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More About This Textbook
Overview
Editorial Reviews
From The Critics
This textbook for a first course in calculus introduces the derivative, the integral, infinite series, vectors and matrices, curves in spaces, partial differentiation, multiple integrals, and vector calculus. The sixth edition adds a chapter on direction fields and Euler's method. The CDROM contains interactive examples and study questions. Annotation c. Book News, Inc., Portland, OR (booknews.com)Product Details
Related Subjects
Meet the Author
C. Henry Edwards is emeritus professor of mathematics at the University of Georgia. He earned his Ph.D. at the University of Tennessee in 1960, and recently retired after 40 years of classroom teaching (including calculus or differential equations almost every term) at the universities of Tennessee, Wisconsin, and Georgia, with a brief interlude at the Institute for Advanced Study (Princeton) as an Alfred P. Sloan Research Fellow. He has received numerous teaching awards, including the University of Georgia's honoratus medal in 1983 (for sustained excellence in honors teaching), its Josiah Meigs award in 1991 (the institution's highest award for teaching), and the 1997 statewide Georgia Regents award for research university faculty teaching excellence. His scholarly career has ranged from research and dissertation direction in topology to the history of mathematics to computing and technology in the teaching and applications of mathematics. In addition to being author or coauthor of calculus, advanced calculus, linear algebra, and differential equations textbooks, he is wellknown to calculus instructors as author of The Historical Development of the Calculus (SpringerVerlag, 1979). During the 1990s he served as a principal investigator on three NSFsupported projects: (1) A school mathematics project including Maple for beginning algebra students, (2) A CalculuswithMathematica program, and (3) A MATLABbased computer lab project for numerical analysis and differential equations students.
David E. Penney, University of Georgia, completed his Ph.D. at Tulane University in 1965 (under the direction of Prof. L.Bruce Treybig) while teaching at the University of New Orleans. Earlier he had worked in experimental biophysics at Tulane University and the Veteran's Administration Hospital in New Orleans under the direction of Robert Dixon McAfee, where Dr. McAfee's research team's primary focus was on the active transport of sodium ions by biological membranes. Penney's primary contribution here was the development of a mathematical model (using simultaneous ordinary differential equations) for the metabolic phenomena regulating such transport, with potential future applications in kidney physiology, management of hypertension, and treatment of congestive heart failure. He also designed and constructed servomechanisms for the accurate monitoring of ion transport, a phenomenon involving the measurement of potentials in microvolts at impedances of millions of megohms. Penney began teaching calculus at Tulane in 1957 and taught that course almost every term with enthusiasm and distinction until his retirement at the end of the last millennium. During his tenure at the University of Georgia he received numerous Universitywide teaching awards as well as directing several doctoral dissertations and seven undergraduate research projects. He is the author of research papers in number theory and topology and is the author or coauthor of textbooks on calculus, computer programming, differential equations, linear algebra, and liberal arts mathematics.
Table of Contents
Functions and Mathematical Modeling. Graphs of Equationsand Functions. Polynomials and Algebraic Functions. TranscendentalFunctions. Preview: What Is Calculus?
2. Prelude to Calculus.
Tangent Lines and Slope Predictors. The Limit Concept. MoreAbout Limits. The Concept of Continuity.
3. The Derivative.
The Derivative and Rates of Change. Basic DifferentiationRules. The Chain Rule. Derivatives of Algebraic Functions. Maximaand Minima of Functions on Closed Intervals. Applied OptimizationProblems. Derivatives of Trigonometric Functions. Exponential andLogarithmic Functions. Implicit Differentiation and Related Rates.Successive Approximations and Newton's Method.
4. Additional Applications of the Derivative.
Introduction. Increments, Differentials, and Linear Approximation.Increasing and Decreasing Functions and the Mean Value Theorem. TheFirst Derivative Test and Applications. Simple Curve Sketching. HigherDerivatives and Concavity. Curve Sketching and Asymptotes. IndeterminateForms and L'Hôpitals' Rule. More Indeterminate Forms.
