Calculus: A New Horizon

by Anton, Howard

• ISBN13: 9780471153061
• ISBN10: 0471153060
• Edition: 6th
• Format: Hardcover
• Copyright: 1998-06-01
• Publisher: John Wiley & Sons Inc

Summary

The new Sixth Edition of Anton2s Calculus is a contemporary text that incorporates the best features of calculus reform, yet preserves the main structure of an established, traditional calculus text. This book is intended for those who want to move slowly into the reform movement. The new edition retains its accessible writing style and a high standard of mathematical precision.

Table of Contents

Introduction. Calculus: A New Horizon from Ancient Roots	1	(15)
Functions	15	(96)
Functions and the Analysis of Graphical Information	16	(8)
Properties of Functions	24	(11)
Graphing Functions on Calculators and Computers; Computer Algebra Systems	35	(12)
New Functions from Old	47	(14)
Mathematical Models; Linear Models	61	(14)
Families of Functions	75	(18)
Parametric Equations	93	(13)
Horizon Module: Iteration and Dynamical Systems	106	(5)
Limits and Continuity	111	(58)
Limits (An Intuitive Introduction)	112	(15)
Limits (Computational Techniques)	127	(11)
Limits (Discussed More Rigorously)	138	(10)
Continuity	148	(11)
Limits and Continuity of Trigonometric Functions	159	(10)
The Derivative	169	(56)
Tangent Lines and Rates of Change	170	(7)
The Derivative	177	(12)
Techniques of Differentiation	189	(11)
Derivatives of Trigonometric Functions	200	(4)
The Chain Rule	204	(6)
Local Linear Approximation; Differentials	210	(11)
Horizon Module: Robotics	221	(4)
Logarithmic and Exponential Functions	225	(64)
Inverse Functions	226	(9)
Logarithmic and Exponential Functions	235	(11)
Implicit Differentiation	246	(9)
Derivatives of Logarithmic and Exponential Functions	255	(6)
Derivatives of Inverse Trigonometric Functions	261	(9)
Related Rates	270	(7)
L'Hospital's Rule; Indeterminate Forms	277	(12)
Analysis of Functions and Their Graphs	289	(40)
Analysis of Functions I: Increase, Decrease, and Concavity	290	(9)
Analysis of Functions II: Relative Extrema; First and Second Derivative Tests	299	(7)
Analysis of Functions III: Applying Technology and the Tools of Calculus	306	(23)
Horizon Module: Functions from Data	324	(5)
Applications of the Derivative	329	(48)
Absolute Maxima and Minima	330	(9)
Applied Maximum and Minimum Problems	339	(13)
Rectilinear Motion (Motion Along a Line)	352	(11)
Newton's Method	363	(5)
Rolle's Theorem; Mean-Value Theorem	368	(9)
Integration	377	(84)
An Overview of the Area Problem	378	(4)
The Indefinite Integral; Integral Curves and Direction Fields	382	(9)
Integration by Substitution	391	(6)
Sigma Notation	397	(7)
The Definite Integral	404	(12)
The Fundamental Theorem of Calculus	416	(11)
Rectilinear Motion Revisited; Average Value	427	(14)
Evaluating Definite Integrals by Substitution	441	(5)
Logarithmic Functions from the Integral Point of View	446	(15)
Horizon Module: Blammo the Human Cannonball	457	(4)
Application of the Definite Integral in Geometry, Science, and Engineering	461	(52)
Area Between Two Curves	462	(6)
Volumes by Slicing; Disks and Washers	468	(7)
Volumes by Cylindrical Shells	475	(5)
Length of a Plane Curve	480	(5)
Area of a Surface of Revolution	485	(4)
Work	489	(7)
Fluid Pressure and Force	496	(4)
Hyperbolic Functions and Hanging Cables	500	(13)
Principles of Integral Evaluation	513	(66)
