# Calculus Early Transcendentals, 10th Edition International Student Version

# Calculus Early Transcendentals, 10th Edition International Student Version

ISBN: 978-1-118-09240-8

Mar 2012

1320 pages

$239.95

Product not available for purchase

## Description

Anton, Bivens & Davis latest issue of*Calculus Early Transcendentals Single Variable*continues to build upon previous editions to fulfill the needs of a changing market by providing flexible solutions to teaching and learning needs of all kinds. The text continues to focus on and incorporate new ideas that have withstood the objective scrutiny of many skilled and thoughtful instructors and their students. This 10

^{th}edition retains Anton's trademark clarity of exposition, sound mathematics, excellent exercises and examples, and appropriate level.

## Related Resources

**0 BEFORE CALCULUS 1**

**0.1** Functions **1**

**0.2** New Functions from Old **15**

**0.3** Families of Functions **27**

**0.4** Inverse Functions; Inverse Trigonometric Functions **38**

**0.5** Exponential and Logarithmic Functions **52**

**1 LIMITS AND CONTINUITY 67**

**1.1** Limits (An Intuitive Approach) **67**

**1.2** Computing Limits **80**

**1.3** Limits at Infinity; End Behavior of a Function **89**

**1.4** Limits (Discussed More Rigorously) **100**

**1.5** Continuity **110**

**1.6** Continuity of Trigonometric, Exponential, and Inverse Functions **121**

**2 THE DERIVATIVE 131**

**2.1** Tangent Lines and Rates of Change **131**

**2.2** The Derivative Function **143**

**2.3** Introduction to Techniques of Differentiation **155**

**2.4** The Product and Quotient Rules **163**

**2.5** Derivatives of Trigonometric Functions **169**

**2.6** The Chain Rule **174**

**3 TOPICS IN DIFFERENTIATION 185**

**3.1** Implicit Differentiation **185**

**3.2** Derivatives of Logarithmic Functions **192**

**3.3** Derivatives of Exponential and Inverse Trigonometric Functions **197**

**3.4** Related Rates **204**

**3.5** Local Linear Approximation; Differentials **212**

**3.6** L’Hôpital’s Rule; Indeterminate Forms **219**

**4 THE DERIVATIVE IN GRAPHING AND APPLICATIONS 232**

**4.1** Analysis of Functions I: Increase, Decrease, and Concavity **232**

**4.2** Analysis of Functions II: Relative Extrema; Graphing Polynomials **244**

**4.3** Analysis of Functions III: Rational Functions, Cusps, and Vertical Tangents **254**

**4.4** Absolute Maxima and Minima **266**

**4.5** Applied Maximum and Minimum Problems **274**

**4.6** Rectilinear Motion **288**

**4.7** Newton’s Method **296**

**4.8** Rolle’s Theorem; Mean-Value Theorem **302**

**5 INTEGRATION 316**

**5.1** An Overview of the Area Problem **316**

**5.2** The Indefinite Integral **322**

**5.3** Integration by Substitution **332**

**5.4** The Definition of Area as a Limit; Sigma Notation **340**

**5.5** The Definite Integral **353**

**5.6** The Fundamental Theorem of Calculus **362**

**5.7** Rectilinear Motion Revisited Using Integration **376**

**5.8** Average Value of a Function and its Applications **385**

**5.9** Evaluating Definite Integrals by Substitution **390**

**5.10** Logarithmic and Other Functions Defined by Integrals **396**

**6 APPLICATIONS OF THE DEFINITE INTEGRAL IN GEOMETRY, SCIENCE, AND ENGINEERING 413**

**6.1** Area Between Two Curves **413**

**6.2** Volumes by Slicing; Disks and Washers **421**

**6.3** Volumes by Cylindrical Shells **432**

**6.4** Length of a Plane Curve **438**

**6.5** Area of a Surface of Revolution **444**

**6.6** Work **449**

**6.7** Moments, Centers of Gravity, and Centroids **458**

**6.8** Fluid Pressure and Force **467**

**6.9** Hyperbolic Functions and Hanging Cables **474**

**7 PRINCIPLES OF INTEGRAL EVALUATION 488**

**7.1** An Overview of Integration Methods **488**

**7.2** Integration by Parts **491**

**7.3** Integrating Trigonometric