9780130920713

Calculus

by ;
  • ISBN13:

    9780130920713

  • ISBN10:

    0130920711

  • Edition: 6th
  • Format: Paperback
  • Copyright: 6/5/2002
  • Publisher: Pearson

Note: Supplemental materials are not guaranteed with Rental or Used book purchases.

Purchase Benefits

  • Free Shipping On Orders Over $59!
    Your order must be $59 or more to qualify for free economy shipping. Bulk sales, PO's, Marketplace items, eBooks and apparel do not qualify for this offer.
  • Get Rewarded for Ordering Your Textbooks! Enroll Now
  • We Buy This Book Back!
    In-Store Credit: $19.95
    Check/Direct Deposit: $19.00
List Price: $117.80 Save up to $94.24
  • Rent Book $23.56
    Add to Cart Free Shipping

    TERM
    PRICE
    DUE
    HURRY! ONLY 1 COPY IN STOCK AT THIS PRICE

Supplemental Materials

What is included with this book?

  • The New copy of this book will include any supplemental materials advertised. Please check the title of the book to determine if it should include any access cards, study guides, lab manuals, CDs, etc.
  • The Used and Rental copies of this book are not guaranteed to include any supplemental materials. Typically, only the book itself is included. This is true even if the title states it includes any access cards, study guides, lab manuals, CDs, etc.

Summary

This book combines traditional mainstream calculus with the most flexible approach to new ideas and calculator/computer technology. It contains superb problem sets and a fresh conceptual emphasis flavored by new technological possibilities.Chapter topics cover functions, graphs, and models; prelude to calculus; the derivative; additional applications of the derivative; the integral; applications of the integral; calculus of transcendental functions; techniques of integration; differential equations; polar coordinates and parametric curves; infinite series; vectors, curves, and surfaces in space; partial differentiation; multiple integrals; and vector calculus.For individuals interested in the study of calculus.

Author Biography

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 of research papers in number theory and topology and is the author or co-author of textbooks on calculus, computer programming, differential equations, linear algebra, and liberal arts mathematics.

