Calculus: Early Transcendentals Single Variable, 8th Edition

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

• ISBN13: 9780471482383
• ISBN10: 0471482382
• Edition: 8th
• Format: Hardcover
• Copyright: 2005-01-01
• 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.

Author Biography

Howard Anton obtained his B.A. from Lehigh University, his M.A. from the University of Illinois, and his Ph.D. from the Polytechnic University of Brooklyn, all in mathematics. In the early 1960's he worked for Burroughs Corporation and Avco Corporation at Cape Canaveral, Florida, where he was involved with the manned space program. In 1968 he joined the Mathematics Department at Drexel University, where he taught full time until 1983. Since that time he has been an adjunct professor at Drexel and has devoted the majority of his time to textbook writing and activities for mathematical associations. Dr. Anton was president of the EPADEL Section of the Mathematical Association of America (MAA), Served on the board of Governors of that organization, and guided the creation of the Student Chapters of the MAA. He has published numerous research papers in functional analysis, approximation theory, and topology, as well as pedagogical papers. He is best known for his textbooks in mathematics, which are among the most widely used in the world. There are currently more than one hundred versions of his books, including translations into Spanish, Arabic, Portuguese, Italian, Indonesian, French, Japanese, Chinese, Hebrew, and German. For relaxation, Dr. Anton enjoys traveling and photography.

Irl C. Bivens, recipient of the George Polya Award and the Merten M. Hasse Prize for Expository Writing in Mathematics, received his A.B. from Pfeiffer College and his Ph.D. from the University of North Carolina at Chapel Hill, both in mathematics. Since 1982, he has taught at Davidson College, where he currently holds the position of professor of mathematics. A typical academic year sees him teaching courses in calculus, topology, and geometry. Dr. Bivens also enjoys mathematical history, and his annual History of Mathematics seminar is a perennial favorite with Davidson mathematics majors. He has published numerous articles on undergraduate mathematics, as well as research papers in his specialty, differential geometry. he is currently a member of the editorial board for the MAA Problem Book series and is a reviewer for Mathematical Reviews. When he is not pursuing mathematics, Professor Bivens enjoys juggling, swimming, walking, and spending time with his son Robert.

Stephen L. Davis received his B.A. from Lindenwood College and his Ph.D. from Rutgers University in mathematics. Having previously taught at Rutgers University and Ohio State University, Dr. Davis came to Davidson College in 1981,  where he is currently a professor of mathematics. He regularly teaches calculus, linear algebra, abstract algebra, and computer science. A sabbatical in 1995-1996 took him to Swarthmore College as a visiting associate professor. Professor Davis has published numerous articles on calculus reform and testing, as well as research papers on finite group theory, his specialty. Professor Davis has held several offices in the Southeastern section of the MAA, including chair and secretary-treasurer. He is currently a faculty consultant for the Educational testing Service Advanced Placement Calculus Test, a board member of the North Carolina, Association of Advanced Placement Mathematics Teachers, and is actively involved in nurturing mathematically talented high school students through leadership in the Charlotte Mathematics Club. He was formerly North Carolina state director for the MAA. For relaxation, he plays basketball, juggles, and travels. Professor Davis and his wife Elisabeth have three children, Laura, Anne, and James, all former calculus 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
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
Horizon Module: Comet Collision	783
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