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Features

Please see "What's New to This Edition" Section.

New To This Edition

What’s New to This Edition

New Section Study Guides Ten true/false items at the end of each section are provided to help students check the accuracy of their reading and retention, and to guide them systematically back through appropriate parts of the section for any further review of facts and concepts that is needed before attempting to work the problems.

    Answers and hints are for these true/false items provided at the back of the book (preceding the odd answers section). Students can first mark each item as true or false, and then consult the answers that are provided. If any of his answers are incorrect, then the hints for the appropriate items can be consulted. The hint for each item steers the student to the appropriate part of the section to read again to see what his or her difficulty was.

New Chapter Reviews Each chapter review consists of two parts–Understanding and Objectives–that precedes the chapter’s miscellaneous problems set.

    The Understanding part consists of concepts, definitions, formulas, results, etc.–with page references provided–to be reviewed section-by-section in preparation for the chapter test. Its premise is that the student who actually needs this review assistance likely can not or has not outlined the chapter for himself. As experienced teachers know, many (if not most) students need help in identifying, locating, and describing briefly the individual items in the chapter whose understanding comprise a knowledge of the chapter as a whole.

    The Objectives part identifies sample problems in each section that are recommended for review. Here again, many students are unable to categorize and recognize the types of problems that have been covered and the skills required for their solution. They have not consistently worked the problems in each section as it was covered in class, and may need help in identifying a manageable number of representative problems to review. Consequently, this part of the chapter review material provides a section-by-section list of the methods and techniques that have been covered and–for each such type–several illustrative problems selected to provide adequate practice in preparation for a chapter test.

Additional Learning Aids

Conceptual Discussion Questions The set of problems that concludes each section is preceded by a brief Concepts: Questions and Discussion set consisting of several open-ended conceptual questions that can be used for either individual study or classroom discussion.

Odd Answers The answers section in the back of the book has been greatly expanded for this edition, principally through the insertion of over 340 new figures. This computer-generated artwork is intended to aid student understanding of those problems whose comprehension has a strong visual component. The result is a more attractive answers section that invites student attention and study in its own right.

Solutions Manuals Paralleling the pedagogical emphasis in the revision of the text itself, the solutions manuals–odd-numbered solutions in the 990-page Student Solutions Manual, all solutions in the 1920-page Instructor’s Solution Manual– have been reworked, especially with all new and substantially improved artwork. These solutions were written exclusively by the authors with the same care devoted to the textbook exposition, and have been checked independently by others.

Student Investigations A number of the text’s investigations (or projects) have been re-written for this edition. These appear following the problem sets at the ends of key sections throughout the text. Most (but not all) of these projects employ some aspect of modern computational technology to illustrate the principal ideas of the preceding section, and many contain additional problems intended for solution with the use of a graphing calculator or computer algebra system. Where appropriate, project discussions are significantly expanded in the project manuals that accompany the text.

Historical Material Historical and biographical chapter openings offer students a sense of the development of our subject by real human beings. Indeed, our exposition of calculus frequently reflects the historical development of the subject–from ancient times to the ages of Newton and Leibniz and Euler to our own era of new computational power and technology.

TEXT ORGANIZATION

The current revision of the text is designed to include

• Early transcendentals fully integrated in Semester I.

• Differential equations and applications in Semester II.

• Multivariable calculus in Semester III.

Complete coverage of the calculus of transcendental functions is fully integrated in Chapters 1 through 6. A chapter on differential equations (Chapter 8) now appears immediately after Chapter 7 on techniques of integration. It includes both direction fields and Euler’s method together with the more elementary symbolic methods (which exploit techniques from Chapter 7) and interesting applications of both first- and second-order equations. Chapter 10 (Infinite Series) ends with a new section on power series solutions of differential equations, thus bringing full circle a unifying focus of second-semester calculus on elementary differential equations.

In More Detail . . .

Introductory Chapters Instead of a routine review of precalculus topics, Chapter 1 concentrates specifically on functions and graphs for use in mathematical modeling. It includes a section cataloging informally the elementary transcendental functions of calculus, as background to their more formal treatment using calculus itself. Chapter 1 concludes with a section addressing the question “What is calculus?” Chapter 2 on limits begins with a section on tangent lines to motivate the official introduction of limits in Section 2.2. Trigonometric limits are treated throughout Chapter 2 in order to encourage a richer and more visual introduction to the limit concept.

