詹姆斯·斯图尔特《微积分早期超越》第六版PDF

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"《Copy of Maths--Essential Calculus Early Transcendentals.pdf》是由James Steward编写的第六版微积分教科书，涵盖了预备微积分、极限、微分、积分等主题，适用于澳大利亚、巴西、加拿大、墨西哥、新加坡、西班牙、英国和美国等多个国家的教育体系。该书由多个专业团队进行编辑、设计、市场推广和生产制作，并且包含相关的商标和版权信息。" 在《Essential Calculus Early Transcendentals》这本教材中，James Steward深入浅出地介绍了微积分的基础概念和重要应用。预备微积分部分是为那些尚未接触过微积分的学生准备的，旨在建立必要的数学基础，包括函数、代数、几何和微积分的初步概念。这部分内容通常涵盖线性函数、二次函数、指数函数、对数函数以及这些函数的图形和性质。极限是微积分的核心概念之一，Steward详细解释了极限如何帮助我们理解函数在特定点的行为，特别是当x值接近某一特定值时，函数值的趋向。他使用了ε-δ定义来形式化极限的概念，并通过实际例子让学生理解和掌握极限的计算。微分是研究函数变化率的工具，书中详述了导数的定义、计算方法以及导数在实际问题中的应用，如速度、加速度、最优化问题等。此外，还包括隐函数的求导、高阶导数、导数的应用（如洛必达法则和泰勒公式）以及微分方程的初步介绍。积分作为微积分的另一大支柱，Stewart介绍了不定积分和定积分，它们分别代表了函数的反导数和区域的面积。书中涵盖了基本积分表、换元法和分部积分法，以及积分在物理、几何和工程问题中的应用，如计算弧长、体积、工作量等。此外，教材还可能涉及微积分的其他高级主题，如多元函数微积分、级数和序列、向量代数以及复数。这些内容对于科学和工程领域的学生至关重要，因为它们提供了解决实际问题的强大数学工具。总体而言，《Essential Calculus Early Transcendentals》是一本全面且深入的微积分教材，适合大学本科初学者使用，它不仅提供了理论知识，而且强调了数学概念的实际应用，有助于培养学生的数学思维和解决问题的能力。

xvi

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PREFACE

Applications of Differentiation The basic facts concerning extreme values and shapes of curves are deduced from the

Mean Value Theorem. Graphing with technology emphasizes the interaction between cal-

culus and calculators and the analysis of families of curves. Some substantial optimization

problems are provided, including an explanation of why you need to raise your head 42°

to see the top of a rainbow.

Integrals The area problem and the distance problem serve to motivate the deﬁnite integral, with

sigma notation introduced as needed. (Full coverage of sigma notation is provided in Appen-

dix E.) Emphasis is placed on explaining the meanings of integrals in various contexts and

on estimating their values from graphs and tables.

Applications of Integration Here I present the applications of integration—area, volume, work, average value—that

can reasonably be done without specialized techniques of integration. General methods are

emphasized. The goal is for students to be able to divide a quantity into small pieces, esti-

mate with Riemann sums, and recognize the limit as an integral.

Te c h n i q u e s o f I n t e g r a t i o n All the standard methods are covered but, of course, the real challenge is to be able to recog-

nize which technique is best used in a given situation. Accordingly, in Section 7.5, I

present a strategy for integration. The use of computer algebra systems is discussed in

Section 7.6.

Here are the applications of integration—arc length and surface area—for which it is use-

ful to have available all the techniques of integration, as well as applications to biology,

economics, and physics (hydrostatic force and centers of mass). I have also included a sec-

tion 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.

Differential Equations Modeling is the theme that uniﬁes this introductory treatment of differential equations.

Direction ﬁelds and Euler’s method are studied before separable and linear equations are

solved explicitly, so that qualitative, numerical, and analytic approaches are given equal

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 intro-

duction to ﬁrst-order differential equations. An optional ﬁnal section uses predator-prey

models to illustrate systems of differential equations.

This chapter introduces parametric and polar curves and applies the methods of calculus

to them. Parametric curves are well suited to laboratory projects; the two presented here

involve families of curves and Bézier curves. A brief treatment of conic sections in polar

coordinates prepares the way for Kepler’s Laws in Chapter 13.

Infinite Sequences and Series The convergence tests have intuitive justiﬁcations (see page 697) as well as formal proofs.

Numerical estimates of sums of series are based on which test was used to prove conver-

gence. The emphasis is on Taylor series and polynomials and their applications to physics.