Table of Contents

About the Authors xi
Preface xiii
Functions, Graphs, and Models
1(52)
Functions and Mathematical Modeling
2(10)
Project: A Square Wading Pool
11(1)
Graphs of Equations and Functions
12(12)
Project: A Broken Tree
23(1)
Polynomials and Algebraic Functions
24(9)
Project: A Leaning Ladder
33(1)
Transcendental Functions
33(12)
Project: A Spherical Asteroid
45(1)
Preview: What Is Calculus?
45(8)
Review: Definitions and Concepts
48(5)
Prelude to Calculus
53(48)
Tangent Lines and Slope Predictors
54(9)
Project: Numerical Slope Investigations
63(1)
The Limit Concept
63(12)
Project: Limits, Slopes, and Logarithms
74(1)
More About Limits
75(13)
Project: Numerical Epsilon-Delta Limit Investigations
87(1)
The Concept of Continuity
88(13)
Review: Definitions, Concepts, Results
99(2)
The Derivative
101(92)
The Derivative and Rates of Change
102(13)
Basic Differentiation Rules
115(11)
The Chain Rule
126(7)
Derivatives of Algebraic Functions
133(9)
Maxima and Minima of Functions on Closed Intervals
142(10)
Project: When Is Your Coffee Cup Stablest?
150(2)
Applied Optimization Problems
152(13)
Derivatives of Trigonometric Functions
165(11)
Successive Approximations and Newton's Method
176(17)
Project: How Deep Does a Floating Ball Sink?
188(1)
Review: Formulas, Concepts, Definitions
189(4)
Additional Applications of the Derivative
193(78)
Implicit Functions and Related Rates
194(10)
Project: Investigating the Folium of Descartes
203(1)
Increments, Differentials, and Linear Approximation
204(8)
Increasing and Decreasing Functions and the Mean Value Theorem
212(10)
The First Derivative Test and Applications
222(10)
Project: Making a Candy Box With Lid
232(1)
Simple Curve Sketching
232(10)
Higher Derivatives and Concavity
242(14)
Curve Sketching and Asymptotes
256(15)
Project: Locating Special Points on Exotic Graphs
267(1)
Review: Definitions, Concepts, Results
267(4)
The Integral
271(94)
Introduction
272(1)
Antiderivatives and Initial Value Problems
272(14)
Elementary Area Computations
286(12)
Riemann Sums and the Integral
298(10)
Project: Calculator/Computer Riemann Sums
307(1)
Evaluation of Integrals
308(10)
The Fundamental Theorem of Calculus
318(10)
Integration by Substitution
328(8)
Areas of Plane Regions
336(10)
Numerical Integration
346(19)
Project: Trapezoidal and Simpson Approximations
359(2)
Review: Definitions, Concepts, Results
361(4)
Applications of the Integral
365(62)
Riemann Sum Approximations
366(10)
Volumes by the Method of Cross Sections
376(11)
Volumes by the Method of Cylindrical Shells
387(9)
Project: Design Your Own Ring!
395(1)
Are Length and Surface Area of Revolution
396(9)
Force and Work
405(11)
Centroids of Plane Regions and Curves
416(11)
Review: Definitions, Concepts, Results
423(4)
Calculus of Transcendental Functions
427(62)
Exponential and Logarithmic Functions
428(13)
Project: Discovering the Number e for Yourself
441(1)
Indeterminate Forms and L'Hopital's Rule
441(8)
More Indeterminate Forms
449(6)
The Natural Logarithm as an Integral
455(12)
Project: Natural Functional Equations
466(1)
Inverse Trigonometric Functions
467(10)
Hyperbolic Functions
477(12)
Review: Formulas, Concepts, Definitions
485(4)
Techniques of Integration
489(56)
Introduction
490(1)
Integral Tables and Simple Substitutions
490(4)
Integration by Parts
494(7)
Trigonometric Integrals
501(7)
Rational Functions and Partial Fractions
508(7)
Trigonometric Substitution
515(6)
Integrals Involving Quadratic Polynomials
521(5)
Improper Integrals
526(19)
Summary
539(6)
Differential Equations
545(78)
Simple Equations and Models
546(12)
Slope Fields and Euler's Method
558(10)
Project: Computer-Assisted Slope Fields and Euler's Method
567(1)
Separable Equations and Applications
568(7)
Linear Equations and Applications
575(12)
Population Models
587(11)
Project: Predator-Prey Equations and Your Own Game Preserve
597(1)
Linear Second-Order Equations
598(9)
Mechanical Vibrations
607(16)
Review: Definitions, Concepts, Results
618(5)
Polar Coordinates and Parametric Curves
623(58)
Analytic Geometry and the Conic Sections
624(5)
Polar Coordinates
629(9)
Area Computations in Polar Coordinates
638(5)
Parametric Curves
643(10)
Project: Trochoid Investigations
652(1)
Integral Computations with Parametric Curves
653(8)
Project: Moon Orbits and Race Tracks
660(1)
Conic Sections and Applications
661(20)
Review: Concepts and Definitions
679(2)
Infinite Series
681(90)
Introduction
682(1)
Infinite Sequences
682(9)
Project: Nested Radicals and Continued Fractions
691(1)
Infinite Series and Convergence
691(11)
Project: Numerical Summation and Geometric Series
701(1)
Taylor Series and Taylor Polynomials
702(13)
Project: Calculating Logarithms on a Deserted Island
715(1)
The Integral Test
715(7)
Project: The Number π, Once and for All
722(1)
Comparison Tests for Positive-Term Series
722(6)
Alternating Series and Absolute Convergence
728(9)
Power Series
737(13)
Power Series Computations
750(8)
Project: Calculating Trigonometric Functions on a Deserted Island
758(1)
Series Solutions of Differential Equations
758(13)
Review: Definitions, Concepts, Results
767(4)
Vectors, Curves, and Surfaces in Space
771(78)
Vectors in the Plane
772(6)
Three-Dimensional Vectors
778(10)
The Cross Product of Vectors
788(8)
Lines and Planes in Space
796(7)
Curves and Motion in Space
803(14)
Project: Does a Pitched Baseball Really Curve?
816(1)
Curvature and Acceleration
817(13)
Cylinders and Quadric Surfaces
830(8)
Cylindrical and Spherical Coordinates
838(11)
Review: Definitions, Concepts, Results
845(4)
Partial Differentiation
849(90)
Introduction
850(1)
Functions of Several Variables
850(10)
Limits and Continuity
860(8)
Partial Derivatives
868(10)
Multivariable Optimization Problems
878(11)
Increments and Linear Approximation
889(7)
The Multivariable Chain Rule
896(11)
Directional Derivatives and the Gradient Vector
907(11)
Lagrange Multipliers and Constrained Optimization
918(9)
Project: Numerical Solution of Lagrange Multiplier Systems
927(1)
Critical Points of Functions of Two Variables
927(12)
Project: Critical Point Investigations
935(1)
Review: Definitions, Concepts, Results
936(3)
Multiple Integrals
939(74)
Double Integrals
940(7)
Project: Midpoint Sums Approximating Double Integrals
947(1)
Double Integrals over More General Regions
947(7)
Area and Volume by Double Integration
954(7)
Double Integrals in Polar Coordinates
961(7)
Applications of Double Integrals
968(11)
Project: Optimal Design of Downhill Race-Car Wheels
978(1)
Triple Integrals
979(9)
Project: Archimedes' Floating Paraboloid
987(1)
Integration in Cylindrical and Spherical Coordinates
988(8)
Surface Area
996(5)
Change of Variables in Multiple Integrals
1001(12)
Review: Definitions, Concepts, Results
1009(4)
Vector Calculus
1013
Vector Fields
1014(5)
Line Integrals
1019(11)
The Fundamental Theorem and Independence of Path
1030(7)
Green's Theorem
1037(10)
Surface Integrals
1047(10)
Project: Surface Integrals and Rocket Nose Cones
1057(1)
The Divergence Theorem
1057(8)
Stokes' Theorem
1065
Review: Definitions, Concepts, Results
1072
APPENDICES 1(44)
A: Real Numbers and Inequalities
1(5)
B: The Coordinate Plane and Straight Lines
6(7)
C: Review of Trigonometry
13(6)
D: Proofs of the Limit Laws
19(4)
E: The Completeness of the Real Number System
23(5)
F: Existence of the Integral
28(5)
G: Approximations and Riemann Sums
33(3)
H: L'Hopital's Rule and Cauchy's Mean Value Theorem
36(2)
I: Proof of Taylor's Formula
38(1)
J: Conic Sections as Sections of a Cone
39(1)
K: Proof of the Linear Approximation Theorem
40(1)
L: Units of Measurements and Conversion Factors
41(1)
M: Formulas from Algebra, Geometry, and Trigonometry
42(2)
N: The Greek Alphabet
44(1)
Answers to Odd-Numbered Problems 45(54)
References For Further Study 99
Index 1(1)
Table of Integrals 1

