Synopses & Reviews
James Stewart's well-received SINGLE VARIABLE CALCULUS: CONCEPTS AND CONTEXTS, Second Edition follows in the path of the other best-selling books by this remarkable author. The First Edition of this book was highly successful because it reconciled two schools of thought: it skillfully merged the best of traditional calculus with the best of the reform movement. This new edition continues to offer the balanced approach along with Stewart's hallmark features: meticulous accuracy, patient explanations, and carefully graded problems. The content has been refined and the examples and exercises have been updated. In addition, CALCULUS: CONCEPTS AND CONTEXTS, Second Edition now includes a free CD-ROM for students that contains animations, activities, and homework hints. The book integrates the use of the CD throughout by using icons that show students when to use the CD to deepen their understanding of a difficult concept. In CALCULUS: CONCEPTS AND CONTEXTS, this well respected author emphasizes conceptual understanding - motivating students with real world applications and stressing the Rule of Four in numerical, visual, algebraic, and verbal interpretations. All concepts are presented in the classic Stewart style: with simplicity, character, and attention to detail. In addition to his clear exposition, Stewart also creates well thought-out problems and exercises. The definitions are precise and the problems create an ideal balance between conceptual understanding and algebraic skills.
Review
"I have appreciated two main things from this textbook. The first is the concise language that Stewart uses. It makes my job much easier. I can embellish, add, emphasize or not easily. The second item is the paring down of the calculus material to an amount that...allows me enough room to add the various exploratory activities that I have my classes use."
Review
"The single feature of this book that I like the most is the breadth in the exercises."
Review
"I want a text that stresses the numerical and graphical as well as the algebraic approach to calculus. But I also want a calculus text that still has a solid rigorous foundation, and the Stewart book provides both."
Review
"Stewart does a good job in extracting the best parts from calculus reform efforts and traditional approaches. The book is well organized, the material is clearly presented, and there is an abundance of problems of varying levels. The problems are the right type to engage students in thinking about the concepts and to develop skills and ability to apply the calculus. . . . The organization and presentation is designed to develop perspective, conceptual understanding and ability to use the concepts and methods to actually solve problems." "I like the author's approach very much...it combines the best features of both [the traditional and the reform approaches], making it possible to present a better course. Stewart's approach contains the most important aspects of that [reform] approach--rule of four, use of projects, use of technology, focus on topics of value to clients, development of conceptual understanding over formalism, writing." "The text is well-informed about the use of calculus and makes good use of realistic settings, not just artificially manufactured information."
Review
"Among the strengths of this text are the clear writing styles of the author, the use of color and diagrams throughout the book, the excellent organization of the book, the superb set of ancillaries both for the student and the instructor, and the excellent homework exercises."
Synopsis
Stewart's clear, direct writing style in SINGLE VARIABLE CALCULUS guides you through key ideas, theorems, and problem-solving steps. Every concept is supported by thoughtfully worked examples and carefully chosen exercises. Many of the detailed examples display solutions that are presented graphically, analytically, or numerically to provide further insight into mathematical concepts. Margin notes expand on and clarify the steps of the solution. iLrn Homework helps you identify where you need additional help, and Personal Tutor with SMARTHINKING gives you live, one-on-one online help from an experienced calculus tutor. In addition, the Interactive Video Skillbuilder CD-ROM takes you step-by-step through examples from the book.
Synopsis
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 the 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.
Synopsis
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.
About the Author
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.
Table of Contents
1. FUNCTIONS AND MODELS. 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. 5. INTEGRALS. 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.