Calculus: Early Transcendentals Combined, 8th Edition

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

• ISBN13: 9780471472445
• ISBN10: 0471472441
• Edition: 8th
• Format: Hardcover
• Copyright: 2005-02-01
• Publisher: WILEY

Summary

Designed for the freshman/sophomore Calculus I-II-III sequence, the eighth 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 such as Anton's trademark clarity of exposition, sound mathematics, excellent exercises and examples, and appropriate level. Anton also incorporates new ideas that have withstood the objective scrutiny of many skilled and thoughtful instructors and their students.

Table of Contents

Functions	1	(100)
Functions	1	(15)
Graphing Functions Using Calculators and Computer Algebra Systems	16	(11)
New Functions from Old	27	(13)
Families of Functions	40	(11)
Inverse Functions; Inverse Trigonometric Functions	51	(14)
Exponential and Logarithmic Functions	65	(11)
Mathematical Models	76	(10)
Parametric Equations	86	(15)
Limits and Continuity	101	(64)
Limits (An Intuitive Approach)	101	(12)
Computing Limits	113	(9)
Limits at Infinity; End Behavior of a Function	122	(12)
Limits (Discussed More Rigorously)	134	(10)
Continuity	144	(11)
Continuity of Trigonometric and Inverse Functions	155	(10)
The Derivative	165	(70)
Tangent Lines, Velocity, and General Rates of Change	165	(13)
The Derivative Function	178	(12)
Techniques of Differentiation	190	(8)
The Product and Quotient Rules	198	(6)
Derivatives of Trigonometric Functions	204	(5)
The Chain Rule	209	(8)
Related Rates	217	(7)
Local Linear Approximation; Differentials	224	(11)
Exponential, Logarithmic, and Inverse Trigonometric Functions	235	(32)
Implicit Differentiation	235	(8)
Derivatives of Logarithmic Functions	243	(5)
Derivatives of Exponential and Inverse Trigonometric Functions	248	(8)
L'Hopital's Rule; Indeterminate Forms	256	(11)
The Derivative in Graphing and Applications	267	(82)
Analysis of Functions I: Increase, Decrease, and Concavity	267	(12)
Analysis of Functions II: Relative Extrema; Graphing Polynomials	279	(10)
More on Curve Sketching: Rational Functions; Curves with Cusps and Vertical Tangent Lines; Using Technology	289	(12)
Absolute Maxima and Minima	301	(8)
Applied Maximum and Minimum Problems	309	(14)
Newton's Method	323	(6)
Rolle's Theorem; Mean-Value Theorem	329	(7)
Rectilinear Motion	336	(13)
Integration	349	(93)
An Overview of the Area Problem	349	(6)
The Indefinite Integral	355	(10)
Integration by Substitution	365	(8)
The Definition of Area as a Limit; Sigma Notation	373	(13)
The Definite Integral	386	(10)
The Fundamental Theorem of Calculus	396	(14)
Rectilinear Motion Revisited Using Integration	410	(9)
Evaluating Definite Integrals by Substitution	419	(6)
Logarithmic Functions from the Integral Point of View	425	(17)
Applications of the Definite Integral in Geometry, Science, and Engineering	442	(68)
Area Between Two Curves	442	(8)
Volumes by Slicing; Disks and Washers	450	(9)
Volumes by Cylindrical Shells	459	(6)
Length of a Plane Curve	465	(6)
Area of a Surface of Revolution	471	(5)
Average Value of a Function and its Applications	476	(5)
Work	481	(9)
Fluid Pressure and Force	490	(6)
Hyperbolic Functions and Hanging Cables	496	(14)
Principles of Integral Evaluation	510	(72)
An Overview of Integration Methods	510	(3)