5. The Integral.
Introduction. Antiderivatives and Initial Value Problems.Elementary Area Computations. Riemann Sums and the Integral. Evaluationof Integrals. The Fundamental Theorem of Calculus. Integration bySubstitution. Areas of Plane Regions. Numerical Integration.
6. Applications of the Integral.
Riemann Sum Approximations. Volumes by the Method of CrossSections. Volumes by the Method of Cylindrical Shells. Arc Lengthand Surface Area of Revolution. Force and Work. Centroids of PlaneRegions and Curves. The NaturalLogarithm as an Integral. Inverse TrigonometricFunctions. Hyperbolic Functions.
7. Techniques of Integration.
Introduction. Integral Tables and Simple Substitutions.Integration by Parts. Trigonometric Integrals. Rational Functionsand Partial Fractions. Trigonometric Substitutions. Integrals InvolvingQuadratic Polynomials. Improper Integrals.
8. Differential Equations.
Simple Equations and Models. Slope Fields and Euler's Method.Separable Equations and Applications. Linear Equations and Applications.Population Models. Linear SecondOrder Equations. Mechanical Vibrations.
9. Polar Coordinates and Parametric Curves.
Analytic Geometry and the Conic Sections. Polar Coordinates.Area Computations in Polar Coordinates. Parametric Curves. IntegralComputations with Parametric Curves. Conic Sections and Applications.
10. Infinite Series.
Introduction. Infinite Sequences. Infinite Series and Convergence.Taylor Series and Taylor Polynomials. The Integral Test. ComparisonTests for PositiveTerm Series. Alternating Series and Absolute Convergence.Power Series. Power Series Computations. Series Solutions of DifferentialEquations.
Appendices.
A. Real Numbers and Inequalities. B. The Coordinate Plane and Straight Lines. C. Review of Trigonometry. D. Proofs of the Limit Laws. E. The Completeness of the Real Number System. F. Existence of the Integral. G. Approximations and Riemann Sums. H. L'Hôpital's Rule and Cauchy's Mean Value Theorem. I. Proof of Taylor's Formula. J. Conic Sections as Sections of a Cone. K. Proof of the Linear Approximation Theorem. L. Units of Measurement and Conversion Factors. M. Formulas from Algebra, Geometry, and Trigonometry. N. The Greek Alphabet.
Answers to OddNumbered Problems.
References for Further Study.
Index.
Table of Integrals.
Preface
Contemporary calculus instructors and students face traditional challenges as well as new ones that result from changes in the role and practice of mathematics by scientists and engineers in the world at large. As a consequence, this sixth edition of our calculus textbook is its most extensive revision since the first edition appeared in 1982.
Two entire chapters of the fifth edition have been replaced in the table of contents by two new ones; most of the remaining chapters have been extensively rewritten. Nearly 160 of the book's over 800 worked examples are new for this edition and the 1850 figures in the text include 250 new computergenerated graphics. Almost 800 of its 7250 problems are new, and these are augmented by over 330 new conceptual discussion questions that now precede the problem sets. Moreover, almost 1100 new true/false questions are included in the Study Guides on the new CDROM that accompanies this edition. In summary, almost 2200 of these 8650plus problems and questions are new, and the text discussion and explanations have undergone corresponding alteration and improvement.
PRINCIPAL NEW FEATURES
The current revision of the text features
Complete coverage of the calculus of transcendental functions is now fully integrated in Chapters 1 through 6—with the result that the Chapter 7 and 8 titles in the 5th edition table of contents do not appear in this 6th edition.
A new chapter on differential equations (Chapter 8)now appears immediately after Chapter 7 on techniques of integration. It includes both direction fields and Eider's method together with the more elementary symbolic methods (which exploit techniques from Chapter 7) and interesting applications of both first and secondorder equations. Chapter 10 (Infinite Series) now ends with a new section on power series solutions of differential equations, thus bringing full circle a unifying focus of secondsemester calculus on elementary differential equations.
