Calculus: Early Transcendentals, 11th Edition Calculus: Early Transcendentals, 11th Edition By Howard Anton, Irl C. Bivens, Stephen Davis Researchers and educators agree that it takes more than academic knowledge to be prepared for college—intrapersonal competencies like conscientiousness have been proven to be strong determinants of success. WileyPLUS with ORION for Calculushelps you identify students’ proficiency early in the semester and intervene as needed. Schedule a Demo Sign Up for a Test Drive Adopt WileyPLUS Want to learn more about WileyPLUS? Click Here Hear from our Authors What’s Inside About the Authors Table of Contents New video program helps student see what they learn Videos of worked examples and problems highlight specific learning objectives in the Single Variable chapters of the Eleventh Edition. Students get the practice they need to master concepts ORION Algebra and Trigonometry Refresher Module helps students master algebra, trigonometry, and polynomial equations. With ORION, students can create a personalized study plan and instructors can use class time to focus on Calculus. Students get feedback at the point of learning New Answer-Specific Feedback Questions give students customized feedback on the actual work they’re doing at the point of learning. What’s New • WileyPLUS is a research-based online environment for effective teaching and learning. Interactive study tools and resources–including the complete online textbook–give students more value for their money. • Industry-leading support from WileyPLUS with ORION: Resources and personal support are available from the first day of class onward through technical support; WileyPLUS account managers; WileyPLUS with QuickStart; and WileyPLUS Student Partner Program. • Relevant student study tools and learning resources: Ensures positive learning outcomes including: graphing and math Palette tutorial videos; interactive illustrations; calculus applets; and student practice activities. • Technology Exercises: In the textbook, these exercises—marked with an icon for easy identification—are designed to be solved using either a graphing calculator or a computer algebra system such as Mathematics, Maple, or Derive. • Quick Check Exercises: Each exercise set begins with approximately five exercises (answers included) that are designed to provide student with an immediate assessment of whether they have mastered key ideas form the section. • Career Preparation: This program has been created at a mathematical level that will prepare students for a wide variety of careers that require a sound mathematical background, including engineering, the various sciences, and business. Howard Anton obtained his B.A. from Lehigh University, his M.A. from the University of Illinois, and his Ph.D. from the Polytechnic Institute of Brooklyn, all in mathematics. He worked in the manned space program at Cape Canaveral in the early 1960’s. In 1968 he became a research professor of mathematics at Drexel University in Philadelphia, where he taught and did mathematical research for 15 years. In 1983 he left Drexel as a Professor Emeritus of Mathematics to become a full-time writer of mathematical textbooks. There are now more than 150 versions of his books in print, including translations into Spanish, Arabic, Portuguese, French, German, Chinese, Japanese, Hebrew, Italian, and Indonesian. He was awarded a Textbook Excellence Award in 1994 by the Textbook Authors Association, and in 2011 that organization awarded his Elementary Linear Algebra text its McGuffey Award. INTRODUCTION: The Roots of Calculus 1 LIMITS AND CONTINUITY1.1 Limits (An Intuitive Approach)1.2 Computing Limits1.3 Limits at Infinity; End Behavior of a Function1.4 Limits (Discussed More Rigorously)1.5 Continuity1.6 Continuity of Trigonometric Functions1.7 Inverse Trigonometric Functions1.8 Exponential and Logarithmic Functions 2 THE DERIVATIVE2.1 Tangent Lines and Rates of Change2.2 The Derivative Function2.3 Introduction to Techniques of Differentiation2.4 The Product and Quotient Rules2.5 Derivatives of Trigonometric Functions2.6 The Chain Rule 3 TOPICS IN DIFFERENTIATION3.1 Implicit Differentiation3.2 Derivatives of Logarithmic Functions3.3 Derivatives of Exponential and Inverse