An Overview of Integration Methods	514	(2)
Integration by Parts	516	(6)
Trigonometric Integrals	522	(8)
Trigonometric Substitutions	530	(6)
Integrating Rational Functions by Partial Fractions	536	(7)
Using Tables of Integrals and Computer Algebra Systems	543
Numerical Integration; Simpson's Rule	533	(31)
Improper Integrals	564	(15)
Horizon Module: Railroad Design	576	(3)
Mathematical Modeling with Differential Equations	579	(36)
First-Order Differential Equations and Applications	580	(12)
Direction Fields; Euler's Method	592	(6)
Modeling with Differential Equations	598	(17)
Infinite Series	615	(84)
Sequences	616	(10)
Monotone Sequences	626	(6)
Infinite Series	632	(8)
Convergence Tests	640	(7)
Taylor and Maclaurin Series	647	(9)
The Comparison, Ratio, and Root Tests	656	(6)
Alternating Series; Conditional Convergence	662	(8)
Power Series	670	(6)
Convergence of Taylor Series; Computational Methods	676	(10)
Differentiating and Integrating Power Series; Modeling with Taylor Series	686	(13)
Analytic Geometry in Calculus	699	(60)
Polar Coordinates	700	(13)
Tangent Lines and Arc Length for Parametric and Polar Curves	713	(7)
Area in Polar Coordinates	720	(6)
Conic Sections in Calculus	726	(17)
Conic Sections in Polar Coordinates	743	(16)
Horizon Module: Comet Collision	755	(4)
Three-Dimensional Space; Vectors	759	(70)
Rectangular Coordinates in 3-Space; Spheres; Cylindrical Surfaces	760	(5)
Vectors	765	(11)
Dot Product; Projections	776	(9)
Cross Product	785	(10)
Parametric Equations of Lines	795	(6)
Planes in 3-Space	801	(7)
Quatric Surfaces	808	(11)
Cylindrical and Spherical Coordinates	819	(10)
Vector-Valued Functions	829	(60)
Introduction to Vector-Valued Functions	830	(6)
Calculus of Vector-Valued Functions	836	(7)
Change of Parameter; Arc Length	843	(10)
Unit Tangent, Normal, and Binormal Vectors	853	(5)
Curvature	858	(9)
Motion Along a Curve	867	(13)
Kepler's Laws of Planetary Motion	880	(9)
Partial Derivatives	889	(88)
Functions of Two or More Variables	890	(11)
Limits and Continuity	901	(9)
Partial Derivatives	910	(10)
Differentiability and Chain Rules	920	(10)
Tangent Planes; Total Differentials for Functions of Two Variables	930	(7)
Directional Derivatives and Gradients for Functions of Two Variables	937	(8)
Differentiability, Directional Derivatives, and Gradients for Functions of Three or More Variables	945	(11)
Maxima and Minima of Functions of Two Variables	956	(11)
Lagrange Multipliers	967	(10)
Multiple Integrals	977	(78)
Double Integrals	978	(7)
Double Integrals over Nonrectangular Regions	985	(8)
Double Integrals in Polar Coordinates	993	(7)
Parametric Surface; Surface Area	1000	(12)
Triple Integrals	1012	(7)
Centroid, Center of Gravity, Theorem of Pappus	1019	(10)
Triple Integrals in Cylindrical and Spherical Coordinates	1029	(10)
Change of Variables in Multiple Integrals; Jacobians	1039	(16)
Topics in Vector Calculus	1055
Vector Fields	1056
Line Integrals	1064
Independence of Path; Conservative Vector Fields	1078
Green's Theorem	1088
Surface Integrals	1094
Applications of Surface Integrals; Flux	1101
The Divergence Theorem	1109
Stokes' Theorem	1117
Horizon Module: Hurricane Modeling	1126
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	A29
Appendix E. Trigonometry Review	A39
Appendix F. Solving Polynomial Equations	A52
Appendix G. Selected Proofs	A57
Answers	A65
Index	I1
Photo Credits	C1