Calculus, 7th Edition, Early Transcendentals Combined, 8th Edition

by Howard Anton (Drexel Univ.); Irl Bivens (Davidson College); Stephen Davis (Davidson College)

• ISBN13: 9780471381563
• ISBN10: 047138156X
• Edition: 7th
• Format: Hardcover
• Copyright: 2002-01-01
• Publisher: Wiley

Summary

Designed for the Calculus I-II-III sequence, the seventh edition continues to evolve to fulfill the needs of a changing market by providing flexible solutions to teaching and learning needs of all kinds. The new edition retains the strengths of earlier editions--its trademark clarity of exposition, sound mathematics, excellent exercises and examples, and appropriate level--while incorporating new ideas that have withstood the objective scrutiny of many skilled and thoughtful instructors. For the first time, the Seventh Edition is available in both Late Transcendentals and Early Transcendentals versions.

Table of Contents

Introduction. Calculus: A New Horizon from Ancient Roots	1	(6)
Function	7	(100)
Functions and the Analysis of Graphical Information	8	(8)
Properties of Functions	16	(11)
Graphing Functions on Calculators and Computers; Computer Algebra Systems	27	(11)
New Functions from Old	38	(13)
Lines	51	(12)
Families of Functions	63	(16)
Mathematical Models	79	(9)
Parametric Equations	88	(19)
Horizon Module: lteration and Dynamical Systems	102	(5)
Limits and Continuity	107	(62)
Limits (An Intuitive Approach)	108	(14)
Computing Limits	122	(9)
Computing Limits: End Behavior	131	(7)
Limits (Discussed More Rigorously)	138	(9)
Continuity	147	(12)
Limits and Continuity of Trigonometric Functions	159	(10)
The Derivative	169	(72)
Slopes and Rates of Change	170	(7)
The Derivative	177	(14)
Techniques of Differentiation	191	(9)
Derivatives of Trigonometric Functions	200	(4)
The Chain Rule	204	(7)
Implicit Differentiation	211	(8)
Related Rates	219	(7)
Local Linear Approximation; Differentials	226	(15)
Horizon Module: Robotics	236	(5)
Exponential, Logarithmic, and Inverse Trigonometric Functions	241	(48)
Inverse Functions	242	(10)
Exponential and Logarithmic Functions	252	(10)
Derivatives of Logarithmic and Exponential Functions	262	(6)
Inverse Trigonometric Functions and Their Derivatives	268	(8)
L'Hopital's Rule; Indeterminate Forms	276	(13)
The Derivative in Graphing and Applications	289	(82)
Analysis of Functions I: Increase, Decrease, and Concavity	290	(10)
Analysis of Functions II: Relative Extrema; First and Second Derivative Tests	300	(8)
Analysis of Functions III: Applying Technology and the Tools of Calculus	308	(14)
Rectilinear Motion (Motion Along a Line)	322	(10)
Absolute Maxima and Minima	332	(9)
Applied Maximum and Minimum Problems	341	(13)
Newton's Method	354	(5)
Rolle's Theorem; Mean-Value Theorem	359	(12)
Integration	371	(96)
An Overview of the Area Problem	372	(5)
The Indefinite Integral; Integral Curves and Direction Fields	377	(10)
Integration by Substitution	387	(7)
Sigma Notation; Area as a Limit	394	(12)
The Definite Integral	406	(9)
The Fundamental Theorem of Calculus	415	(12)
Rectilinear Motion Revisited; Average Value	427	(13)
Evaluating Definite Integrals by Substitution	440	(6)
Logarithmic Functions from the Integral Point of View	446	(21)
Horizon Module: Blammo the Human Cannonball	462	(5)
Applications of the Definite Integral in Geometry, Science, and Engineering	467	(56)
Area Between Two Curves	468	(6)
Volumes by Slicing; Disks and Washers	474	(8)
Volumes by Cylindrical Shells	482	(4)
Length of a Plane Curve	486	(5)
Area of a Surface of Revolution	491	(4)
Work	495	(8)
Fluid Pressure and Force	503	(6)
Hyperbolic Functions and Hanging Cables	509	(14)
