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Calculus : Early Transcendentals,9780534393212
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Calculus : Early Transcendentals

by
Edition:
5th
ISBN13:

9780534393212

ISBN10:
0534393217
Format:
Paperback
Pub. Date:
12/24/2002
Publisher(s):
Brooks Cole
List Price: $180.95

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Summary

Stewart's CALCULUS: EARLY TRANSCENDENTALS, Fifth Edition has the mathematical precision, accuracy, clarity of exposition and outstanding examples and problem sets that have characterized the first four editions. Stewart retains the focus on problem solving and the pedagogical system that has made the book a favorite of students and instructors in a wide variety of colleges and universities throughout the world. The structure of CALCULUS: EARLY TRANSCENDENTALS, Fifth Edition, remains largely unchanged, the sole exception being that the review of inverse trigonometric functions has been moved from an appendix to Section 1.6. Stewart has made hundreds of small improvements: new examples, additional steps in existing examples, updating of data in existing examples and exercises, new phrases and margin notes to clarify the exposition, references to other sources and web sites, redrawn art, and references to the TEC CD (Tools for Enriching Calculus). These refinements ensure that students and instructors using this text are using the best resource available. The number of pages in the book, however, remains unchanged from the 4th edition. This edition is complemented with and expanded array of supplementary material for both students and instructors. These best-selling texts differ from CALCULUS, Fifth Edition in that the exponential and logarithmic functions are covered earlier. In the Fifth Edition of CALCULUS, EARLY TRANSCENDENTALS these functions are introduced in the first chapter and their limits and derivatives are found in Chapters 2 and 3 at the same time as polynomials and other elementary functions.

