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Early Transcendentals The single variable material in chapters 1–9 is a mod- The book includes some exercises and examples from Elementary Calculus: .. A few figures in the pdf and print versions of the book are marked with “(AP)” at. Calculus, Eighth Edition, is similar to the present textbook except that the exponen- .. Student Solutions Manual Single Variable Early Transcendentals Linear. Single Variable Calculus: Early Transcendentals | 8th Edition. James Stewart. View as Instructor. Product cover for Single Variable Calculus: Early.

Rewrite by completing the square. We will give a precise definition of a tangent line in Copyright Cengage Learning. The use of online homework is growing and its appeal depends on ease of use, grading precision, and reliability. It directs you to modules in which you can explore aspects of calculus for which the computer is particularly useful. With each positive number r there is associated one value of A, and we say that A is a function of r. Lockhart, Daniel S.

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Mathematica is a registered trademark of Wolfram Research, Inc. Tools for Enriching Calculus is a trademark used herein under license. Purchase any of our products at your local college store or at our preferred online store www. Contents v 5 5. See the Preface. Contents vii 9.

Contents ix Preface A great discovery solves a great problem but there is a grain of discovery in the solution of any problem. Your problem may be modest; but if it challenges your curiosity and brings into play your inventive faculties, and if you solve it by your own means, you may experience the tension and enjoy the triumph of discovery.

I have tried to write a book that assists students in discovering calculus—both for its practical power and its surprising beauty. In this edition, as in the first seven editions, I aim to convey to the student a sense of the utility of calculus and develop technical competence, but I also strive to give some appreciation for the intrinsic beauty of the subject.

Newton undoubtedly experienced a sense of triumph when he made his great discoveries. I want students to share some of that excitement.

The emphasis is on understanding concepts. I think that nearly everybody agrees that this should be the primary goal of calculus instruction. In fact, the impetus for the current calculus reform movement came from the Tulane Conference in , which formulated as their first recommendation: Focus on conceptual understanding.

I have tried to implement this goal through the Rule of Three: More recently, the Rule of Three has been expanded to become the Rule of Four by emphasizing the verbal, or descriptive, point of view as well. In writing the eighth edition my premise has been that it is possible to achieve conceptual understanding and still retain the best traditions of traditional calculus.

The book contains elements of reform, but within the context of a traditional curriculum. I have written several other calculus textbooks that might be preferable for some instructors.

Most of them also come in single variable and multivariable versions. Early Transcendentals, Eighth Edition, is similar to the present textbook except that the exponential, logarithmic, and inverse trigonometric functions are covered in the first semester. The relative brevity is achieved through briefer exposition of some topics and putting some features on the website. Early Transcendentals, Second Edition, resembles Essential Calculus, but the exponential, logarithmic, and inverse trigonometric functions are covered in Chapter 3.

Concepts and Contexts, Fourth Edition, emphasizes conceptual understanding even more strongly than this book. The coverage of topics is not encyclopedic and the material on transcendental functions and on parametric equations is woven throughout the book instead of being treated in separate chapters. Early Vectors introduces vectors and vector functions in the first semester and integrates them throughout the book.

It is suitable for students taking engineering and physics courses concurrently with calculus. Calculus for the Life Sciences is intended to show students in the life sciences how calculus relates to biology. Calculus for the Life Sciences as well as three additional chapters covering probability and statistics. New examples have been added see Examples 5. And the solutions to some of the existing examples have been amplified.

Three new projects have been added: The project Planes and Birds: Minimizing Energy page asks how birds can minimize power and energy by flapping their wings versus gliding.

The project Controlling Red Blood Cell Loss During Surgery page describes the ANH procedure, in which blood is extracted from the patient before an operation and is replaced by saline solution. In the project The Speedo LZR Racer page it is explained that this suit reduces drag in the water and, as a result, many swimming records were broken.

Students are asked why a small decrease in drag can have a big effect on performance. I have streamlined Chapter 15 Multiple Integrals by combining the first two sections so that iterated integrals are treated earlier.

Here are some of my favorites: In addition, there are some good new Problems Plus. See Problems 10—12 on page , Problem 10 on page , Problems 14—15 on pages —54, and Problem 8 on page Preface xiii Conceptual Exercises The most important way to foster conceptual understanding is through the problems that we assign. To that end I have devised various types of problems. Some exercise sets begin with requests to explain the meanings of the basic concepts of the section.

See, for instance, the first few exercises in Sections 1. Other exercises test conceptual understanding through graphs or tables see Exercises 2.

Another type of exercise uses verbal description to test conceptual understanding see Exercises 1. I particularly value problems that combine and compare graphical, numerical, and algebraic approaches see Exercises 2.

Graded Exercise Sets Each exercise set is carefully graded, progressing from basic conceptual exercises and skill-development problems to more challenging problems involving applications and proofs. Real-World Data My assistants and I spent a great deal of time looking in libraries, contacting companies and government agencies, and searching the Internet for interesting real-world data to introduce, motivate, and illustrate the concepts of calculus.

As a result, many of the examples and exercises deal with functions defined by such numerical data or graphs. See, for instance, Figure 1 in Section 1.

