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Calculus

by
Edition:
5th
ISBN13:

9780534393397

ISBN10:
053439339X
Format:
Hardcover
Pub. Date:
12/24/2002
Publisher(s):
Brooks Cole
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Summary

Stewart's CALCULUS, 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. In this Fifth Edition, he 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 have the best materials available. The number of pages in the book, however, remains unchanged from the 4th edition. Further support for students and instructors is now available through a vast array of supplementary material.

Table of Contents

Preface xiv
To the Student xxvi
A Preview of Calculus 2(8)
Functions and Models
10(54)
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(16)
Review
55(3)
Principles of Problem Solving
58(6)
Limits and Rates of Change
64(62)
The Tangent and Velocity Problems
65(5)
The Limit of a Function
70(12)
Calculating Limits Using the Limit Laws
82(10)
The Precise Definition of a Limit
92(10)
Continuity
102(10)
Tangents, Velocities, and Other Rates of Change
112(14)
Review
121(3)
Problems Plus
124(2)
Derivatives
126(96)
Derivatives
127(7)
Writing Project Early Methods for Finding Tangents
133(1)
The Derivative as a Function
134(11)
Differentiation Formulas
145(12)
Rates of Change in the Natural and Social Sciences
157(12)
Derivatives of Trigonometric Functions
169(6)
The Chain Rule
175(9)
Implicit Differentiation
184(6)
Higher Derivatives
190(8)
Applied Project Where Should a Pilot Start Descent?
197(1)
Applied Project Building a Better Roller Coaster
198(1)
Related Rates
198(7)
Linear Approximations and Differentials
205(17)
Laboratory Project Taylor Polynomials
212(1)
Review
213(5)
Problems Plus
218(4)
Applications of Differentiation
222(92)
Maximum and Minimum Values
223(11)
Applied Project The Calculus of Rainbows
232(2)
The Mean Value Theorem
234(6)
How Derivatives Affect the Shape of a Graph
240(9)
Limits at Infinity; Horizontal Asymptotes
249(14)
Summary of Curve Sketching
263(8)
Graphing with Calculus and Calculators
271(7)
Optimization Problems
278(11)
Applied Project The Shape of a Can
288(1)
Applications to Business and Economics
289(5)
Newton's Method
294(6)
Antiderivatives
300(14)
Review
308(3)
Problems Plus
311(3)
Integrals
314(60)
Areas and Distances
315(11)
The Definite Integral
326(14)
Discovery Project Area Functions
339(1)
The Fundamental Theorem of Calculus
340(10)
Indefinite Integrals and the Net Change Theorem
350(10)
Writing Project Newton, Leibniz, and the Invention of Calculus
359(1)
The Substitution Rule
360(14)
Review
368(4)
Problems Plus
372(2)
Applications of Integration
374(38)
Areas between Curves
375(7)
Volumes
382(11)
Volumes by Cylindrical Shells
393(5)
Work
398(4)
Average Value of a Function
402(10)
Review
406(2)
Problems Plus
408(4)
Inverse Functions: Exponential, Logarithmic, and Inverse Trigonometric Functions
412(98)
Inverse Functions
413(8)
Instructors may cover either Sections 7.2--7.4 or Sections 7.2*--7.4*. See the Preface
Exponential Functions and Their Derivatives
421(13)
Logarithmic Functions
434(7)
Derivatives of Logarithmic Functions
441(10)
The Natural Logarithmic Function
451(9)
The Natural Exponential Function
460(7)
General Logarithmic and Exponential Functions
467(10)
Inverse Trigonometric Functions
477(9)
Applied Project Where to Sit at the Movies
485(1)
Hyperbolic Functions
486(7)
Indeterminate Forms and L'Hospital's Rule
493(17)
Writing Project The Origins of L'Hospital's Rule
504(1)
Review
504(4)
Problems Plus
508(2)
Techniques of Integration
510(72)
Integration by Parts
511(7)
Trigonometric Integrals
518(7)
Trigonometric Substitution
525(7)
Integration of Rational Functions by Partial Fractions
532(9)
Strategy for Integration
541(6)
Integration Using Tables and Computer Algebra Systems
547(7)
Discovery Project Patterns in Integrals
553(1)
Approximate Integration
554(12)
Improper Integrals
566(16)
Review
576(3)
Problems Plus
579(3)
Further Applications of Integration
582(40)
Arc Length
583(7)
Discovery Project Arc Length Contest
590(1)
Area of a Surface of Revolution
590(7)
Discovery Project Rotating on a Slant
596(1)
Applications to Physics and Engineering
597(10)
Applications to Economics and Biology
607(4)