Excerpts

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 chapters of the fifth edition have been combined in a single more tightly organized one. An entirely new chapter now appears in the table of contents, and most of the remaining chapters have been extensively rewritten. About 125 of the book's over 750 worked examples are new for this edition and the 1825 figures in the text include 225 new computer-generated graphics. About 600 of its over 7000 problems are new, and these are augmented by 320 new conceptual discussion questions that now precede the problem sets. Moreover, 1050 new true/false questions are included in the Study Guides on the new CD-ROM that accompanies this edition. In summary, almost 2000 of these 8400-plus problems and questions are new, and the text discussion and explanations have undergone corresponding alteration and improvement. PRINCIPAL NEW FEATURESThe current revision of the text features More unified treatment oftranscendental functionsin Chapter 7, and A new Chapter 9 ondifferential equationsand applications.The new chapter on differential equations now appears immediately after Chapter 8 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 8) and interesting applications of both first- and second-order equations. Chapter 11 (Infinite Series) now 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. NEW LEARNING RESOURCESConceptual Discussion Questions:The set of problems that concludes each section is now preceded by a briefConcepts: Questions and Discussionset consisting of several open-ended conceptual questions that can be used for either individual study or classroom discussion.The Text CD-ROM:The content of the new CD-ROM that accompanies this text is fully integrated with the textbook material, and is designed specifically for use hand-in-hand with study of the book itself. This CD-ROM features the following resources to support learning and teaching: Interactive True/False Study Guidesthat reinforce and encourage student reading of the text. Ten author-written questions for each section carefully guide students through the section, and students can request individual hints suggesting where in the section to look for needed information. Live Examplesfeature dynamic multimedia and computer algebra presentations--many accompanied by audio explanations--which enhance student intuition and understanding. These interactive examples expand upon many of the textbook's principal examples; students can change input data and conditions and then observe the resulting changes in step-by-step solutions and accompanying graphs and figures.Walkthrough videosdemonstrate how students can interact with these live examples. Homework Startersfor the principal types of computational problems in each textbook section, featuring both interactive presentations similar to the live examples and (Web-linked) voice-narrated videos of pencil-and-paper investigations illustrating typical initial steps in the solution of selected textbook problems. Computing Project Resourcessupport most of the almost three dozen projects that follow key sections in the text. For each such project marked in the text by a CD-ROM icon, more extended discussions illustrating Maple,Mathematica,MATLAB,

Rewards Program

Write a Review