Brief Calculus and Its Applications (9th Edition)

From the Inside FlapPrefaceWe have been very pleased with the enthusiastic response to the first seven editions of Brief Calculus and Its Applications by teachers and students alike. The present work incorporates many of the suggestions they have put forward.Although there are many changes, we have preserved the approach and the flavor. Our goals remain the same: to begin the calculus as soon as possible; to present calculus in an intuitive yet intellectually satisfying way; and to illustrate the many applications of calculus to the biological, social, and management sciences.The distinctive order of topics has proven over the years to be successful-easier for students to learn, and more interesting because students see significant applications early. For instance, the derivative is explained geometrically before the analytic material on limits is presented. This approach gives the students an understanding of the derivative at least as strong as that obtained from the traditional approach. To reach the applications in Chapter 2 quickly, we present only the differentiation rules and the curve sketching needed for those applications. Advanced topics come later when they are needed. Other aspects of this student-oriented approach follow below. ApplicationsWe provide realistic applications that illustrate the uses of calculus in other disciplines. See the Index of Applications on the inside cover. Wherever possible, we have attempted to use applications to motivate the mathematics. ExamplesThe text includes many more worked examples than is customary. Furthermore, we have included computational details to enhance readability by students whose basic skills are weak. ExercisesThe exercises comprise about one-quarter of the text-the most important part of the text in our opinion. The exercises at the ends of the sections are usually arranged in the order in which the text proceeds, so that the homework assignments may easily be made after only part of a section is discussed. Interesting applications and more challenging problems tend to be located near the ends of the exercise sets. Supplementary exercises at the end of each chapter expand the other exercise sets and include problems that require skills from earlier chapters. Practice ProblemsThe practice problems have proven to be a popular and useful feature. Practice Problems are carefully selected questions located at the end of each section, just before the exercise set. Complete solutions are given following the exercise set. The practice problems often focus on points that are potentially confusing or are likely to be overlooked. We recommend that the reader seriously attempt the practice problems and study their solutions before moving on to the exercises. In effect, the practice problems constitute a built-in workbook. Minimal PrerequisitesIn Chapter 0, we review those concepts that the reader needs to study calculus. Some important topics, such as the laws of exponents, are reviewed again when they are used in a later chapter. Section 0.6 prepares students for applied problems that appear throughout the text. A reader familiar with the content of Chapter 0 should begin with Chapter 1 and use Chapter 0 as a reference, whenever needed. New in this EditionAmong the many changes in this edition, the following are the most significant:Delta Notation We introduce delta notation in Chapter 0 and use it in our discussion of the derivative. As in previous editions, we have tried to minimize the use of complicated notation, preferring instead verbal descriptions. However, in the case of the delta notation, we feel that the clarity achieved is worth the extra notation. Derivative as a Rate of Change We preview the derivative as a rate of change at the beginning of Chapter 1, anticipating the more detailed discussion in Section 1.8. Since students have difficulty interpreting the derivative as a rate of change, we felt it prudent to allow them to practice repeatedly with t
Author: Larry J. Goldstein

Publisher: Prentice Hall College Div

Binding: Hardcover

Language: English

ISBN-10: 0130873039

ISBN-13: 9780130873033