Probability
611(11)
Review
618(2)
Problems Plus
620(2)
Differential Equations
622(64)
Modeling with Differential Equations
623(5)
Direction Fields and Euler's Method
628(9)
Separable Equations
637(10)
Applied Project How Fast Does a Tank Drain?
645(1)
Applied Project Which Is Faster, Going Up or Coming Down?
646(1)
Exponential Growth and Decay
647(12)
Applied Project Calculus and Baseball
658(1)
The Logistic Equation
659(9)
Linear Equations
668(6)
Predator-Prey Systems
674(12)
Review
680(4)
Problems Plus
684(2)
Parametric Equations and Polar Coordinates
686(50)
Curves Defined by Parametric Equations
687(9)
Laboratory Project Running Circles around Circles
695(1)
Calculus with Parametric Curves
696(9)
Laboratory Project Bezier Curves
705(1)
Polar Coordinates
705(10)
Areas and Lengths in Polar Coordinates
715(5)
Conic Sections
720(8)
Conic Sections in Polar Coordinates
728(8)
Review
732(3)
Problems Plus
735(1)
Infinite Sequences and Series
736(92)
Sequences
737(12)
Laboratory Project Logistic Sequences
749(1)
Series
749(10)
The Integral Test and Estimates of Sums
759(7)
The Comparison Tests
766(5)
Alternating Series
771(5)
Absolute Convergence and the Ratio and Root Tests
776(7)
Strategy for Testing Series
783(2)
Power Series
785(5)
Representations of Functions as Power Series
790(6)
Taylor and Maclaurin Series
796(12)
Laboratory Project An Elusive Limit
808(1)
The Binomial Series
808(4)
Writing Project How Newton Discovered the Binomial Series
812(1)
Applications of Taylor Polynomials
812(16)
Applied Project Radiation from the Stars
821(1)
Review
822(3)
Problems Plus
825(3)
Vectors and the Geometry of Space
828(56)
Three-Dimensional Coordinate Systems
829(5)
Vectors
834(9)
The Dot Product
843(7)
The Cross Product
850(8)
Discovery Project The Geometry of a Tetrahedron
858(1)
Equations of Lines and Planes
858(10)
Laboratory Project Putting 3D in Perspective
868(1)
Cylinders and Quadric Surfaces
868(7)
Cylindrical and Spherical Coordinates
875(9)
Laboratory Project Families of Surfaces
880(1)
Review
880(3)
Problems Plus
883(1)
Vector Functions
884(38)
Vector Functions and Space Curves
885(7)
Derivatives and Integrals of Vector Functions
892(6)
Arc Length and Curvature
898(8)
Motion in Space: Velocity and Acceleration
906(16)
Applied Project Kepler's Laws
916(1)
Review
917(3)
Problems Plus
920(2)
Partial Derivatives
922(94)
Functions of Several Variables
923(15)
Limits and Continuity
938(7)
Partial Derivatives
945(14)
Tangent Planes and Linear Approximations
959(8)
The Chain Rule
967(9)
Directional Derivatives and the Gradient Vector
976(13)
Maximum and Minimum Values
989(12)
Applied Project Designing a Dumpster
999(1)
Discovery Project Quadratic Approximations and Critical Points
1000(1)
Lagrange Multipliers
1001(15)
Applied Project Rocket Science
1008(1)
Applied Project Hydro-Turbine Optimization
1009(1)
Review
1010(4)
Problems Plus
1014(2)
Multiple Integrals
1016(74)
Double Integrals over Rectangles
1017(8)
Iterated Integrals
1025(6)
Double Integrals over General Regions
1031(8)
Double Integrals in Polar Coordinates
1039(6)
Applications of Double Integrals
1045(10)
Surface Area
1055(4)
Triple Integrals
1059(10)
Discovery Project Volumes of Hyperspheres
1068(1)
Triple Integrals in Cylindrical and Spherical Coordinates
1069(8)
Applied Project Roller Derby
1075(1)
Discovery Project The Intersection of Three Cylinders
1076(1)
Change of Variables in Multiple Integrals
1077(13)
Review
1085(3)
Problems Plus
1088(2)
Vector Calculus
1090(86)
Vector Fields
1091(7)
Line Integrals
1098(12)
The Fundamental Theorem for Line Integrals
1110(9)
Green's Theorem
1119(7)
Curl and Divergence
1126(8)
Parametric Surfaces and Their Areas
1134(11)
Surface Integrals
1145(12)
Stokes' Theorem
1157(6)
Writing Project Three Men and Two Theorems
1162(1)
The Divergence Theorem
1163(7)
Summary
1170(6)
Review
1171(3)
Problems Plus
1174(2)
Second-Order Differential Equations
1176
Second-Order Linear Equations
1177(6)
Nonhomogeneous Linear Equations
1183(8)
Applications of Second-Order Differential Equations
1191(8)
Series Solutions
1199
Review
1203
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(9)
G Complex Numbers
48(8)
H Answers to Odd-Numbered Exercises
56(69)
Index 125


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