Calculus

C__**alculus**__, Tenth Edition continues to evolve to fulfill the needs of a changing market by providing flexible solutions to teaching and learning needs of all kinds. __**Calculus**__, Tenth Edition excels in increasing student comprehension and conceptual understanding of the mathematics. The new edition retains the strengths of earlier editions: e.g., Anton's trademark clarity of exposition; sound mathematics; excellent exercises and examples; and appropriate level, while incorporating more skill and drill problems within WileyPLUS. The seamless integration of Howard Anton’s __**Calculus**__, Tenth Edition with WileyPLUS, a research-based, online environment for effective teaching and learning, continues Anton’s vision of building student confidence in mathematics because it takes the guesswork out of studying by providing them with a clear roadmap: what to do, how to do it, and if they did it right. **WileyPLUS sold separately from text.** Cover Page 1 For the Student 4 Title Page 5 Copyright Page 6 Didication 8 Preface 9 Supplements 11 Acknowledgments 13 Contents 15 The Roots of Calculus 20 0: Before Calculus 23 0.1: Functions 23 0.2: New Functions from Old 37 0.3: Families of Functions 49 0.4: Inverse Functions 60 1: Limits and Continuity 71 1.1: Limits (An Intuitive Approach) 71 1.2: Computing Limits 84 1.3: Limits at Infinity; End Behavior of a Function 93 1.4: Limits (Discussed More Rigorously) 103 1.5: Continuity 112 1.6: Continuity of Trigonometric Functions 123 2: The Derivative 132 2.1: Tangent Lines and Rates of Change 132 2.2: The Derivative Function 144 2.3: Introduction to Techniques of Differentiation 156 2.4: The Product and Quotient Rules 164 2.5: Derivatives of Trigonometric Functions 170 2.6: The Chain Rule 175 2.7: Implicit Differentiation 183 2.8: Related Rates 190 2.9: Local Linear Approximation; Differentials 197 3: The Derivative in Graphing and Applications 209 3.1: Analysis of Functions I: Increase, Decrease, and Concavity 209 3.2: Analysis of Functions II: Relative Extrema; Graphing Polynomials 219 3.3: Analysis of Functions III: Rational Functions, Cusps, and Vertical Tangents 229 3.4: Absolute Maxima and Minima 238 3.5: Applied Maximum and Minimum Problems 246 3.6: Rectilinear Motion 260 3.7: Newton's Method 268 3.8: Rolle's Theorem; Mean-Value Theorem 274 4: Integration 287 4.1: An Overview of the Area Problem 287 4.2: The Indefinite Integral 293 4.3: Integration by Substitution 303 4.4: The Definition of Area as a Limit; Sigma Notation 309 4.5: The Definite Integral 322 4.6: The Fundamental Theorem of Calculus 331 4.7: Rectilinear Motion Revisited Using Integration 344 4.8: Average Value of a Function and its Applications 354 4.9: Evaluating Definite Integrals by Substitution 359 5: Applications of the Definite Integral in Geometry, Science, and Engineering 369 5.1: Area between Two Curves 369 5.2: Volumes by Slicing; Disks and Washers 377 5.3: Volumes by Cylindrical Shells 387 5.4: Length of a Plane Curve 393 5.5: Area of a Surface of Revolution 399 5.6: Work 404 5.7: Moments, Centers of Gravity, and Centroids 413 5.8: Fluid Pressure and Force 422 6: Exponential, Logarithmic, and Inverse Trigonometric Functions 431 6.1: Exponential and Logarithmic Functions 431 6.2: Derivatives and Integrals Involving Logarithmic Functions 442 6.3: Derivatives of Inverse Functions; Derivatives and Integrals Involving Exponential Functions 449 6.4: Graphs and Applications Involving Logarithmic and Exponential Functions 456 6.5: L'Hôpital's Rule; Indeterminate Forms 463 6.6: Logarithmic and Other Functions Defined by Integrals 472 6.7: Derivatives and Integrals Involving Inverse Trigonometric Functions 484 6.8: Hyperbolic Functions and Hanging Cables 494 7: Principles of Integral Evaluation 510 7.1: An Overview of Integration Methods 510 7.2: Integration by Parts 513 7.3: Integrating Trigonometric Functions 522 7.4: Trigonometric Substitutions 530 7.5: Integrating Rational Functions by Partial Fractions 536 7.6: Using Computer Algebra Systems and Tables of Integrals 545 7.7: Numerical Integration; Simpson's Rule 555 7.8: Improper Integrals 569 8: Mathematical Modeling with Differential Equations 583 8.1: Modeling with Differential Equations 583 8.2: Separation of Variables 590 8.3: Slope Fields; Euler's Method 601 8.4: First-Order Differential Equations and Applications 