Functions **500**

**7.4** Trigonometric Substitutions **508**

**7.5** Integrating Rational Functions by Partial Fractions **514**

**7.6** Using Computer Algebra Systems and Tables of Integrals **523**

**7.7** Numerical Integration; Simpson’s Rule **533**

**7.8** Improper Integrals **547**

**8 MATHEMATICAL MODELING WITH DIFFERENTIAL** **EQUATIONS 561**

**8.1** Modeling with Differential Equations **561**

**8.2** Separation of Variables **568**

**8.3** Slope Fields; Euler’s Method **579**

**8.4** First-Order Differential Equations and Applications **586**

**9 INFINITE SERIES 596**

**9.1** Sequences **596**

**9.2** Monotone Sequences **607**

**9.3** Infinite Series **614**

**9.4** Convergence Tests **623**

**9.5** The Comparison, Ratio, and Root Tests **631**

**9.6** Alternating Series; Absolute and Conditional Convergence **638**

**9.7** Maclaurin and Taylor Polynomials **648**

**9.8** Maclaurin and Taylor Series; Power Series **659**

**9.9** Convergence of Taylor Series **668**

**9.10** Differentiating and Integrating Power Series; Modeling with Taylor Series **678**

**10 PARAMETRIC AND POLAR CURVES; CONIC SECTIONS 692**

**10.1** Parametric Equations; Tangent Lines and Arc Length for Parametric Curves **692**

**10.2** Polar Coordinates **705**

**10.3** Tangent Lines, Arc Length, and Area for Polar Curves **719**

**10.4** Conic Sections **730**

**10.5** Rotation of Axes; Second-Degree Equations **748**

**10.6** Conic Sections in Polar Coordinates **754**

**11 THREE-DIMENSIONAL SPACE; VECTORS 767**

**11.1** Rectangular Coordinates in 3-Space; Spheres; Cylindrical Surfaces **767**

**11.2** Vectors **773**

**11.3** Dot Product; Projections **785**

**11.4** Cross Product **795**

**11.5** Parametric Equations of Lines **805**

**11.6** Planes in 3-Space **813**

**11.7** Quadric Surfaces **821**

**11.8** Cylindrical and Spherical Coordinates **832**

**12 VECTOR-VALUED FUNCTIONS 841**

**12.1** Introduction to Vector-Valued Functions **841**

**12.2** Calculus of Vector-Valued Functions **848**

**12.3** Change of Parameter; Arc Length **858**

**12.4** Unit Tangent, Normal, and Binormal Vectors **868**

**12.5** Curvature **873**

**12.6** Motion Along a Curve **882**

**12.7** Kepler’s Laws of Planetary Motion **895**

**13 PARTIAL DERIVATIVES 906**

**13.1** Functions of Two or More Variables **906**

**13.2** Limits and Continuity **917**

**13.3** Partial Derivatives **927**

**13.4** Differentiability, Differentials, and Local Linearity **940**

**13.5** The Chain Rule **949**

**13.6** Directional Derivatives and Gradients **960**

**13.7** Tangent Planes and Normal Vectors **971**

**13.8** Maxima and Minima of Functions of Two Variables **977**

**13.9** Lagrange Multipliers **989**

**14 MULTIPLE INTEGRALS 1000**

**14.1** Double Integrals **1000**

**14.2** Double Integrals over Nonrectangular Regions **1009**

**14.3** Double Integrals in Polar Coordinates **1018**

**14.4** Surface Area; Parametric Surfaces **1026**

**14.5** Triple Integrals **1039**

**14.6** Triple Integrals in Cylindrical and Spherical Coordinates **1048**

**14.7** Change of Variables in Multiple Integrals; Jacobians **1058**

**14.8** Centers of Gravity Using Multiple Integrals **1071**

**15 TOPICS IN VECTOR CALCULUS 1084**

**15.1** Vector Fields **1084**

**15.2** Line Integrals **1094**

**15.3** Independence of Path; Conservative Vector Fields **1111**

**15.4** Green’s Theorem **1122**

**15.5** Surface Integrals **1130**

**15.6** Applications of Surface Integrals; Flux **1138**

**15.7** The Divergence Theorem **1148**

**15.8** Stokes’ Theorem **1158**

**A APPENDICES**

**A GRAPHING FUNCTIONS USING CALCULATORS AND** **COMPUTER ALGEBRA SYSTEMS A1**

**B TRIGONOMETRY REVIEW A13**

**C SOLVING POLYNOMIAL EQUATIONS A27**

**D SELECTED PROOFS A34**

ANSWERS TO ODD-NUMBERED EXERCISES **A45**