Trigonometric Functions3.4 Related Rates3.5 Local Linear Approximation; Differentials3.6 L’Hôpital’s Rule; Indeterminate Forms 4 THE DERIVATIVE IN GRAPHING AND APPLICATIONS4.1 Analysis of Functions I: Increase, Decrease, and Concavity4.2 Analysis of Functions II: Relative Extrema; Graphing Polynomials4.3 Analysis of Functions III: Rational Functions, Cusps, and Vertical Tangents4.4 Absolute Maxima and Minima4.5 Applied Maximum and Minimum Problems4.6 Rectilinear Motion4.7 Newton’s Method4.8 Rolle’s Theorem; Mean-Value Theorem 5 INTEGRATION5.1 An Overview of the Area Problem5.2 The Indefinite Integral5.3 Integration by Substitution5.4 The Definition of Area as a Limit; Sigma Notation5.5 The Definite Integral5.6 The Fundamental Theorem of Calculus5.7 Rectilinear Motion Revisited Using Integration5.8 Average Value of a Function and its Applications5.9 Evaluating Definite Integrals by Substitution5.10 Logarithmic and Other Functions Defined by Integrals 6 APPLICATIONS OF THE DEFINITE INTEGRAL IN GEOMETRY, SCIENCE, AND ENGINEERING6.1 Area Between Two Curves6.2 Volumes by Slicing; Disks and Washers6.3 Volumes by Cylindrical Shells6.4 Length of a Plane Curve6.5 Area of a Surface of Revolution6.6 Work6.7 Moments, Centers of Gravity, and Centroids6.8 Fluid Pressure and Force6.9 Hyperbolic Functions and Hanging Cables 7 PRINCIPLES OF INTEGRAL EVALUATION7.1 An Overview of Integration Methods7.2 Integration by Parts7.3 Integrating Trigonometric Functions7.4 Trigonometric Substitutions7.5 Integrating Rational Functions by Partial Fractions7.6 Using Computer Algebra Systems and Tables of Integrals7.7 Numerical Integration; Simpson’s Rule7.8 Improper Integrals 8 MATHEMATICAL MODELING WITH DIFFERENTIAL EQUATIONS8.1 Modeling with Differential Equations8.2 Separation of Variables8.3 Slope Fields; Euler’s Method8.4 First-Order Differential Equations and Applications 9 INFINITE SERIES9.1 Sequences9.2 Monotone Sequences9.3 Infinite Series9.4 Convergence Tests9.5 The Comparison, Ratio, and Root Tests9.6 Alternating Series; Absolute and Conditional Convergence9.7 Maclaurin and Taylor Polynomials9.8 Maclaurin and Taylor Series; Power Series9.9 Convergence of Taylor Series9.10 Differentiating and Integrating Power Series; Modeling with Taylor Series 10 PARAMETRIC AND POLAR CURVES; CONIC SECTIONS10.1 Parametric Equations; Tangent Lines and Arc Length for Parametric Curves10.2 Polar Coordinates10.3 Tangent Lines, Arc Length, and Area for Polar Curves10.4 Conic Sections10.5 Rotation of Axes; Second-Degree Equations10.6 Conic Sections in Polar Coordinates 11 THREE-DIMENSIONAL SPACE; VECTORS11.1 Rectangular Coordinates in 3-Space; Spheres; Cylindrical Surfaces11.2 Vectors11.3 Dot Product; Projections11.4 Cross Product11.5 Parametric Equations of Lines11.6 Planes in 3-Space11.7 Quadric Surfaces11.8 Cylindrical and Spherical Coordinates 12 VECTOR-VALUED FUNCTIONS12.1 Introduction to Vector-Valued Functions12.2 Calculus of Vector-Valued Functions12.3 Change of Parameter; Arc Length12.4 Unit Tangent, Normal, and Binormal Vectors12.5 Curvature12.6 Motion Along a Curve12.7 Kepler’s Laws of Planetary Motion 13 PARTIAL DERIVATIVES13.1 Functions of Two or More Variables13.2 Limits and Continuity13.3 Partial Derivatives13.4 Differentiability, Differentials, and Local Linearity13.5 The Chain Rule13.6 Directional Derivatives and Gradients13.7 Tangent Planes and Normal Vectors13.8 Maxima and Minima of Functions of Two Variables13.9 Lagrange Multipliers 14 MULTIPLE INTEGRALS14.1 Double Integrals14.2 Double Integrals over Nonrectangular Regions14.3 Double Integrals in Polar Coordinates14.4 Surface Area; Parametric Surfaces14.5 Triple Integrals14.6 Triple Integrals in Cylindrical and Spherical Coordinates14.7 Change of Variables in Multiple Integrals; Jacobians14.8 Centers of Gravity Using Multiple Integrals 15 TOPICS IN VECTOR CALCULUS15.1 Vector Fields15.2 Line Integrals15.3 Independence of Path; Conservative Vector Fields15.4 Green’s Theorem15.5 Surface Integrals15.6 Applications of Surface Integrals; Flux15.7 The Divergence Theorem15.8 Stokes’ Theorem APPENDICESA TRIGONOMETRY SUMMARYB FUNCTIONS (SUMMARY)C NEW FUNCTIONS FROM OLD (SUMMARY)D FAMILIES OF FUNCTIONS (SUMMARY) Wiley Team for Success. 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