Summary: Stewart's SINGLE VARIABLE CALCULUS: CONCEPTS AND CONTEXTS, THIRD EDITION offers a streamlined approach to teaching calculus, focusing on major concepts and supporting those with precise definitions, patient explanations, and carefully graded problems. SINGLE VARIABLE CALCULUS: CONCEPTS AND CONTEXTS is highly regarded because it has successfully brought peace to departments that were split between reform and traditional approaches to teaching calculus. Not only does t...show morehe text help reconcile the two schools of thought by skillfully merging the best of traditional calculus with the best of the reform movement, it does so with innovation and meticulous accuracy.
NEW! More than 25% of the problems in each chapter are new, with additional conceptual and technology exercises and three new projects. However, the number of pages in the text remains unchanged.
Presents a streamlined approach to calculus for instructors who want to focus on concepts, but with a balanced presentation of theory.
The concept of the derivative is introduced in Chapter 2, but Rules of Differentiation are not given until Chapter 3. This is intended to force students to think about the numerical and geometric meanings and consequences of derivatives before the differentiation formulas are covered.
Antiderivatives are introduced soon after derivatives, revisited frequently, and then summarized in section 4.10.
The integration chapter challenges students to understand the meaning of integrals in diverse contexts. There is no separate chapter on techniques of integration, but substitution and parts are covered here and other methods are treated briefly.
Parametric curves are introduced early to help students draw curves easily, with technology, whenever needed throughout the text.
Differential equations occur immediately after applications of integration, and stress direction fields, numerical methods, and models of population growth.
Margin notes clarify and expand on topics presented in the main body of the text.
"Principles of Problem Solving" (based on Polya's approach) is introduced at the end of Chapter One. "Focus on Problem Solving" sections then occur at the end of every chapter to reinforce this essential skill. These sections include more challenging problems.
Laboratory Projects, Discovery Projects, Writing Papers, and Applied Projects appear throughout the book to reinforce concepts, provide group-learning experiences, and help students understand the relevance of what they are learning.
Each chapter ends with a comprehensive review that includes "Concept Check Questions," a true/false quiz, and exercises for every principle covered in that chapter.
NEW! The text contains 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 new references to the TEC CD-ROM (Tools for Enriching Calculus).
NEW! The only major structural change in this edition is that the two sections on linear approximations (2.9 and 3.8) have been combined as Section 3.8.
NEW! This text presents a more streamlined approach to calculus. For the convenience of instructors who wish to cover topics not in the book, the web site www.stewartcalculus.com contains additional topics and expanded coverage of some topics. These are available as PDFs. These topics include: Trigonometric Integrals, Trigonometric Substitution, Strategy for Integration, Volumes by Cylindrical Shells, Area of a Surface of Revolution, Linear Differential Equations, Strategy for Testing Series, Using Series to Solve Differential Equations, Second Order Differential Equations, Nonhomogeneous Linear Equations, Applications of Second Order Differential Equations.
NEW! The TOOLS FOR ENRICHING CALCULUS CD-ROM has been significantly enhanced for this edition and now includes modules for multivariable calculus. This powerful CD-ROM contains visualizations, interactive modules, and homework hints that significantly enrich students' learning experience.
NEW! iLrn Homework allows instructors to assign machine-gradable homework problems that help students identify where they need additional help. By entering a PIN code packaged with their textbook, students gain access to both iLrn and vMentor--live, one-on-one online help from an experienced calculus tutor. If assigned by the professor, this system provides necessary problem solving practice that is automatically graded and requires very little intervention from instructors.
NEW! The Interactive Video Skillbuilder CD-ROM, takes students step-by-step through examples from the book, reinforcing the problem-solving skills they need to learn.
NEW! Preloaded with content and available free via PIN code when packaged with this text, WebTutor ToolBox pairs all the content of this text's rich Book Companion Web Site with all the sophisticated course management functionality of a WebCT or Blackboard product. It's an ideal solution for online and distance learning needs.
NEW! A "V" symbol has been placed beside examples (an average of three per section) for which there are videos of instructors explaining the example in more detail. These videos are free to adopters.
Four Ways to Represent a Function. Mathematical Models. New Functions from Old Functions. Graphing Calculators and Computers. Exponential Functions. Inverse Functions and Logarithms. Parametric Curves. 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. Tangents, Velocities, and Other Rates of Change. Derivatives. The Derivative as a Function. Linear Approximations. What does f' say about f? Review. Focus on Problem Solving.
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. Derivatives of Logarithmic Functions. Linear Approximations and Differentials. Review. Focus on Problem Solving.
4. APPLICATIONS OF DIFFERENTIATION.
Related Rates. Maximum and Minimum Values. Derivatives and the Shapes of Curves. Graphing with Calculus and Calculators. Indeterminate Forms and l'Hospital's Rule. Optimization Problems. Applications to Economics. Newton's Method. Antiderivatives. Review. Focus on Problem Solving.
Areas and Distances. The Definite Integral. Evaluating Definite Integrals. The Fundamental Theorem of Calculus. The Substitution Rule. Integration by Parts. Additional Techniques of Integration. Integration Using Tables and Computer Algebra Systems. Approximate Integration. Improper Integrals. Review. Focus on Problem Solving.
6. APPLICATIONS OF INTEGRATION.
More about Areas. Volumes. Arc Length. Average Value of a Function. Applications to Physics and Engineering. 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. Exponential Growth and Decay. The Logistic Equation. Predator-Prey Systems. Review. Focus on Problem Solving.
8. INFINITE SEQUENCES AND SERIES.
Sequences. Series. The Integral and Comparison Tests; Estimating Sums. Other Convergence Tests. Power Series. Representation of Functions as Power Series. Taylor and Maclaurin Series. The Binomial Series. Applications of Taylor Polynomials. Review. Focus on Problem Solving.
Appendix A: Intervals, Inequalities, And Absolute Values. Appendix B: Coordinate Geometry. Appendix C: Trigonometry. Appendix D: Precise Definitions Of Limits. Appendix E: A Few Proofs. Appendix F: Sigma Notation. Appendix G: Integration Of Rational Functions By Partial Fractions. Appendix H: Polar Coordinates. Appendix I: Complex Numbers. Appendix J: Answers To Odd-Numbered Exercises. Index.
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