Linear systems and matrices, ending with an elementary treatment of eigenvalues and eigenvectors, are now introduced in Chapter 11. The subsequent coverage of multivariable calculus now integrates matrix methods and terminology with the traditional notation and approach—including (for instance) introduction and extensive application of the chain rule in matrixproduct form.
NEW LEARNING RESOURCES
CONCEPTUAL DISCUSSION QUESTIONS. The set of problems that concludes each section is now preceded by a brief Concepts: Questions and Discussion set consisting of several openended conceptual questions that can be used for either individual study or classroom discussion.
THE TEXT CDROM. The content of the new CDROM that accompanies this text is fully integrated with the textbook material, and is designed specifically for use handinhand with study of the book itself. This CDROM features the following resources to support learning and teaching:
COMPUTERIZED HOMEWORK GRADING SYSTEM. About 2000 of the textbook problems are incorporated in an automated grading system that is now available. Each problem solution in the system is structured algorithmically so that students can work in a computer lab setting to submit homework assignments for automatic grading. (There is a small annual fee per participating student.)
NEW SOLUTIONS MANUALS. The entirely new 1900page Instructor's Solutions Manual (available in two volumes) includes a detailed solution for every problem in the book. These solutions were written exclusively by the authors and have been checked independently by others.
The entirely new 950page Student Solutions Manual (available in two volumes) includes a detailed solution for every oddnumbered problem in the text. The answers (alone) to most of these oddnumbered problems are included in the answers section at the back of this book.
NEW TECHNOLOGY MANUALS. Each of the following manuals is available shrinkwrapped with any version of the text for half the normal price of the manual (all of which are inexpensive):
THE TEXT IN MORE DETAIL...
In preparing this edition, we have taken advantage of many valuable comments and suggestions from users of the first five editions. This revision was so pervasive that the individual changed are too numerous to be detailed in a preface, but the following paragraphs summarize those that may be of widest interest.
TEXT ORGANIZATION
The mean value theorem and its applications are deferred to Chapter 4. In addition, a dominant theme of Chapter 4 is the use of calculus both to construct graphs of functions and to explain and interpret graphs that have been constructed by a calculator or computer. This theme is developed in Sections 4.4 on the first derivative test and 4.6 on higher derivatives and concavity. But it may also be apparent in Sections 4.8 and 4.9 on 1'Hôpital's rule, which now appears squarely in the context of differential calculus and is applied here to round out the calculus of exponential and logarithmic functions.
Chapter 6 begins with a largely new section on Riemann sum approximations, with new examples centering on fluid flow and medical applications. Section 6.6 is a new treatment of centroids of plane regions and curves. Section 6.7 gives the integral approach to logarithms, and Sections 6.8 and 6.9 cover both the differential and the integral calculus of inverse trigonometric functions and of hyperbolic functions.
Chapter 7 (Techniques of Integration) is organized to accommodate those instructors who feel that methods of formal integration now require less emphasis, in view of modern techniques for both numerical and symbolic integration. Integration by parts (Section 7.3) precedes trigonometric integrals (Section 7.4). The method of partial fractions appears in Section 7.5, and trigonometric substitutions and integrals involving quadratic polynomials follow in Sections 7.6 and 7.7. Improper integrals appear in Section 7.8, with new and substantial subsections on special functions and probability and random sampling. This rearrangement of Chapter 7 makes it more convenient to stop wherever the instructor desires.
OPTIONS IN TEACHING CALCULUS
The present version of the text is accompanied by a more traditional version that treats transcendental functions later in single variable calculus and omits matrices in multivariable calculus. Both versions of the complete text are also available in twovolume split editions. By appropriate selection of first and second volumes, the instructor can therefore construct a complete text for a calculus sequence with