Calculus

It is assumed that these students have completed high school algebra. This text's primary goal is to teach the techniques of differential and integral calculus that students are likely to encounter in undergraduate courses in their majors and in subsequent professional activities. The exposition is designed to provide a sound, intuitive understanding of the basic concepts of calculus without sacrificing mathematical accuracy. Thus, the main results are stated carefully and completely, and whenever possible, explanations are intuitive or geometric.Realistic Examples: Each topic in the textbook is motivated by realistic worked examples. Many new practical examples have been added in the Seventh Edition and many existing examples have been modified throughout the text. In particular, examples introducing key topics such as the limit, the derivative, and the integral have been carefully rewritten with an eye toward realism.Algebra Review: For students needing to brush up on their high school algebra, an extensive algebra review is included in an appendix. This appendix includes worked examples and applied practice problems for the student. Students are advised throughout the text when it might be appropriate to consult this material. A new feature in this edition are algebra boxes in the margin that remind students of key facts and procedures, such as the quadratic formula, at the point in the material that such procedures will be useful.Focused Topic Coverage: The focus of the text has been improved by eliminating subjects generally viewed as unnecessary to the intended audience. In particular, Chapter 8, Sequences and Series, and Chapter 9, Trigonometric Functions, of the sixth edition have been removed from the seventh edition.Referenced Examples and Exercises: Every chapter includes a number of referenced examples and problems that are based on journal articles or information found in texts. Some of these problems are routine and others challenging, but all are tied to issues of practical interest relating mathematics to the real world.Definitions: Definitions and key concepts are set off in shaded boxes for easy referencing by the student.Exercises: This text provides students with ample opportunities to practice problem-solving strategies. All exercise sets are carefully graded so that the more routine exercises are placed first in the exercise set, followed by more challenging exercises and applications. Exercise sets follow each section, and Review Exercises follow each chapter.Writing Exercises: Every exercise set includes writing problems that are related to issues raised in the examples and exercises and are designated by the writing icon. These problems challenge a student's critical thinking skills and invite students to research topics on their own and to communicate about mathematics using words, not just symbols. Usually, there is no set answer to these problems, and individual responses many vary.Applications: Solving applied problems is the core focus of an applied calculus course. The authors believe that topics should be applied to practical problems very soon after they are introduced, and a strong attempt has been made to put this belief into effect in the seventh edition. This text provides methods for dealing with both routine computations and practical problems. These problem-solving methods and strategies are introduced in examples and are followed by both end of section exercises and extensive set of review problems at the end of each chapter. All concepts covered in the text are applied to a variety of practical situations from business and economics and the social, managerial, environmental, and life sciences. For easy reference, an applications index can be found on the front and back insider covers of the text.Think About It Essays: Each chapter ends with a special Think About It essay. These essays are designed to introduce modeling procedures based on referenced journal articles. Each Think About It essay provided background information on an applied situation and then invites students to answer a series of bite-sized questions culminating in a question of some importance in the social, managerial, or biological sciences. In this way, students are introduced to ideas and methods that might otherwise be beyond the scope of the text. Answers to these problems may be found in the Instructor's Manual.Technology: The use of technology in conjunction with this text is entirely optional. In the Sixth Edition of the text, Explore! boxes were introduced to guide students in the use of graphing utilities to study the concepts and procedures of calculus. These Explore! boxes have been extensively revised in this edition, and new explorations included. Additionally, each chapter ends with an Explore! Update, which contains hints for using a graphing utility and solutions to selected Explore! box exercise. Each problem set also includes numerous problems involving the use of a calculator that are denoted by a calculator icon.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. Visiting the Message Center allows students to discuss difficult concepts among themselves, while 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.