608 9: Infinite Series 618 9.1: Sequences 618 9.2: Monotone Sequences 629 9.3: Infinite Series 636 9.4: Convergence Tests 645 9.5: The Comparison, Ratio, and Root Tests 653 9.6: Alternating Series; Absolute and Conditional Convergence 660 9.7: Maclaurin and Taylor Polynomials 670 9.8: Maclaurin and Taylor Series; Power Series 681 9.9: Convergence of Taylor Series 690 9.10: Differentiating and Integrating Power Series; Modeling with Taylor Series 700 10: Parametric and Polar Curves; Conic Sections 714 10.1: Parametric Equations; Tangent Lines and Arc Length for Parametric Curves 714 10.2: Polar Coordinates 727 10.3: Tangent Lines, Arc Length, and Area for Polar Curves 741 10.4: Conic Sections 752 10.5: Rotation of Axes; Second-Degree Equations 770 10.6: Conic Sections in Polar Coordinates 776 11: Three-Dimensional Space; Vectors 789 11.1: Rectangular Coordinates in 3-Space; Spheres; Cylindrical Surfaces 789 11.2: Vectors 795 11.3: Dot Product; Projections 807 11.4: Cross Product 817 11.5: Parametric Equations of Lines 827 11.6: Planes in 3-Space 835 11.7: Quadric Surfaces 843 11.8: Cylindrical and Spherical Coordinates 854 12: Vector-Valued Functions 863 12.1: Introduction to Vector-Valued Functions 863 12.2: Calculus of Vector-Valued Functions 870 12.3: Change of Parameter; Arc Length 880 12.4: Unit Tangent, Normal, and Binormal Vectors 890 12.5: Curvature 895 12.6: Motion along a Curve 904 12.7: Kepler's laws of Planetary Motion 917 13: Partial Derivatives 928 13.1: Functions of Two or More Variables 928 13.2: Limits and Continuity 939 13.3: Partial Derivatives 949 13.4: Differentiability, Differentials, and Local Linearity 962 13.5: The Chain Rule 971 13.6: Directional Derivatives and Gradients 982 13.7: Tangent Planes and Normal Vectors 993 13.8: Maxima and Minima of Functions of Two Variables 999 13.9: Lagrange Multipliers 1011 14: Multiple Integrals 1022 14.1: Double Integrals 1022 14.2: Double Integrals over Nonrectangular Regions 1031 14.3: Double Integrals in Polar Coordinates 1040 14.4: Surface Area; Parametric Surfaces 1048 14.5: Triple Integrals 1061 14.6: Triple Integrals in Cylindrical and Spherical Coordinates 1070 14.7: Change of Variables in Multiple Integrals; Jacobians 1080 14.8: Centers of Gravity Using Multiple Integrals 1093 15: Topics in Vector Calculus 1106 15.1: Vector Fields 1106 15.2: Line Integrals 1116 15.3: Independence of Path; Conservative Vector Fields 1133 15.4: Green's Theorem 1144 15.5: Surface Integrals 1152 15.6: Applications of Surface Integrals; Flux 1160 15.7: The Divergence Theorem 1170 15.8: Stokes' Theorem 1180 Appendices 1191 A: Graphing Functions Using Calculators and Computer Algebra Systems 1191 B: Trigonometry Review 1203 C: Solving Polynomial Equations 1217 D: Selected Proofs 1224 Answers to Odd-Numbered Exercises 1235 Index 1287 C alculus , Tenth Edition continues to evolve to fulfill the needs of a changing market by providing flexible solutions to teaching and learning needs of all kinds. Calculus , Tenth Edition excels in increasing student comprehension and conceptual understanding of the mathematics. The new edition retains the strengths of earlier editions: e.g., Anton's trademark clarity of exposition; sound mathematics; excellent exercises and examples; and appropriate level, while incorporating more skill and drill problems within WileyPLUS. The seamless integration of Howard Anton’s Calculus , Tenth Edition with WileyPLUS, a research-based, online environment for effective teaching and learning, continues Anton’s vision of building student confidence in mathematics because it takes the guesswork out of studying by providing them with a clear roadmap: what to do, how to do it, and if they did it right. WileyPLUS sold separately from text. The New Edition Of Calculus Continues To Bring Together The Best Of Both New And Traditional Curricula In An Effort To Meet The Needs Of Even More Instructors Teaching Calculus. The Author Team's Extensive Experience Teaching From Both Traditional And Innovative Books And Their Expertise In Developing Innovative Problems Put Them In An Unique Position To Make This New Curriculum Meaningful For Those Going Into Mathematics And Those Going Into The Sciences And Engineering. This New Text Exhibits The Same Strengths From Earlier Editions Including An Emphasis On Modeling And A Flexible Approach To Technology.