Principles of Integral Evaluation	523	(72)
An Overview of Integration Methods	524	(2)
Integration by Parts	526	(8)
Trigonometric Integrals	534	(8)
Trigonometric Substitutions	542	(6)
Integrating Rational Functions by Partial Fractions	548	(7)
Using Tables of Integrals and Computer Algebra Systems	555	(10)
Numerical Integration; Simpson's Rule	565	(14)
Improper Integrals	579	(16)
Horizon Module: Railroad Design	590	(5)
Mathematical Modeling with Differential Equations	595	(42)
First-Order Differential Equations and Applications	596	(12)
Direction Fields; Euler's Method	608	(7)
Modeling with First-Order Differential Equations	615	(10)
Second-Order Linear Homogeneous Differential Equations; The Vibrating Spring	625	(12)
Infinite Series	637	(86)
Maclaurin and Taylor Polynomial Approximations	638	(9)
Sequences	647	(11)
Monotone Sequences	658	(6)
Infinite Series	664	(8)
Convergence Tests	672	(7)
The Comparison, Ratio, and Root Tests	679	(6)
Alternating Series; Conditional Convergence	685	(8)
Maclaurin and Taylor Series; Power Series	693	(8)
Convergence of Taylor Series; Computational Methods	701	(9)
Differentiating and Integrating Power Series; Modeling with Taylor Series	710	(13)
Analytic Geometry in Calculus	723	(66)
Polar Coordinates	724	(12)
Tangent Lines and Arc Length for Parametric and Polar Curves	736	(8)
Area in Polar Coordinates	744	(5)
Conic Sections in Calculus	749	(17)
Rotation of Axes; Second-Degree Equations	766	(6)
Conic Sections in Polar Coordinates	772	(17)
Horizon Module: Comet Collision	785	(4)
Three-Dimensional Space; Vectors	789	(70)
Rectangular Coordinates in 3-Space; Spheres; Cylindrical Surfaces	790	(5)
Vectors	795	(11)
Dot Product; Projections	806	(9)
Cross Product	815	(10)
Parametric Equations of Lines	825	(6)
Planes in 3-Space	831	(7)
Quadric Surfaces	838	(11)
Cylindrical and Spherical Coordinates	849	(10)
Vector-Valued Functions	859	(62)
Introduction to Vector-Valued Functions	860	(6)
Calculus of Vector-Valued Functions	866	(9)
Change of Parameter; Arc Length	875	(10)
Unit Tangent, Normal, and Binormal Vectors	885	(5)
Curvature	890	(8)
Motion Along a Curve	898	(13)
Kepler's Laws of Planetary Motion	911	(10)
Partial Derivatives	921	(92)
Functions of Two or More Variables	922	(10)
Limits and Continuity	932	(9)
Partial Derivatives	941	(12)
Differentiability, Local Linearity, and Differentials	953	(10)
The Chain Rule	963	(11)
Directional Derivatives and Gradients	974	(11)
Tangent Planes and Normal Vectors	985	(6)
Maxima and Minima of Functions of Two Variables	991	(12)
Lagrange Multipliers	1003	(10)
Multiple Integrals	1013	(78)
Double Integrals	1014	(7)
Double Integrals over Nonrectangular Regions	1021	(8)
Double Integrals in Polar Coordinates	1029	(7)
Parametric Surfaces; Surface Area	1036	(12)
Triple Integrals	1048	(8)
Centroid, Center of Gravity, Theorem of Pappus	1056	(9)
Triple Integrals in Cylindrical and Spherical Coordinates	1065	(10)
Change of Variables in Multiple Integrals; Jacobians	1075	(16)
Topics in Vector Calculus	1091
Vector Fields	1092
Line Integrals	1100
Independence of Path; Conservative Vector Fields	1114
Green's Theorem	1124
Surface Integrals	1130
Applications of Surface Integrals; Flux	1137
The Divergence Theorem	1145
Stokes' Theorem	1154
Horizon Module: Hurricane Modeling	1162
Appendix A. Real Numbers, Intervals, and Inequalities	A1
Appendix B. Absolute Value	A11
Appendix C. Coordinate Planes and Lines	A16
Appendix D. Distance, Circles, and Quadratic Equations	A28
Appendix E. Trigonometry Review	A37
Appendix F. Solving Polynomial Equations	A50
Appendix G. Selected Proofs	A57
Answers	A63
Photo Credits	C1
Index	I-1