Students who have used Smith/Minton's Calculus say it was easier to read than any other math book they've used. That testimony underscores the success of the authors’ approach, which combines the best elements of reform with the most reliable aspects of mainstream calculus teaching, resulting in a motivating, challenging book. Smith/Minton also provide exceptional, reality-based applications that appeal to students’ interests and demonstrate the elegance of math in the world around us. New features include: · A new organization placing all transcendental functions early in the book and consolidating the introduction to L'Hôpital's Rule in a single section. · More concisely written explanations in every chapter. · Many new exercises (for a total of 7,000 throughout the book) that require additional rigor not found in the 2nd Edition. · New exploratory exercises in every section that challenge students to synthesize key concepts to solve intriguing projects. · New commentaries (“Beyond Formulas”) that encourage students to think mathematically beyond the procedures they learn. · New counterpoints to the historical notes, “Today in Mathematics,” that stress the contemporary dynamism of mathematical research and applications, connecting past contributions to the present. · An enhanced discussion of differential equations and additional applications of vector calculus.
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NEW COVERAGE: In response to comments from reviewers and users of the Premiere Edition, the authors have expanded Section 3.1 by using linear approximation to provide an introduction to L'Hopital's Rule. A full treatment of indeterminate forms and L'Hopital's Rule is then found in Section 7.6. As a result of this revision, Newton's method has been moved to a section of its own, Section 3.2.
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EARLY COVERAGE OF TRIGONOMETRIC, EXPONENTIAL AND LOGARITHMIC FUNCTIONS: The table of contents features an early introduction to the calculus of logarithms, exponentials and the trigonometric functions. The calculus of all of these functions is introduced in Chapter 2, along with all of the other rules of differentiation. Numerical evidence and nearly complete algebraic proofs of the derivations of the derivatives of the natural logarithm and exponentials are given at this point. The definition of the natural logarithm as an integral and complete derivations of the derivative formulas are provided in Chapter 6. In the intervening chapters, the authors routinely use logarithms and exponentials to provide more varied and interesting examples in their discussion of the applications of integration.
EMPHASIS ON PROBLEM SOLVING: This text features a strong problem-solving emphasis, including the introduction of many topics from graphical, numerical and algebraic points of view. In many instances, the emphasis on graphical and numerical methods allows the authors to present more realistic and complex problems than are often presented in calculus. As a result, students will have a more complete idea of the usefulness of calculus and can solve a wider variety of problems.
TECHNOLOGY USE: The authors have employed a generic use of technology throughout the text, using only features that are shared by virtually all graphing calculators and computer algebra systems. Only those features of technology that clearly aid in the understanding of the concepts of calculus are used. The authors believe that technology can and should be introduced as a natural part of a coherent development of calculus. Throughout the text, advice and guidance on the proper use of technology is provided, as well as tools to help students determine when the use of technology is most appropriate. Users are expected to have access to a graphing calculator or a computer algebra system and to use it routinely.
FLEXIBLE EXERCISE SETS: This text contains more than 7000 exercises, found at the end of each section, as well as review exercises at the end of each chapter. Each exercise set has been carefully designed to provide a wide variety of routine, moderate, and challenging exercises. The authors have taken great care to create original and imaginative exercises that provide an appropriate review of the topics covered in each section and chapter.
WRITING EXERCISES: Each exercise set begins with a variety of writing exercises, clearly labeled as such by a writing icon. These exercises can be used as springboards for discussion and are intended to give students an opportunity to carefully consider important mathematical concepts and ideas and to express these in their own words.
APPLICATIONS: This textbook contains numerous applications designed to engage the attention and imagination of students from a variety of backgrounds and with diverse interests. The applications are realistic and many are unique, covering a broad spectrum of topic areas.
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