Differentiation Chapters The sequence of topics in Chapters 3 and 4 differs a bit from the most traditional order. We attempt to build student confidence by introducing topics more nearly in order of increasing difficulty. The chain rule appears quite early (in Section 3.3) and we cover the basic techniques for differentiating algebraic functions before discussing maxima and minima in Sections 3.5 and 3.6. Section 3.7 treats the derivatives of all six trigonometric functions, and Section 3.8 introduces the exponential and logarithmic functions. Implicit differentiation and related rates are combined in a single section (Section 3.9). The authors’ fondness for Newton’s method (Section 3.10) will be apparent.

    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 l’Hˆopital’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.

Integration Chapters Chapter 5 begins with a section on antiderivatives– which could logically be included in the preceding chapter, but benefits from the use of integral notation. When the definite integral is introduced in Sections 5.3 and 5.4, we emphasize endpoint and midpoint sums rather than upper and lower and more general Riemann sums. This concrete emphasis carries through the chapter to its final section on numerical integration.

    Chapter 6 begins with a section on Riemann sum approximations, with examples centering on fluid flow and medical applications. Section 6.6 is a 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 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.

Differential Equations This chapter begins with the most elementary differential equations and applications (Section 8.1) and then proceeds to introduce both graphical (slope field) and numerical (Euler) methods in Section 8.2. Subsequent sections of the chapter treat separable and linear first-order differential equations and (in more depth than usual in a calculus course) applications such as population growth (including logistic and predator-prey populations) and motion with resistance. The final two sections of Chapter 8 treat second-order linear equations and applications to mechanical vibrations. Instructors desiring still more coverage of differential equations can arrange with the publisher to bundle and use appropriate sections of Edwards and Penney, Differential Equations: Computing and Modeling 3/e (Prentice Hall, 2004).

Parametric Curves and Polar Coordinates Instead of the three separate sections on parabolas, ellipses, and hyperbolas that appear in some texts, Chapter 9 concludes with a single Section 9.6 that provides a unified treatment of all the conic sections.

Infinite Series After the usual introduction to convergence of infinite sequences and series in Sections 10.2 and 10.3, a combined treatment of Taylor polynomials and Taylor series appears in Section 10.4. This makes it possible for the instructor to experiment with a briefer treatment of infinite series, but still include some exposure to the Taylor series that are so important for applications. Perhaps the most novel feature of Chapter 10 is a final section on power series methods and their use to introduce new transcendental functions, thereby concluding the middle third of the book with a return to differential equations.

Multivariable Calculus The treatment of calculus of more than a single variable is rather traditional, beginning with vectors, curves, and surfaces in Chapter 11. Chapter 12 (Partial Differentiation) is followed by Chapters 13 (Multiple Integrals) and 14 (Vector Calculus), and itself features a strong treatment of multivariable maximum-minimum problems in Sections 12.5 (initial approach to these problems), 12.9 (Lagrange multipliers), and 12.10 (critical points of functions of two variables).

Table of Contents

TABLE OF CONTENTS    

About the Authors

Preface

            1.1 Functions and Mathematical Modeling

            Investigation:   Designing a Wading Pool  

            1.2 Graphs of Equations and Functions

            1.3 Polynomials and Algebraic Functions

            1.4 Transcendental Functions

            1.5 Preview:  What Is Calculus?

            REVIEW — Understanding: Concepts and Definitions

            Objectives:  Methods and Techniques    

            2.1 Tangent Lines and Slope Predictors

            Investigation:   Numerical Slope Investigations  

            2.2 The Limit Concept

            Investigation:   Limits, Slopes, and Logarithms  

            2.3 More About Limits

            Investigation:   Numerical Epsilon-Delta Limits  

            2.4 The Concept of Continuity

            REVIEW – Understanding: Concepts and Definitions

            Objectives:  Methods and Techniques 

3 The Derivative

            3.1 The Derivative and Rates of Change

            3.2 Basic Differentiation Rules

            3.3 The Chain Rule 

            3.4 Derivatives of Algebraic Functions

            3.5 Maxima and Minima of Functions on Closed Intervals

            Investigation:   When Is Your Coffee Cup Stablest?  

