About the Book
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:
chapter one FUNCTIONS 11.1 Functions 11.2 Graphing Functions Using Calculators and Computer Algebra Systems161.3 New Functions from Old 271.4 Families of Functions 401.5 Inverse Functions; Inverse Trigonometric Functions 511.6 Exponential and Logarithmic Functions 651.6 Mathematical Models 761.7 Parametric Equations 86chapter two LIMITS AND CONTINUITY 1012.1 Limits (An Intuitive Approach) 1012.2 Computing Limits 1132.3 Limits at Infinity; End Behavior of a Function 1222.4 Limits (Discussed More Rigorously) 1342.5 Continuity 1442.6 Continuity of Trigonometric and Inverse Functions 155chapter three THE DERIVATIVE 1653.1 Tangent Lines, Velocity, and General Rates of Change 1653.2 The Derivative Function 1783.3 Techniques of Differentiation 1903.4 The Product and Quotient Rules 1983.5 Derivatives of Trigonometric Functions 2043.6 The Chain Rule 2093.7 Related Rates 2173.8 Local Linear Approximation; Differentials 224chapter four EXPONENTIAL, LOGARITHMIC, AND INVERSE TRIGONOMETRIC FUNCTIONS 2354.1 Implicit Differentiation 2354.2 Derivatives of Logarithmic Functions 2434.3 Derivatives of Exponential and Inverse Trigonometric Functions 2484.4 L'Hopital's Rule; Indeterminate Forms 256chapter five THE DERIVATIVE IN GRAPHING AND APPLICATIONS 2675.1 Analysis of Functions I: Increase, Decrease, and Concavity 2675.2 Analysis of Functions II: Relative Extrema; Graphing Polynomials 2795.3 More on Curve Sketching: Rational Functions; Curves with Cusps and Vertical Tangent Lines; Using Technology 2895.4 Absolute Maxima and Minima 3015.5 Applied Maximum and Minimum Problems 3095.6 Newton's Method 3235.7 Rolle's Theorem; Mean-Value Theorem 3295.8 Rectilinear Motion 336 chapter six INTEGRATION 3496.1 An Overview of the Area Problem 3496.2 The Indefinite Integral 3556.3 Integration by Substitution 3656.4 The Definition of Area as a Limit; Sigma Notation 3736.5 The Definite Integral 3866.6 The Fundamental Theorem of Calculus 3966.7 Rectilinear Motion Revisited Using Integration 4106.8 Evaluating Definite Integrals by Substitution 419 chapter seven APPLICATIONS OF THE DEFINITE INTEGRAL IN GEOMETRY, SCIENCE, AND ENGINEERING 44207.1 Area Between Two Curves 4427.2 Volumes by Slicing; Disks and Washers 4507.3 Volumes by Cylindrical Shells 4597.4 Length of a Plane Curve 4657.5 Area of a Surface of Revolution 4717.6 Average Value of a Function and its Applications 4767.7 Work 4817.8 Fluid Pressure and Force 4907.9 Hyperbolic Functions and Hanging Cables 496 chapter eight PRINCIPLES OF INTEGRAL EVALUATION 5108.1 An Overview of Integration Methods 5108.2 Integration by Parts 5138.3 Trigonometric Integrals 5228.4 Trigonometric Substitutions 5308.5 Integrating Rational Functions by Partial Fractions 5378.6 Using Computer Algebra Systems and Tables of Integrals 5458.7 Numerical Integration; Simpson's Rule 5568.8 Improper Integrals 569 chapter 9 MATHEMATICAL MODELING WITH DIFFERENTIAL EQUATIONS 5829.1 First-Order Differential Equations and Applications 5829.2 Slope Fields; Euler's Method 5969.3 Modeling with First-Order Differential Equations 6039.4 Second-Order Linear Homogeneous Differential Equations; The Vibrating Spring 612 chapter ten INFINITE SERIES 62410.1 Sequences 62410.2 Monotone Sequences 63510.3 Infinite Series 64310.4 Convergence Tests 65210.5 The Comparison, Ratio, and Root Tests 65910.6 Alternating Series; Conditional Convergence 66610.7 Maclaurin and Taylor Polynomials 67510.8 Maclaurin and Taylor Series; PowerSeries 68510.9 Convergence of Taylor Series 69410.10 Differentiating and Integrating Power Series; Modeling with Taylor Series 704 chapter eleven ANALYTIC GEOMETRY IN CALCULUS 71711.1 Polar Coordinates 71711.2 Tangent Lines and Arc Length for Parametric and Polar Curves 73111.3 Area in Polar Coordinates 74011.4 Conic Sections in Calculus 74611.5 Rotation of Axes; Second-Degree Equations 76511.6 Conic Sections in Polar Coordinates 771Horizon Module: Comet Collision 783 appendix a TRIGONOMETRY REVIEW A1appendix b SOLVING POLYNOMIAL EQUATIONS A15appendix c SELECTED PROOFS A22ANSWERS A33PHOTOCREDITS C1INDEX I-1web appendix d REAL NUMBERS,INTERVALS, AND INEQUALITIES W1web appendix e ABSOLUTE VALUE W11web appendix f COORDINATE PLANES, LINES, AND LINEAR FUNCTIONS W16web appendix g DISTANCE, CIRCLES, AND QUADRATIC FUNCTIONS W32web appendix h THE DISCRIMINANT W41
About the Author :
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.