Error estimates include those from graphing devices.

The material on three-dimensional analytic geometry and vectors is divided into two chap-

ters. Chapter 12 deals with vectors, the dot and cross products, lines, planes, and surfaces.

Vec tors an d

The Geometry of Space

Parametric Equations

and Polar Coordinates

Further Applications

of Integration

PREFACE

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xvii

Vec tor Fun ctions This chapter covers vector-valued functions, their derivatives and integrals, the length and

curvature of space curves, and velocity and acceleration along space curves, culminating

in Kepler’s laws.

Partial Derivatives Functions of two or more variables are studied from verbal, numerical, visual, and alge-

braic points of view. 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. Directional derivatives are estimated from

contour maps of temperature, pressure, and snowfall.

Multiple Integrals Contour maps and the Midpoint Rule are used to estimate the average snowfall and average

temperature in given regions. 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 eval-

uating triple integrals.

Vec tor Cal culus Vect or ﬁe ld s a re in tr od uc ed th rou gh pic tu re s o f v elo ci ty ﬁe ld s s how in g S an F ra nc is co Ba y

wind patterns. The similarities among the Fundamental Theorem for line integrals, Green’s

Theorem, Stokes’ Theorem, and the Divergence Theorem are emphasized.

Since ﬁrst-order differential equations are covered in Chapter 9, this ﬁnal chapter deals

with second-order linear differential equations, their application to vibrating springs and

electric circuits, and series solutions.

ANCILLARIES

Calculus, Early Transcendentals, Sixth Edition, is supported by a complete set of ancil-

laries 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.

ACKNOWLEDGMENTS

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.

