariable Calculus: Concepts and Contexts, 4th Edition (Chapters 9-13 of Stewart's Calculus: Concepts and Contexts, 4th Edition).

#### Complete Solutions Manual (Chapters 1-8)

ISBN: 9780495560609

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

### FOR STUDENTS

#### Study Guide for Single Variable Calculus: Concepts and Contexts, Enhanced Edition

ISBN: 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.

#### Web Site

ISBN: 9780495561224

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

#### Study Guide for Multivariable Calculus: Concepts and Contexts, Enhanced Edition

ISBN: 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.

#### Student Solutions Manual (Chapters 1-8)

ISBN: 9780495560616

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

#### Student Solutions Manual (Chapters 9-13)

ISBN: 9780495560555

This manual includes worked-out solutions to every odd-numbered exercise in Multivariable Calculus: Concepts and Contexts, Enhanced Edition, 4th Edition (Chapters 9-13 of Stewart's Calculus: Concepts and Contexts, 4th Edition).