            3.6 Applied Optimization Problems

            3.7 Derivatives of Trigonometric Functions

            3.8 Exponential and Logarithmic Functions 

            Investigation:   Discovering the Number  e  for Yourself 

            3.9 Implicit Differentiation and Related Rates

            Investigation:   Constructing the Folium of Descartes 

            3.10 Successive Approximations and Newton's Method

            Investigation:   How Deep Does a Floating Ball Sink? 

            REVIEW — Understanding: Concepts, Definitions, and Formulas

            Objectives:  Methods and Techniques  

4 Additional Applications of the Derivative

            4.1 Introduction

            4.2 Increments, Differentials, and Linear Approximation

            4.3 Increasing and Decreasing Functions and the Mean Value Theorem

            4.4 The First Derivative Test and Applications

            Investigation:   Constructing a Candy Box With Lid  

            4.5 Simple Curve Sketching

            4.6 Higher Derivatives and Concavity

            4.7 Curve Sketching and Asymptotes

            Investigation:   Locating Special Points on Exotic Graphs  

            4.8 Indeterminate Forms and L'Hôpital's Rule

            4.9 More Indeterminate Forms

            REVIEW – Understanding: Concepts, Definitions, and Results

            Objectives:  Methods and Techniques   

5 The Integral  

            5.1 Introduction

            5.2 Antiderivatives and Initial Value Problems

            5.3 Elementary Area Computations

            5.4 Riemann Sums and the Integral

            Investigation:   Calculator/Computer Riemann Sums  

            5.5 Evaluation of Integrals

            5.6 The Fundamental Theorem of Calculus

            5.7 Integration by Substitution

            5.8 Areas of Plane Regions

            5.9 Numerical Integration

            Investigation:   Trapezoidal and Simpson Approximations 

            REVIEW — Understanding: Concepts, Definitions, and Results

            Objectives:  Methods and Techniques   

6 Applications of the Integral

            6.1 Riemann Sum Approximations

            6.2 Volumes by the Method of Cross Sections

            6.3 Volumes by the Method of Cylindrical Shells

            Investigation:   Design Your Own Ring!