SIXTH EDITION REVIEWERS

Marilyn Belkin, Villanova University

Philip L. Bowers, Florida State University

Amy Elizabeth Bowman, University of Alabama in Huntsville

M. Hilary Davies, University of Alaska Anchorage

Frederick Gass, Miami University

Paul Triantaﬁlos Hadavas, Armstrong Atlantic State University

Nets Katz, Indiana University Bloomington

James McKinney, California State Polytechnic University, Pomona

Martin Nakashima, California State Polytechnic University, Pomona

Lila Roberts, Georgia College and State University

Second-Order

Differential Equations

xviii

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PREFACE

Maria Andersen, Muskegon Community College

Eric Aurand, Eastﬁeld College

Joy Becker, University of Wisconsin–Stout

Przemyslaw Bogacki, Old Dominion University

Amy Elizabeth Bowman, University of Alabama in Huntsville

Monica Brown, University of Missouri–St. Louis

Roxanne Byrne, University of Colorado at Denver

and Health Sciences Center

Teri Christiansen, University of Missouri–Columbia

Bobby Dale Daniel, Lamar University

Jennifer Daniel, Lamar University

Andras Domokos, California State University, Sacramento

Timothy Flaherty, Carnegie Mellon University

Lee Gibson, University of Louisville

Jane Golden, Hillsborough Community College

Semion Gutman, University of Oklahoma

Diane Hoffoss, University of San Diego

Lorraine Hughes, Mississippi State University

Jay Jahangiri, Kent State University

John Jernigan, Community College of Philadelphia

Brian Karasek, South Mountain Community College

Jason Kozinski, University of Florida

Carole Krueger, The University of Texas at Arlington

Ken Kubota, University of Kentucky

John Mitchell, Clark College

Donald Paul, Tulsa Community College

Chad Pierson, University of Minnesota, Duluth

Lanita Presson, University of Alabama in Huntsville

Karin Reinhold, State University of New York at Albany

Thomas Riedel, University of Louisville

Christopher Schroeder, Morehead State University

Angela Sharp, University of Minnesota, Duluth

Patricia Shaw, Mississippi State University

Carl Spitznagel, John Carroll University

Mohammad Tabanjeh, Virginia State University

Capt. Koichi Takagi, United States Naval Academy

Lorna TenEyck, Chemeketa Community College

Roger Werbylo, Pima Community College

David Williams, Clayton State University

Zhuan Ye, Northern Illinois University

PREVIOUS EDITION REVIEWERS

TECHNOLOGY REVIEWERS

B. D. Aggarwala, University of Calgary

John Alberghini, Manchester Community College

Michael Albert, Carnegie-Mellon University

Daniel Anderson, University of Iowa

Donna J. Bailey, Northeast Missouri State University

Wayne Barber, Chemeketa Community College

Neil Berger, University of Illinois, Chicago

David Berman, University of New Orleans

Richard Biggs, University of Western Ontario

Robert Blumenthal, Oglethorpe University

Martina Bode, Northwestern University

Barbara Bohannon, Hofstra University

Philip L. Bowers, Florida State University

Jay Bourland, Colorado State University

Stephen W. Brady, Wichita State University

Michael Breen, Te n nessee Tech n ological Univ e rs ity

Robert N. Bryan, University of Western Ontario

David Buchthal, University of Akron

Jorge Cassio, Miami-Dade Community College

Jack Ceder, University of California, Santa Barbara

Scott Chapman, Trinity University

James Choike, Oklahoma State University

Barbara Cortzen, DePaul University

Carl Cowen, Purdue University

Philip S. Crooke, Vanderbilt University

Charles N. Curtis, Missouri Southern State College

Daniel Cyphert, Armstrong State College

Robert Dahlin

Gregory J. Davis, University of Wisconsin–Green Bay

Elias Deeba, University of Houston–Downtown

Daniel DiMaria, Suffolk Community College

Seymour Ditor, University of Western Ontario

Greg Dresden, Washington and Lee University

Daniel Drucker, Wayne State University

Kenn Dunn, Dalhousie University

Dennis Dunninger, Michigan State University

Bruce Edwards, University of Florida

David Ellis, San Francisco State University

John Ellison, Grove City College

Martin Erickson, Truman State University

Garret Etgen, University of Houston

Theodore G. Faticoni, Fordham University

Laurene V. Fausett, Georgia Southern University

Norman Feldman, Sonoma State University

Newman Fisher, San Francisco State University

José D. Flores, The University of South Dakota

William Francis, Michigan Technological University

James T. Franklin, Valencia Community College, East

Stanley Friedlander, Bronx Community College

Patrick Gallagher, Columbia University–New York

Paul Garrett, University of Minnesota–Minneapolis

Frederick Gass, Miami University of Ohio

PREFACE

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xix

Bruce Gilligan, University of Regina

Matthias K. Gobbert, University of Maryland,

Baltimore County

Gerald Goff, Oklahoma State University

Stuart Goldenberg, California Polytechnic State University

John A. Graham, Buckingham Browne & Nichols School

Richard Grassl, University of New Mexico

Michael Gregory, University of North Dakota

Charles Groetsch, University of Cincinnati

Salim M. Haïdar, Grand Valley State University

D. W. Hall, Michigan State University

Robert L. Hall, University of Wisconsin–Milwaukee

Howard B. Hamilton, California State University, Sacramento

Darel Hardy, Colorado State University

Gary W. Harrison, College of Charleston

Melvin Hausner, New York University/Courant Institute

Curtis Herink, Mercer University

Russell Herman, University of North Carolina at Wilmington

Allen Hesse, Rochester Community College

Randall R. Holmes, Auburn University