INDEX **I-1**

**WEB APPENDICES (online only)**

Available for download at www.wiley.com*/*go*/*global*/*anton and in *WileyPLUS*.

**E REAL NUMBERS, INTERVALS, AND INEQUALITIES**

**F ABSOLUTE VALUE**

**G COORDINATE PLANES, LINES, AND LINEAR FUNCTIONS**

**H DISTANCE, CIRCLES, AND QUADRATIC EQUATIONS**

**I EARLY PARAMETRIC EQUATIONS OPTION**

**J MATHEMATICAL MODELS**

**K THE DISCRIMINANT**

**L SECOND-ORDER LINEAR HOMOGENEOUS DIFFERENTIAL** **EQUATIONS**

**WEB PROJECTS: Expanding the Calculus Horizon (online only)**

Available for download at www.wiley.com*/*go*/*global*/*anton and in *WileyPLUS*.

**BLAMMO THE HUMAN CANNONBALL**

**COMET COLLISION**

**HURRICANE MODELING**

**ITERATION AND DYNAMICAL SYSTEMS**

**RAILROAD DESIGN**

**ROBOTICS**

- Exercise sets have been modified to correspond more closely to questions in Wiley Plus. In addition, more WileyPLUS questions now correspond to specific exercises in the text.
- New applied exercises have been added to the book and existing applied exercises have been updated.
- There will be more rich content – including assignable questions as well as new applets for visualization and exploration – in the WileyPLUS environment.

**Readability Balanced with Rigor:**The authors' goal is to present precise mathematics to the fullest extent possible in an introductory treatment.**Commitment to Student Success:**Clear writing, effective pedagogy--including special exercises designed for self-assessment--and visual representations of the mathematics help students from a variety of backgrounds to learn. Recognizing variations in learning styles, the authors take a "rule of four" approach, presenting concepts from the verbal, algebraic, visual, and numerical points of view to foster deeper understanding whenever appropriate.**Dependability:**Anton provides thorough topic coverage organized to fit standard curricula and carefully-constructed exercise sets that users of previous editions have come to depend upon.**Flexibility:**This edition is designed to serve a broad spectrum of calculus philosophies-from traditional to "reform." Technology can be emphasized or not, and the order of many topics can be adapted to accommodate each instructor's specific needs.**Quick Check Exercises:**Each exercise set begins with approximately five exercises (answers included) that are designed to provide the student with an immediate assessment of whether he or she has mastered key ideas from the section. They require a minimum of computation and can usually be answered by filling in the blanks.**Focus on Concepts Exercises:**Each exercise set contains a clearly-identified group of problems that focus on the main ideas of the section.**Technology Exercises:**Most sections include exercises that are designed to be solved using either a graphing calculator or a computer algebra system such as Mathematica, Maple, or Derive. These exercises are marked with an icon for easy identification.**Expository Excellence:**Clear explanations allow students to build confidence and provide flexibility for the instructor to use class time for problem solving, applications and explanation of difficult concepts.**Mathematical Level:**The book is written at a mathematical level that is suitable for students planning on careers in engineering or science.**Applicability of Calculus:**One of the primary goals of this text is to link calculus to the real world and the student s own experience. This theme is carried through in the examples and exercises.**Historical Notes:**The biographies and historical notes have been a hallmark of this text from its first edition and have been maintained in this edition. All of the biographical materials have been distilled from standard sources with the goal of capturing the personalities of the great mathematicians and bringing them to life for the student.