Multivariable Calculus: Early Transcendentals, 6th Edition

Success in your calculus course starts here! James Stewart's CALCULUS texts are world-wide best-sellers for a reason: they are clear, accurate, and filled with relevant, real-world examples. With CALCULUS: EARLY TRANCENDENTALS, Sixth Edition, Stewart conveys not only the utility of calculus to help you develop technical competence, but also gives you an appreciation for the intrinsic beauty of the subject. His patient examples and built-in learning aids will help you build your mathematical confidence and achieve your goals in the course! MuPDF error: syntax error: invalid key in dict MuPDF error: syntax error: invalid key in dict MuPDF error: syntax error: invalid key in dict MuPDF error: syntax error: invalid key in dict MuPDF error: syntax error: invalid key in dict MuPDF error: syntax error: invalid key in dict MuPDF error: syntax error: invalid key in dict MuPDF error: syntax error: invalid key in dict MuPDF error: syntax error: invalid key in dict Front Cover 1 Title Page 4 Copyright 5 Contents 8 Preface 12 To the Student 22 10 Parametric Equations and Polar Coordinates 25 10.1 Curves Defined by Parametric Equations 26 10.2 Calculus with Parametric Curves 35 10.3 Polar Coordinates 44 10.4 Areas and Lengths in Polar Coordinates 55 10.5 Conic Sections 59 10.6 Conic Sections in Polar Coordinates 67 Review 74 Problems Plus 77 11 Infinite Sequences and Series 79 11.1 Sequences 80 11.2 Series 92 11.3 The Integral Test and Estimates of Sums 102 11.4 The Comparison Tests 110 11.5 Alternating Series 115 11.6 Absolute Convergence and the Ratio and Root Tests 119 11.7 Strategy for Testing Series 126 11.8 Power Series 128 11.9 Representations of Functions as Power Series 133 11.10 Taylor and Maclaurin Series 139 11.11 Applications of Taylor Polynomials 154 Review 163 Problems Plus 166 12 Vectors and the Geometry of Space 169 12.1 Three-Dimensional Coordinate Systems 170 12.2 Vectors 175 12.3 The Dot Product 184 12.4 The Cross Product 191 12.5 Equations of Lines and Planes 199 12.6 Cylinders and Quadric Surfaces 209 Review 217 Problems Plus 220 13 Vector Functions 221 13.1 Vector Functions and Space Curves 222 13.2 Derivatives and Integrals of Vector Functions 229 13.3 Arc Length and Curvature 235 13.4 Motion in Space: Velocity and Acceleration 243 Review 254 Problems Plus 257 14 Partial Derivatives 259 14.1 Functions of Several Variables 260 14.2 Limits and Continuity 275 14.3 Partial Derivatives 283 14.4 Tangent Planes and Linear Approximations 297 14.5 The Chain Rule 306 14.6 Directional Derivatives and the Gradient Vector 315 14.7 Maximum and Minimum Values 327 14.8 Lagrange Multipliers 339 Review 349 Problems Plus 353 15 Multiple Integrals 355 15.1 Double Integrals over Rectangles 356 15.2 Iterated Integrals 364 15.3 Double Integrals over General Regions 370 15.4 Double Integrals in Polar Coordinates 379 15.5 Applications of Double Integrals 385 15.6 Triple Integrals 395 15.7 Triple Integrals in Cylindrical Coordinates 405 15.8 Triple Integrals in Spherical Coordinates 410 15.9 Change of Variables in Multiple Integrals 417 Review 426 Problems Plus 429 16 Vector Calculus 431 16.1 Vector Fields 432 16.2 Line Integrals 439 16.3 The Fundamental Theorem for Line Integrals 451 16.4 Green’s Theorem 460 16.5 Curl and Divergence 466 16.6 Parametric Surfaces and Their Areas 475 16.7 Surface Integrals 486 16.8 Stokes’ Theorem 497 16.9 The Divergence Theorem 504 16.10 Summary 510 Review 511 Problems Plus 514 17 Second-Order Differential Equations 515 17.1 Second-Order Linear Equations 516 17.2 Nonhomogeneous Linear Equations 522 17.3 Applications of Second-Order Differential Equations 530 17.4 Series Solutions 538 Review 542 Appendixes 544 F Proofs of Theorems 545 H Complex Numbers 548 I Answers to Odd-Numbered Exercises 556 Index 584