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, including exponential and logarithmic functions, from these four points of view. Limits are treated from descriptive, graphical, numerical, and algebraic points of view. Section 2.

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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, including exponential and logarithmic functions, from these four points of view. Limits are treated from descriptive, graphical, numerical, and algebraic points of view.

Section 2. Sections Copyright Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part.

Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.

Here the examples and exercises explore the meanings of derivatives in various contexts. Higher derivatives are introduced in Section 2. When derivatives are computed in applied situations, students are asked to explain their meanings.

Exponential growth and decay are now covered in this chapter. 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. 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.

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. Copyright Cengage Learning. Preface xvii 11 Infinite Sequences and Series The convergence tests have intuitive justifications see page as well as formal proofs.

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, Early Transcendentals, 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. The preparation of this and previous editions has involved much time spent reading the reasoned but sometimes contradictory advice from a large number of astute reviewers. I greatly appreciate the time they spent to understand my motivation for the approach taken.

I have learned something from each of them. Arthur Robinson, Jr. They have all done an outstanding job. 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.

Selected Visuals and Modules are available at www. 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. 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 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 I.

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: 5. This indicates that Homework Hints are available for the exercise.

These hints can be found on stewartcalculus. The homework hints ask you questions that allow you to make progress toward a solution without actually giving you the answer. You need to pursue each hint in an active manner with pencil and paper to work out the details. I recommend that you keep this book for reference purposes after you finish the course. Because you will likely forget some of the specific details of calculus, the book will serve as a useful reminder when you need to use calculus in subsequent courses.

And, because this book contains more material than can be covered in any one course, it can also serve as a valuable resource for a working scientist or engineer. Calculus is an exciting subject, justly considered to be one of the greatest achievements of the human intellect. I hope you will discover that it is not only useful but also intrinsically beautiful. Similar functionality is available using a web interface at WolframAlpha. Handheld calculators are becoming more powerful, as are software programs and Internet resources.

In addition, many mathematical applications have been released for smartphones and tablets such as the iPad. Some exercises in this text are marked with a graphing icon ; , which indicates that the use of some technology is required.

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