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Preface
We 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 studentoriented approach follow below.
Applications
We 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.
Examples
The text includes many more worked examples than is customary. Furthermore, we have included computational details toenhance readability by students whose basic skills are weak.
Exercises
The exercises comprise about onequarter of the textthe 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 Problems
The 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 builtin workbook.
Minimal Prerequisites
In 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 Edition
Among the many changes in this edition, the following are the most significant:
This edition contains more material than can be covered in most onesemester courses. Optional sections are starred in the table of contents. In addition, the level of theoretical material may be adjusted to the needs of the students. For instance, only the first two pages of Section 1.4 are required in order to introduce the limit notation.
A Study Guide for students containing detailed explanations and solutions for every sixth exercise is available. The Study Guide also includes helpful hints and strategies for studying that will help students improve their performance in the course. In addition, the Study Guide contains a copy of Visual Calculus, the popular, easytouse software for IBM compatible computers. Visual Calculus contains over 20 routines that provide additional insights into the topics discussed in the text. Also, instructors find the software valuable for constructing graphs for exams.
An Instructor's Solutions Manual contains worked solutions to every exercise.
TestGen EQ provides nearly 1000 suggested test questions, keyed to chapter and section. TestGen EQ is a textspecific testing program networkable for administering tests and capturing grades online. Edit and add your own questions, or use the new "Function Plotter" to create a nearly unlimited number of tests and drill worksheets.
Designed to complement and expand upon the text, the text Web site offers a variety of interactive teaching and learning tools. Since many of the text projects use reallife data, we made the data easier to use by making it available in Excel spreadsheets on the Web site. The Web site also includes links to related Web sites, quizzes, Syllabus Builder, and more. For more information, visit www.prenhall.com/goldstein or contact your local Prentice Hall representative.
Table of Contents
1. The Derivative.
2. Applications of the Derivative.
3. Techniques of Differentiation.
4. The Exponential and Natural Logarithm Functions.
5. Applications of the Exponential and Natural Logarithm Functions.
6. The Definite Integral.
7. Functions of Several Variables.
8. The Trigonometric Functions.
Preface
Preface
We 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 studentoriented approach follow below.
Applications
We 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.
Examples
The text includes many more worked examples than is customary. Furthermore, we have included computational details to enhancereadability by students whose basic skills are weak.
Exercises
The exercises comprise about onequarter of the textthe 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 Problems
The 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 builtin workbook.
Minimal Prerequisites
In 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 Edition
Among the many changes in this edition, the following are the most significant:
This edition contains more material than can be covered in most onesemester courses. Optional sections are starred in the table of contents. In addition, the level of theoretical material may be adjusted to the needs of the students. For instance, only the first two pages of Section 1.4 are required in order to introduce the limit notation.
A Study Guide for students containing detailed explanations and solutions for every sixth exercise is available. The Study Guide also includes helpful hints and strategies for studying that will help students improve their performance in the course. In addition, the Study Guide contains a copy of Visual Calculus, the popular, easytouse software for IBM compatible computers. Visual Calculus contains over 20 routines that provide additional insights into the topics discussed in the text. Also, instructors find the software valuable for constructing graphs for exams.
An Instructor's Solutions Manual contains worked solutions to every exercise.
TestGen EQ provides nearly 1000 suggested test questions, keyed to chapter and section. TestGen EQ is a textspecific testing program networkable for administering tests and capturing grades online. Edit and add your own questions, or use the new "Function Plotter" to create a nearly unlimited number of tests and drill worksheets.
Designed to complement and expand upon the text, the text Web site offers a variety of interactive teaching and learning tools. Since many of the text projects use reallife data, we made the data easier to use by making it available in Excel spreadsheets on the Web site. The Web site also includes links to related Web sites, quizzes, Syllabus Builder, and more. For more information, visit www.prenhall.com/goldstein or contact your local Prentice Hall representative.