Calculus
Robert Smith
Wydawnictwo: angielskie
Data wydania: 2001
Kategoria: Popularnonaukowe
ISBN: 978-0-07-112481-2
Liczba stron: 0
Dodał/a książkę:Wojciech Polak
The wide-ranging debate brought about by the calculus reform movement has had a significant impact on calculus textbooks. In response to many of the questions and concerns surrounding this debate, the authors have written a modern calculus textbook, intended for students majoring in mathematics, physics, chemistry, engineering and related fields. The text is written for the average student -- one who does not already know the subject, whose background is somewhat weak in spots, and who requires a significant motivation to study calculus.The authors follow a relatively standard order of presentation, while integrating technology and thought-provoking exercises throughout the text. Some minor changes have been made in the order of topics to reflect shifts in the importance of certain applications in engineering and science. This text also gives an early introduction to logarithms, exponentials and the trigonometric functions. Wherever practical, concepts are developed from graphical, numerical, and algebraic perspectives (the Rule of Three) to give students a full understanding of calculus. This text places a significant emphasis on problem solving and presents realistic applications, as well as open-ended problems.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.NETTUTOR: NetTutor is a revolutionary new web-based learning environment for the live dissemination of mathematical content. NetTutor offers your students live, personalized tutoring via the internet. Using NetTutor's powerful WWWhiteboard software, students can post a question and receive prompt feedback from an expert in their subject. The WWWhiteboard allows students and tutors to use proper mathematical notation as well as other highlighting features - truly making this a unique learning experience. Students may also post questions to the Q&A Center and receive a reply within 24 hours. The Archive Center provides a browseable list of questions and answers maintained by the subject tutor. NetTutor is FREE and an invaluable aid for all students; the study partner who always has the answer.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.