Integration by Parts	513	(9)
Trigonometric Integrals	522	(8)
Trigonometric Substitutions	530	(7)
Integrating Rational Functions by Partial Fractions	537	(8)
Using Computer Algebra Systems and Tables of Integrals	545	(11)
Numerical Integration; Simpson's Rule	556	(13)
Improper Integrals	569	(13)
Mathematical Modeling with Differential Equations	582	(42)
First-Order Differential Equations and Applications	582	(14)
Slope Fields; Euler's Method	596	(7)
Modeling with First-Order Differential Equations	603	(9)
Second-Order Linear Homogeneous Differential Equations; The Vibrating Spring	612	(12)
Infinite Series	624	(93)
Sequences	624	(11)
Monotone Sequences	635	(8)
Infinite Series	643	(9)
Convergence Tests	652	(7)
The Comparison, Ratio, and Root Tests	659	(7)
Alternating Series; Conditional Convergence	666	(9)
Maclaurin and Taylor Polynomials	675	(10)
Maclaurin and Taylor Series; Power Series	685	(9)
Convergence of Taylor Series	694	(10)
Differentiating and Integrating Power Series; Modeling with Taylor Series	704	(13)
Analytic Geometry in Calculus	717	(69)
Polar Coordinates	717	(14)
Tangent Lines and Arc Length for Parametric and Polar Curves	731	(9)
Area in Polar Coordinates	740	(6)
Conic Sections in Calculus	746	(19)
Rotation of Axes; Second-Degree Equations	765	(6)
Conic Sections in Polar Coordinates	771	(15)
Horizon Module: Comet Collision	783	(3)
Three-Dimensional Space; Vectors	786	(73)
Rectangular Coordinates in 3-Space; Spheres; Cylindrical Surfaces	786	(6)
Vectors	792	(12)
Dot Product; Projections	804	(9)
Cross Product	813	(11)
Parametric Equations of Lines	824	(7)
Planes in 3-Space	831	(8)
Quadric Surfaces	839	(11)
Cylindrical and Spherical Coordinates	850	(9)
Vector-Valued Functions	859	(65)
Introduction to Vector-Valued Functions	859	(6)
Calculus of Vector-Valued Functions	865	(11)
Change of Parameter; Arc Length	876	(10)
Unit Tangent, Normal, and Binormal Vectors	886	(6)
Curvature	892	(9)
Motion Along a Curve	901	(13)
Kepler's Laws of Planetary Motion	914	(10)
Partial Derivatives	924	(94)
Functions of Two or More Variables	924	(12)
Limits and Continuity	936	(9)
Partial Derivatives	945	(14)
Differentiability, Differentials, and Local Linearity	959	(9)
The Chain Rule	968	(10)
Directional Derivatives and Gradients	978	(11)
Tangent Planes and Normal Vectors	989	(7)
Maxima and Minima of Functions of Two Variables	996	(12)
Lagrange Multipliers	1008	(10)
Multiple Integrals	1018	(84)
Double Integrals	1018	(8)
Double Integrals over Nonrectangular Regions	1026	(9)
Double Integrals in Polar Coordinates	1035	(8)
Parametric Surfaces; Surface Area	1043	(13)
Triple Integrals	1056	(9)
Centroid, Center of Gravity, Theorem of Pappus	1065	(11)
Triple Integrals in Cylindrical and Spherical Coordinates	1076	(11)
Change of Variables in Multiple Integrals; Jacobians	1087	(15)
Topics in Vector Calculus	1102
Vector Fields	1102	(10)
Line Integrals	1112	(17)
Independence of Path; Conservative Vector Fields	1129	(10)
Green's Theorem	1139	(8)
Surface Integrals	1147	(8)
Applications of Surface Integrals; Flux	1155	(9)
The Divergence Theorem	1164	(9)
Stokes' Theorem	1173
Horizon Module: Hurricane Modeling	1183
appendix a Trigonometry Review	1	(14)
appendix b Solving Polynomial Equations	15	(7)
appendix c Selected Proofs	22	(11)
Answers	33
Photo Credits	1	(1)
Index	1