Multivariable Calculus

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 MULTIVARIABLE CALCULUS, Eighth 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. Cover Half Title Title Statement Copyright Dedication Contents Preface To the Student Ch 10: Parametric Equations and Polar Coordinates Ch 10: Introduction 10.1: Curves Defined by Parametric Equations 10.2: Calculus with Parametric Curves 10.3: Polar Coordinates 10.4: Areas and Lengths in Polar Coordinates 10.5: Conic Sections 10.6: Conic Sections in Polar Coordinates Ch 10: Review Ch 10: Problems Plus Ch 11: Infinite Sequences and Series Ch 11: Introduction 11.1: Sequences 11.2: Series 11.3: The Integral Test and Estimates of Sums 11.4: The Comparison Tests 11.5: Alternating Series 11.6: Absolute Convergence and the Ratio and Root Tests 11.7: Strategy for Testing Series 11.8: Power Series 11.9: Representations of Functions as Power Series 11.10: Taylor and Maclaurin Series 11.11: Applications of Taylor Polynomials Ch 11: Review Ch 11: Problems Plus Ch 12: Vectors and the Geometry of Space Ch 12: Introduction 12.1: Three-Dimensional Coordinate Systems 12.2: Vectors 12.3: The Dot Product 12.4: The Cross Product 12.5: Equations of Lines and Planes 12.6: Cylinders and Quadric Surfaces Ch 12: Review Ch 12: Problems Plus Ch 13: Vector Functions Ch 13: Introduction 13.1: Vector Functions and Space Curves 13.2: Derivatives and Integrals of Vector Functions 13.3: Arc Length and Curvature 13.4: Motion in Space: Velocity and Acceleration Ch 13: Review Ch 13: Problems Plus Ch 14: Partial Derivatives Ch 14: Introduction 14.1: Functions of Several Variables 14.2: Limits and Continuity 14.3: Partial Derivatives 14.4: Tangent Planes and Linear Approximations 14.5: The Chain Rule 14.6: Directional Derivatives and the Gradient Vector 14.7: Maximum and Minimum Values 14.8: Lagrange Multipliers Ch 14: Review Ch 14: Problems Plus Ch 15: Multiple Integrals Ch 15: Introduction 15.1: Double Integrals over Rectangles 15.2: Double Integrals over General Regions 15.3: Double Integrals in Polar Coordinates 15.4: Applications of Double Integrals 15.5: Surface Area 15.6: Triple Integrals 15.7: Triple Integrals in Cylindrical Coordinates 15.8: Triple Integrals in Spherical Coordinates 15.9: Change of Variables in Multiple Integrals Ch 15: Review Ch 15: Problems Plus Ch 16: Vector Calculus Ch 16: Introduction 16.1: Vector Fields 16.2: Line Integrals 16.3: The Fundamental Theorem for Line Integrals 16.4: Green’s Theorem 16.5: Curl and Divergence 16.6: Parametric Surfaces and Their Areas 16.7: Surface Integrals 16.8: Stokes’ Theorem 16.9: The Divergence Theorem 16.10: Summary Ch 16: Review Ch 16: Problems Plus Ch 17: Second-Order Differential Equations Ch 17: Introduction 17.1: Second-Order Linear Equations 17.2: Nonhomogeneous Linear Equations 17.3: Applications of Second-Order Differential Equations 17.4: Series Solutions Ch 17: Review Appendixes Appendix F: Proofs of Theorems Appendix G: Complex Numbers Appendix H: Answers to Odd-Numbered Exercises Index Parametric Equations And Polar Coordinates -- Infinite Sequences And Series -- Vectors And The Geometry Of Space -- Vector Functions -- Partial Derivatives -- Multiple Integrals -- Vector Calculus -- Second-order Differential Equations. James Stewart, Mcmaster University And University Of Toronto. Includes Index.