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

by Stewart, James

• ISBN13: 9780534393212
• ISBN10: 0534393217
• Edition: 5th
• Format: Hardcover
• Copyright: 2002-12-24
• Publisher: Brooks Cole

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