            6.4 Arc Length and Surface Area of Revolution

            6.5 Force and Work

            6.6 Centroids of Plane Regions and Curves

            6.7 The Natural Logarithm as an Integral

            Investigation:   Natural Functional Equations

            6.8 Inverse Trigonometric Functions

            6.9 Hyperbolic Functions

            REVIEW – Understanding: Concepts, Definitions, and Formulas

            Objectives:  Methods and Techniques        

7 Techniques of Integration 

            7.1 Introduction

            7.2 Integral Tables and Simple Substitutions

            7.3 Integration by Parts

            7.4 Trigonometric Integrals

            7.5 Rational Functions and Partial Fractions

            7.6 Trigonometric Substitutions

            7.7 Integrals Involving Quadratic Polynomials

            7.8 Improper Integrals

            SUMMARY — Integration Strategies 

            REVIEW – Understanding: Concepts and Techniques

            Objectives:  Methods and Techniques    

8 Differential Equations    

            8.1 Simple Equations and Models

            8.2 Slope Fields and Euler's Method

            Investigation:   Computer-Assisted Slope Fields and Euler's Method 

            8.3 Separable Equations and Applications

            8.4 Linear Equations and Applications

            8.5 Population Models

            Investigation:   Predator-Prey Equations and Your Own Game Preserve

            8.6 Linear Second-Order Equations

            8.7 Mechanical Vibrations

            REVIEW — Understanding: Concepts, Definitions, and Methods

            Objectives:  Methods and Techniques    

9 Polar Coordinates and Parametric Curves  

            9.1 Analytic Geometry and the Conic Sections

            9.2 Polar Coordinates

            9.3 Area Computations in Polar Coordinates

            9.4 Parametric Curves

            Investigation:   Trochoids Galore

            9.5 Integral Computations with Parametric Curves

            Investigation:   Moon Orbits and Race Tracks

            9.6 Conic Sections and Applications 

            REVIEW – Understanding: Concepts, Definitions, and Formulas

            Objectives:  Methods and Techniques 

10 Infinite Series  

            10.1 Introduction

            10.2 Infinite Sequences

            Investigation:   Nested Radicals and Continued Fractions

            10.3 Infinite Series and Convergence

            Investigation:   Numerical Summation and Geometric Series

            10.4 Taylor Series and Taylor Polynomials

            Investigation:   Calculating Logarithms on a Deserted Island 

            10.5 The Integral Test

            Investigation:   The Number  p, Once and for All

            10.6 Comparison Tests for Positive-Term Series

            10.7 Alternating Series and Absolute Convergence

            10.8 Power Series

            10.9 Power Series Computations

            Investigation:   Calculating Trigonometric Functions on a Deserted Island  

            10.10 Series Solutions of differential Equations

            REVIEW — Understanding: Concepts, and Results

            Objectives:  Methods and Techniques    

11 Vectors, Curves, and Surfaces in Space

            11.1 Vectors in the Plane

            11.2 Three-Dimensional Vectors

            11.3 The Cross Product of Two Vectors

            11.4 Lines and Planes in Space

            11.5 Curves and Motion in Space

            Investigation:   Does a Pitched Baseball Really Curve?

            11.6 Curvature and Acceleration

            11.7 Cylinders and Quadric Surfaces

            11.8 Cylindrical and Spherical Coordinates

            REVIEW – Understanding: Concepts, Definitions, and Results

            Objectives:  Methods and Techniques    

12 Partial Differentiation

            12.1 Introduction

            12.2 Functions of Several Variables

            12.3 Limits and Continuity

            12.4 Partial Derivatives

            12.5 Multivariable Optimization Problems

            12.6 Increments and Linear Approximation

            12.7 The Multivariable Chain Rule

            12.8 Directional Derivatives and the Gradient Vector

            12.9 Lagrange Multipliers and Constrained Optimization

            Investigation:   Numerical Solution of Lagrange Multiplier Systems

            12.10 Critical Points of Functions of Two Variables

            Investigation:   Critical Point Investigations

            REVIEW — Understanding: Concepts, Definitions, and Results

            Objectives:  Methods and Techniques    

13 Multiple Integrals      

            13.1 Double Integrals

            Investigation:   Midpoint Sums Approximating Double Integrals 

            13.2 Double Integrals over More General Regions

            13.3 Area and Volume by Double Integration

            13.4 Double Integrals in Polar Coordinates

            13.5 Applications of Double Integrals

            Investigation:   Optimal Design of Race Car Wheels 

            13.6 Triple Integrals

            Investigation:   Archimedes' Floating Paraboloid

            13.7 Integration in Cylindrical and Spherical Coordinates

            13.8 Surface Area

            13.9 Change of Variables in Multiple Integrals

            REVIEW – Understanding: Concepts, Definitions, and Results

            Objectives:  Methods and Techniques    

14 Vector Calculus  

            14.1 Vector Fields

            14.2 Line Integrals

            14.3 The Fundamental Theorem and Independence of Path

            14.4 Green's Theorem

            14.5 Surface Integrals

            Investigation:   Surface Integrals and Rocket Nose Cones 

            14.6 The Divergence Theorem

            14.7 Stokes' Theorem

            REVIEW — Understanding: Concepts, Definitions, and Results

            Objectives:  Methods and Techniques    

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 Odd-Numbered Problems

References for Further Study

Index

Courses

Calculus  [COMPLETE TEXTS (CALCULUS 1-3)]   (Mathematics)

Author Bios

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 co-author of calculus, advanced calculus, linear algebra, and differential equations textbooks, he is well-known to calculus instructors as author of The Historical Development of the Calculus (Springer-Verlag, 1979).  During the 1990s, he served as a principal investigator on three NSF-supported projects: (1) A school mathematics project including Maple for beginning algebra students, (2) A Calculus-with-Mathematica program, and (3) A MATLAB-based 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 University-wide teaching awards as well as directing several doctoral dissertations and seven undergraduate research projects.  He is the author or co-author of textbooks on calculus, computer programming, differential equations, linear algebra, and liberal arts mathematics.

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Package ISBN-10: 0135133610 | ISBN-13: 9780135133613
©2008 | Instock
Suggested retail price: $201.33  Buy from myPearsonStore
Net price: $151.00  (What's this?)
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Package ISBN-10: 013236414X | ISBN-13: 9780132364140
©2008 | Instock
Suggested retail price: $204.67  Buy from myPearsonStore
Net price: $153.50  (What's this?)
This package contains:

Package ISBN-10: 0132364522 | ISBN-13: 9780132364522
©2008 | Instock
Suggested retail price: $208.00  Buy from myPearsonStore
Net price: $156.00  (What's this?)
This package contains: