Single Variable Calculus Early Transcendentals (with Tools for Enriching Calculus, Video Skillbuilder CD-ROM, iLrn™ Homework, and Personal Tutor)

by Stewart, James

• ISBN13: 9780534393304
• ISBN10: 0534393306
• Edition: 5th
• Format: Hardcover
• Copyright: 2002-12-16
• Publisher: Brooks Cole

Summary

This edition of James Stewart's best-selling calculus book has been revised with the consistent dedication to excellence that has characterized all his books. Stewart's Calculus is successful throughout the world because he explains the material in a way that makes sense to a wide variety of readers. His explanations make ideas come alive, and his problems challenge, to reveal the beauty of calculus. Stewart's examples stand out because they are not just models for problem solving or a means of demonstrating techniques--they also encourage readers to develp an analytic view of the subject. This edition includes new problems, examples, and projects. This version of Stewart's book introduced exponential and logarithmic functions in the first chapter and their limits and derivatives are found in Chapters 2 and 3.

Table of Contents

Preface	xiii
To the Student	xxiv
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)
Are 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
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
Applied Project Radiation from the Stars	785	(1)
Review	786	(3)
Problems Plus	789
Appendixes	1	(104)
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	(8)
G Complex Numbers	47	(8)
H Answers to Odd-Numbered Exercises	55	(50)
Index	105