Functions of two variables are illustrated by a table of values of the wind-chill index as a function of air temperature and wind speed Example Partial derivatives are introduced in Section This example is pursued further in connection with linear approximations Example Directional derivatives are introduced in Section Double integrals are used to estimate the average snowfall in Colorado on December 20—21, Example Vector fields are introduced in Section Projects One way of involving students and making them active learners is to have them work perhaps in groups on extended projects that give a feeling of substantial accomplishment when completed.

I have included four kinds of projects: Applied Projects involve applications that are designed to appeal to the imagination of students. The project after Section 9.

The answer might surprise you. The project after Section Laboratory Projects involve technology; the one following Section Suggested references are supplied. Discovery Projects anticipate results to be discussed later or encourage discovery through pattern recognition see the one following Section 7. Others explore aspects of geometry: Position from Samples. Problem Solving Students usually have difficulties with problems for which there is no single well-defined procedure for obtaining the answer.

They are applied, both explicitly and implicitly, throughout the book. After the other chapters I have placed sections called Problems Plus, which feature examples of how to tackle challenging calculus problems. In selecting the varied problems for these sections I kept in mind the following advice from David Hilbert: Here I reward a student significantly for ideas toward a solution and for recognizing which problem-solving principles are relevant.

Dual Treatment of Exponential and Logarithmic Functions There are two possible ways of treating the exponential and logarithmic functions and each method has its passionate advocates. Because one often finds advocates of both approaches teaching the same course, I include full treatments of both methods. In Sections 6. Students have seen these functions introduced this way since high school. In the alternative approach, presented in Sections 6.

This latter method is, of course, less intuitive but more elegant. You can use whichever treatment you prefer. If the first approach is taken, then much of Chapter 6 can be covered before Chapters 4 and 5, if desired. To accommodate this choice of presentation there are specially identified problems involving integrals of exponential and logarithmic functions at the end of the appropriate sections of Chapters 4 and 5.

This order of presentation allows a faster-paced course to teach the transcendental functions and the definite integral in the first semester of the course.

For instructors who would like to go even further in this direction I have prepared an alternate edition of this book, called Calculus: Early Transcendentals, Eighth Edition, in which the exponential and logarithmic functions are introduced in the first chapter. Their limits and derivatives are found in the second and third chapters at the same time as polynomials and the other elementary functions.

Tools for Enriching Calculus TEC is a companion to the text and is intended to enrich and complement its contents.

Selected Visuals and Modules are available at www. Preface xv approach. In sections of the book where technology is particularly appropriate, marginal icons direct students to TEC Modules that provide a laboratory environment in which they can explore the topic in different ways and at different levels. Visuals are animations of figures in text; Modules are more elaborate activities and include exercises.

Instructors can choose to become involved at several different levels, ranging from simply encouraging students to use the Visuals and Modules for independent exploration, to assigning specific exercises from those included with each Module, or to creating additional exercises, labs, and projects that make use of the Visuals and Modules.

TEC also includes Homework Hints for representative exercises usually odd-numbered in every section of the text, indicated by printing the exercise number in red. These hints are usually presented in the form of questions and try to imitate an effective teaching assistant by functioning as a silent tutor. They are constructed so as not to reveal any more of the actual solution than is minimally necessary to make further progress. Enhanced WebAssign Technology is having an impact on the way homework is assigned to students, particularly in large classes.

The use of online homework is growing and its appeal depends on ease of use, grading precision, and reliability. With the Eighth Edition we have been working with the calculus community and WebAssign to develop an online homework system.

The system also includes Active Examples, in which students are guided in step-bystep tutorials through text examples, with links to the textbook and to video solutions. Website Visit CengageBrain. A Preview of Calculus This is an overview of the subject and includes a list of questions to motivate the study of calculus.

A discussion of mathematical models leads to a review of the standard functions from these four points of view. The material on limits is motivated by a prior discussion of the tangent and velocity problems. Limits are treated from descriptive, graphical, numerical, and algebraic points of view. Section 1. The examples and exercises explore the meanings of derivatives in various contexts. Higher derivatives are introduced in Section 2.

Graphing with technology emphasizes the interaction between calculus and calculators and the analysis of families of curves. Full coverage of sigma notation is provided in Appendix E. Emphasis is placed on explaining the meanings of integrals in various contexts and on estimating their values from graphs and tables. General methods are emphasized. The goal is for students to be able to divide a quantity into small pieces, estimate with Riemann sums, and recognize the limit as an integral.

As discussed more fully on page xiv, only one of the two treatments of these functions need be covered. Exponential growth and decay are covered in this chapter.

Accordingly, in Section 7. The use of computer algebra systems is discussed in Section 7. I have also included a section on probability. There are more applications here than can realistically be covered in a given course.

Instructors should select applications suitable for their students and for which they themselves have enthusiasm. Preface xvii consideration. These methods are applied to the exponential, logistic, and other models for population growth. The first four or five sections of this chapter serve as a good introduction to first-order differential equations.