Table of Contents

Preface xiv
To the Student xxvi
A Preview of Calculus 2(8)
Functions and Models
10(76)
Four Ways to Represent a Function
11(14)
Mathematical Models: A Catalog of Essential Functions
25(13)
New Functions from Old Functions
38(10)
Graphing Calculators and Computers
48(7)
Exponential Functions
55(8)
Inverse Functions and Logarithms
63(23)
Review
77(3)
Principles of Problem Solving
80(6)
Limits and Derivatives
86(96)
The Tangent and Velocity Problems
87(5)
The Limit of a Function
92(12)
Calculating Limits Using the Limit Laws
104(10)
The Precise Definition of a Limit
114(10)
Continuity
124(11)
Limits at Infinity; Horizontal Asymptotes
135(14)
Tangents, Velocities, and Other Rates of Change
149(9)
Derivatives
158(7)
Writing Project Early Methods for Finding Tangents
164(1)
The Derivative as a Function
165(17)
Review
176(4)
Problems Plus
180(2)
Differentiation Rules
182(96)
Derivatives of Polynomials and Exponential Functions
183(9)
The Product and Quotient Rules
192(7)
Rates of Change in the Natural and Social Sciences
199(12)
Derivatives of Trigonometric Functions
211(6)
The Chain Rule
217(10)
Implicit Differentiation
227(9)
Higher Derivatives
236(8)
Applied Project Where Should a Pilot Start Descent?
243(1)
Applied Project Building a Better Roller Coaster
243(1)
Derivatives of Logarithmic Functions
244(6)
Hyperbolic Functions
250(6)
Related Rates
256(6)
Linear Approximations and Differentials
262(16)
Laboratory Project Taylor Polynomials
269(1)
Review
270(4)
Problems Plus
274(4)
Applications of Differentiation
278(90)
Maximum and Minimum Values
279(11)
Applied Project The Calculus of Rainbows
288(2)
The Mean Value Theorem
290(6)
How Derivatives Affect the Shape of a Graph
296(11)
Indeterminate Forms and L'Hospital's Rule
307(9)
Writing Project The Origins of L'Hospital's Rule
315(1)
Summary of Curve Sketching
316(8)
Graphing with Calculus and Calculators
324(7)
Optimization Problems
331(11)
Applied Project The Shape of a Can
341(1)
Applications to Business and Economics
342(5)
Newton's Method
347(6)
Antiderivatives
353(15)
Review
361(4)
Problems Plus
365(3)
Integrals
368(68)
Areas and Distances
369(11)
The Definite Integral
380(14)
Discovery Project Area Functions
393(1)
The Fundamental Theorem of Calculus
394(11)
Indefinite Integrals and the Net Change Theorem
405(9)
Writing Project Newton, Leibniz, and the Invention of Calculus
413(1)
The Substitution Rule
414(8)
The Logarithm Defined as an Integral
422(14)
Review
430(4)
Problems Plus
434(2)
Applications of Integration
436(38)
Areas between Curves
437(7)
Volumes
444(11)
Volumes by Cylindrical Shells
455(5)
Work
460(4)
Average Value of a Function
464(10)
Applied Project Where to Sit at the Movies
468(1)
Review
468(2)
Problems Plus
470(4)
Techniques of Integration
474(72)
Integration by Parts
475(7)
Trigonometric Integrals
482(7)
Trigonometric Substitution
489(7)
Integration of Rational Functions by Partial Fractions
496(9)
Strategy for Integration
505(6)
Integration Using Tables and Computer Algebra Systems
511(7)
Discovery Project Patterns in Integrals
517(1)
Approximate Integration
518(12)
Improper Integrals
530(16)
Review
540(3)
Problems Plus
543(3)
Further Applications of Integration
546(40)
Arc Length
547(7)
Discovery Project Arc Length Contest
554(1)
Area of a Surface of Revolution
554(7)
Discovery Project Rotating on a Slant
560(1)
Applications to Physics and Engineering
561(10)
Applications to Economics and Biology
571(4)
Probability
575(11)
Review
582(2)
Problems Plus
584(2)
Differential Equations
586(64)
Modeling with Differential Equations
587(5)
Direction Fields and Euler's Method
592(9)
Separable Equations
601(10)
Applied Project How Fast Does a Tank Drain?
609(1)
Applied Project Which Is Faster, Going Up or Coming Down?
610(1)
Exponential Growth and Decay
611(12)
Applied Project Calculus and Baseball
622(1)
The Logistic Equation
623(9)
Linear Equations
632(6)
Predator-Prey Systems
638(12)
Review
644(4)
Problems Plus
648(2)
Parametric Equations and Polar Coordinates
650(50)
Curves Defined by Parametric Equations
651(9)
Laboratory Project Running Circles around Circles
659(1)
Calculus with Parametric Curves
660(9)
Laboratory Project Bezier Curves
669(1)
Polar Coordinates
669(10)
Areas and Lengths in Polar Coordinates
679(5)
Conic Sections
684(8)
Conic Sections in Polar Coordinates
692(8)
Review
696(3)
Problems Plus
699(1)
Infinite Sequences and Series
700(92)
Sequences
701(12)
Laboratory Project Logistic Sequences
713(1)
Series
713(10)
The Integral Test and Estimates of Sums
723(7)
The Comparison Tests
730(5)
Alternating Series
735(5)
Absolute Convergence and the Ratio and Root Tests
740(7)
Strategy for Testing Series
747(2)
Power Series
749(5)
Representations of Functions as Power Series
754(6)
Taylor and Maclaurin Series
760(12)
Laboratory Project An Elusive Limit
772(1)
The Binomial Series
772(4)
Writing Project How Newton Discovered the Binomial Series
776(1)
Applications of Taylor Polynomials
776(16)
Applied Project Radiation from the Stars
785(1)
Review
786(3)
Problems Plus
789(3)
Vectors and the Geometry of Space
792(56)
Three-Dimensional Coordinate Systems
793(5)
Vectors
798(9)
The Dot Product
807(7)
The Cross Product
814(8)
Discovery Project The Geometry of a Tetrahedron
822(1)
Equations of Lines and Planes
822(10)
Laboratory Project Putting 3D in Perspective
832(1)
Cylinders and Quadric Surfaces
832(7)
Cylindrical and Spherical Coordinates
839(9)
Laboratory Project Families of Surfaces
844(1)
Review
844(3)
Problems Plus
847(1)
Vector Functions
848(38)
Vector Functions and Space Curves
849(7)
Derivatives and Integrals of Vector Functions
856(6)
Arc Length and Curvature
862(8)
Motion in Space: Velocity and Acceleration
870(16)
Applied Project Kepler's Laws
880(1)
Review
881(3)
Problems Plus
884(2)
Partial Derivatives
886(94)
Functions of Several Variables
887(15)
Limits and Continuity
902(7)
Partial Derivatives
909(14)
Tangent Planes and Linear Approximations
923(8)
The Chain Rule
931(9)
Directional Derivatives and the Gradient Vector
940(13)
Maximum and Minimum Values
953(12)
Applied Project Designing a Dumpster
963(1)
Discovery Project Quadratic Approximations and Critical Points
964(1)
Lagrange Multipliers
965(15)
Applied Project Rocket Science
972(1)
Applied Project Hydro-Turbine Optimization
973(1)
Review
974(4)
Problems Plus
978(2)
Multiple Integrals
980(74)
Double Integrals over Rectangles
981(8)
Iterated Integrals
989(6)
Double Integrals over General Regions
995(8)
Double Integrals in Polar Coordinates
1003(6)
Applications of Double Integrals
1009(10)
Surface Area
1019(4)
Triple Integrals
1023(10)
Discovery Project Volumes of Hyperspheres
1032(1)
Triple Integrals in Cylindrical and Spherical Coordinates
1033(8)
Applied Project Roller Derby
1039(1)
Discovery Project The Intersection of Three Cylinders
1040(1)
Change of Variables in Multiple Integrals
1041(13)
Review
1049(3)
Problems Plus
1052(2)
Vector Calculus
1054(86)
Vector Fields
1055(7)
Line Integrals
1062(12)
The Fundamental Theorem for Line Integrals
1074(9)
Green's Theorem
1083(7)
Curl and Divergence
1090(8)
Parametric Surfaces and Their Areas
1098(11)
Surface Integrals
1109(12)
Stokes' Theorem
1121(6)
Writing Project Three Men and Two Theorems
1126(1)
The Divergence Theorem
1127(7)
Summary
1134(6)
Review
1135(3)
Problems Plus
1138(2)
Second-Order Differential Equations
1140
Second-Order Linear Equations
1141(6)
Nonhomogeneous Linear Equations
1147(8)
Applications of Second-Order Differential Equations
1155(8)
Series Solutions
1163
Review
1167
Appendixes 1(124)
A Numbers, Inequalities, and Absolute Values
2(8)
B Coordinate Geometry and Lines
10(6)
C Graphs of Second-Degree Equations
16(8)
D Trigonometry
24(10)
E Sigma Notation
34(5)
F Proofs of Theorems
39(10)
G Complex Numbers
49(8)
H Answers to Odd-Numbered Exercises
57(68)
Index 125


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