James F. Hurley, University of Connecticut

Matthew A. Isom, Arizona State University

Gerald Janusz, University of Illinois at Urbana-Champaign

John H. Jenkins, Embry-Riddle Aeronautical University,

Prescott Campus

Clement Jeske, University of Wisconsin, Platteville

Carl Jockusch, University of Illinois at Urbana-Champaign

Jan E. H. Johansson, University of Vermont

Jerry Johnson, Oklahoma State University

Zsuzsanna M. Kadas, St. Michael’s College

Matt Kaufman

Matthias Kawski, Arizona State University

Frederick W. Keene, Pasadena City College

Robert L. Kelley, University of Miami

Virgil Kowalik, Texas A&I Uni v ersity

Kevin Kreider, University of Akron

Leonard Krop, DePaul University

Mark Krusemeyer, Carleton College

John C. Lawlor, University of Vermont

Christopher C. Leary, State University of New York

at Geneseo

David Leeming, University of Victoria

Sam Lesseig, Northeast Missouri State University

Phil Locke, University of Maine

Joan McCarter, Arizona State University

Phil McCartney, Northern Kentucky University

Igor Malyshev, San Jose State University

Larry Mansﬁeld, Queens College

Mary Martin, Colgate University

Nathaniel F. G. Martin, University of Virginia

Gerald Y. Matsumoto, American River College

Tom Metzger, University of Pittsburgh

Michael Montaño, Riverside Community College

Teri Jo Murphy, University of Oklahoma

Richard Nowakowski, Dalhousie University

Hussain S. Nur, California State University, Fresno

Wayne N. Palmer, Utica College

Vincent Panico, University of the Paciﬁc

F. J. Papp, University of Michigan–Dearborn

Mike Penna, Indiana University–Purdue University

Indianapolis

Mark Pinsky, Northwestern University

Lothar Redlin, The Pennsylvania State University

Joel W. Robbin, University of Wisconsin–Madison

E. Arthur Robinson, Jr.,

The George Washington University

Richard Rockwell, Paciﬁc Union College

Rob Root, Lafayette College

Richard Ruedemann, Arizona State University

David Ryeburn, Simon Fraser University

Richard St. Andre, Central Michigan University

Ricardo Salinas, San Antonio College

Robert Schmidt, South Dakota State University

Eric Schreiner, Western Michigan University

Mihr J. Shah, Kent State University–Trumbull

Theodore Shifrin, University of Georgia

Wayne Skrapek, University of Saskatchewan

Larry Small, Los Angeles Pierce College

Teresa Morgan Smith, Blinn College

William Smith, University of North Carolina

Donald W. Solomon, University of Wisconsin–Milwaukee

Edward Spitznagel, Washington University

Joseph Stampﬂi, Indiana University

Kristin Stoley, Blinn College

M. B. Tavakoli, Chaffey College

Paul Xavier Uhlig, St. Mary’s University, San Antonio

Stan Ver Nooy, University of Oregon

Andrei Verona, California State University–Los Angeles

Russell C. Walker, Carnegie Mellon University

William L. Walton, McCallie School

Jack Weiner, University of Guelph

Alan Weinstein, University of California, Berkeley

Theodore W. Wilcox, Rochester Institute of Technology

Steven Willard, University of Alberta

Robert Wilson, University of Wisconsin–Madison

Jerome Wolbert, University of Michigan–Ann Arbor

Dennis H. Wortman, University of Massachusetts, Boston

Mary Wright, Southern Illinois University–Carbondale

Paul M. Wright, Austin Community College

Xian Wu, University of South Carolina

||||

PREFACE

In addition, I would like to thank George Bergman, David Cusick, Stuart Goldenberg,

Larry Peterson, Dan Silver, Norton Starr, Alan Weinstein, and Gail Wolkowicz for their

suggestions; Dan Clegg for his research in libraries and on the Internet; Al Shenk and Den-

nis Zill for permission to use exercises from their calculus texts; John Ringland for his

reﬁnements of the multivariable Maple art; COMAP for permission to use project mate-

rial; George Bergman, David Bleecker, Dan Clegg, Victor Kaftal, Anthony Lam, Jamie

Lawson, Ira Rosenholtz, Paul Sally, Lowell Smylie, and Larry Wallen for ideas for exer-

cises; Dan Drucker for the roller derby project; Thomas Banchoff, Tom Farmer, Fred Gass,

John Ramsay, Larry Riddle, and Philip Strafﬁn for ideas for projects; Dan Anderson, Dan

Clegg, Jeff Cole, Dan Drucker, and Barbara Frank for solving the new exercises and sug-

gesting ways to improve them; Marv Riedesel and Mary Johnson for accuracy in proof-

reading; and Jeff Cole and Dan Clegg for their careful preparation and proofreading of the

answer manuscript.

In addition, I thank those who have contributed to past editions: Ed Barbeau, Fred

Brauer, Andy Bulman-Fleming, Bob Burton, Tom DiCiccio, Garret Etgen, Chris Fisher,

Arnold Good, Gene Hecht, Harvey Keynes, Kevin Kreider, E. L. Koh, Zdislav Kovarik,

Emile LeBlanc, David Leep, Gerald Leibowitz, Lothar Redlin, Carl Riehm, Peter Rosen-

thal, Doug Shaw, and Saleem Watson.

I also thank Kathi Townes, Stephanie Kuhns, and Brian Betsill of TECHarts for their

production services and the following Brooks/Cole staff: Cheryll Linthicum, editorial pro-

duction project manager; Mark Santee, Melissa Wong, and Bryan Vann, marketing team;

Stacy Green, assistant editor, and Elizabeth Rodio, editorial assistant; Sam Subity, technol-

ogy project manager; Rob Hugel, creative director, and Vernon Boes, art director; and

Becky Cross, print buyer. 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 two decades: Ron Munro, Harry Campbell, Craig Barth, Jeremy

Hayhurst, Gary Ostedt, and now Bob Pirtle. Bob continues in that tradition of editors who,

while offering sound advice and ample assistance, trust my instincts and allow me to write

the books that I want to write.

JAMES STEWART

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