An optional final section uses predatorprey models to illustrate systems of differential equations. Numerical estimates of sums of series are based on which test was used to prove convergence. The emphasis is on Taylor series and polynomials and their applications to physics.

Error estimates include those from graphing devices. Chapter 12 deals with vectors, the dot and cross products, lines, planes, and surfaces. In particular, I introduce partial derivatives by looking at a specific column in a table of values of the heat index perceived air temperature as a function of the actual temperature and the relative humidity.

Double and triple integrals are used to compute probabilities, surface areas, and in projects volumes of hyperspheres and volumes of intersections of three cylinders. Cylindrical and spherical coordinates are introduced in the context of evaluating triple integrals. Calculus, Eighth Edition, is supported by a complete set of ancillaries developed under my direction.

Each piece has been designed to enhance student understanding and to facilitate creative instruction. The tables on pages xxi—xxii describe each of these ancillaries. I greatly appreciate the time they spent to understand my motivation for the approach taken. I have learned something from each of them.

Crooke, Vanderbilt University Charles N. Faticoni, Fordham University Laurene V. Holmes, Auburn University James F. Kadas, St. Lawlor, University of Vermont Christopher C. Martin, University of Virginia Gerald Y. Arthur Robinson, Jr. In addition, I thank those who have contributed to past editions: Cheryll Linthicum, content project manager; Stacy Green, senior content developer; Samantha Lugtu, associate content developer; Stephanie Kreuz, product assistant; Lynh Pham, media developer; Ryan Ahern, marketing manager; and Vernon Boes, art director.

They have all done an outstanding job. I have been very fortunate to have worked with some of the best mathematics editors in the business over the past three decades: All of them have contributed greatly to the success of this book. Cengage Learning Testing Powered by Cognero login. The Flash simulation modules in TEC include instructions, written and audio explanations of the concepts, and exercises.

The meticulously crafted pedagogy and exercises in our proven texts become even more effective in Enhanced WebAssign, supplemented by multimedia tutorial support and immediate feedback as students complete their assignments. Key features include: Instructors can further customize the text by adding instructor-created or YouTube video links.

Additional media assets include animated figures, video clips, highlighting and note-taking features, and more. YouBook is available within Enhanced WebAssign. CourseMate CourseMate is a perfect self-study tool for students, and requires no set up from instructors. CourseMate brings course concepts to life with interactive learning, study, and exam preparation tools that support the printed textbook.

For instructors, CourseMate includes Engagement Tracker, a first-of-its-kind tool that monitors student engagement. At the CengageBrain. This will take you to the product page where these resources can be found. Cole, and Daniel Drucker ISBN Multivariable By Dan Clegg and Barbara Frank ISBN Provides completely worked-out solutions to all oddnumbered exercises in the text, giving students a chance to check their answer and ensure they took the correct steps to arrive at the answer.

The Student Solutions Manual can be ordered or accessed online as an eBook at www.

Andre ISBN For each section of the text, the Study Guide provides students with a brief introduction, a short list of concepts to master, and summary and focus questions with explained answers. The Study Guide also contains self-tests with exam-style questions. The Study Guide can be ordered or accessed online as an eBook at www.

A Companion to Calculus By Dennis Ebersole, Doris Schattschneider, Alicia Sevilla, and Kay Somers ISBN Written to improve algebra and problem-solving skills of students taking a calculus course, every chapter in this companion is keyed to a calculus topic, providing conceptual background and specific algebra techniques needed to understand and solve calculus problems related to that topic. It is designed for calculus courses that integrate the review of precalculus concepts or for individual use.

Order a copy of the text or access the eBook online at www. Linear Algebra for Calculus by Konrad J. Heuvers, William P. Francis, John H. Kuisti, Deborah F. Lockhart, Daniel S. Moak, and Gene M. Ortner ISBN This comprehensive book, designed to supplement the calculus course, provides an introduction to and review of the basic ideas of linear algebra.

To the Student Reading a calculus textbook is different from reading a newspaper or a novel, or even a physics book. You should have pencil and paper and calculator at hand to sketch a diagram or make a calculation. Some students start by trying their homework problems and read the text only if they get stuck on an exercise. I suggest that a far better plan is to read and understand a section of the text before attempting the exercises.

In particular, you should look at the definitions to see the exact meanings of the terms.

And before you read each example, I suggest that you cover up the solution and try solving the problem yourself. Part of the aim of this course is to train you to think logically. Learn to write the solutions of the exercises in a connected, step-by-step fashion with explanatory sentences— not just a string of disconnected equations or formulas.

The answers to the odd-numbered exercises appear at the back of the book, in Appendix H. Some exercises ask for a verbal explanation or interpretation or description. The icon ; indicates an exercise that definitely requires the use of either a graphing calculator or a computer with graphing software. The symbol CAS is reserved for problems in which the full resources of a computer algebra system like Maple, Mathematica, or the TI are required.

You will also encounter the symbol , which warns you against committing an error. I have placed this symbol in the margin in situations where I have observed that a large proportion of my students tend to make the same mistake. It directs you to modules in which you can explore aspects of calculus for which the computer is particularly useful. You will notice that some exercise numbers are printed in red: