Calculus Multivariable

Description

The Larson Calculus program has a long history of innovation in the calculus market. It has been widely praised by a generation of users for its solid and effective pedagogy that addresses the needs of a broad range of teaching and learning styles and environments. Each title is just one component in a comprehensive calculus course program that carefully integrates and coordinates print, media, and technology products for successful teaching and learning. Front Cover Book Title Copyright Contents A Word from the Authors Textbook Features CHAPTER 11 Vectors and the Geometry of Space 11.1 Vectors in the Plane Component Form of a Vector Vector Operations Standard Unit Vectors Applications of Vectors 11.2 Space Coordinates and Vectors in Space Coordinates in Space Vectors in Space Application 11.3 The Dot Product of Two Vectors The Dot Product Angle Between Two Vectors Direction Cosines Projections and Vector Components Work 11.4 The Cross Product of Two Vectors in Space The Cross Product The Triple Scalar Product 11.5 Lines and Planes in Space Lines in Space Planes in Space Sketching Planes in Space Distances Between Points, Planes, and Lines SECTION PROJECT: Distances in Space 11.6 Surfaces in Space Cylindrical Surfaces Quadric Surfaces Surfaces of Revolution 11.7 Cylindrical and Spherical Coordinates Cylindrical Coordinates Spherical Coordinates Review Exercises Problem Solving CHAPTER 12 Vector-Valued Functions 12.1 Vector-Valued Functions Space Curves and Vector-Valued Functions Limits and Continuity SECTION PROJECT: Witch of Agnesi 12.2 Differentiation and Integration of Vector-Valued Functions Differentiation of Vector-Valued Functions Integration of Vector-Valued Functions 12.3 Velocity and Acceleration Velocity and Acceleration Projectile Motion 12.4 Tangent Vectors and Normal Vectors Tangent Vectors and Normal Vectors Tangential and Normal Components of Acceleration 12.5 Arc Length and Curvature Arc Length Arc Length Parameter Curvature Application Review Exercises Problem Solving CHAPTER 13 Functions of Several Variables 13.1 Introduction to Functions of Several Variables Functions of Several Variables The Graph of a Function of Two Variables Level Curves Level Surfaces Computer Graphics 13.2 Limits and Continuity Neighborhoods in the Plane Limit of a Function of Two Variables Continuity of a Function of Two Variables Continuity of a Function of Three Variables 13.3 Partial Derivatives Partial Derivatives of a Function of Two Variables Partial Derivatives of a Function of Three or More Variables Higher-Order Partial Derivatives SECTION PROJECT: Moiré Fringes 13.4 Differentials Increments and Differentials Differentiability Approximation by Differentials 13.5 Chain Rules for Functions of Several Variables Chain Rules for Functions of Several Variables Implicit Partial Differentiation 13.6 Directional Derivatives and Gradients Directional Derivative The Gradient of a Function of Two Variables Applications of the Gradient Functions of Three Variables 13.7 Tangent Planes and Normal Lines Tangent Plane and Normal Line to a Surface The Angle of Inclination of a Plane A Comparison of the Gradients SECTION PROJECT: Wildflowers 13.8 Extrema of Functions of Two Variables Absolute Extrema and Relative Extrema The Second Partials Test 13.9 Applications of Extrema of Functions of Two Variables Applied Optimization Problems The Method of Least Squares SECTION PROJECT: Building a Pipeline 13.10 Lagrange Multipliers Lagrange Multipliers Constrained Optimization Problems The Method of Lagrange Multipliers with Two Constraints Review Exercises Problem Solving CHAPTER 14 Multiple Integration 14.1 Iterated Integrals and Area in the Plane Iterated Integrals Area of a Plane Region 14.2 Double Integrals and Volume Double Integrals and Volume of a Solid Region Properties of Double Integrals Evaluation of Double Integrals Average Value of a Function 14.3 Change of Variables: Polar Coordinates Double Integrals in Polar Coordinates 14.4 Center of Mass and Moments of Inertia Mass Moments and Center of Mass Moments of Inertia SECTION PROJECT: Center of Pressure on a Sail 14.5 Surface Area Surface Area SECTION PROJECT: Capillary Action 14.6 Triple Integrals and Applications Triple Integrals Center of Mass and Moments of Inertia 14.7 Triple Integrals in Cylindrical and Spherical Coordinates Triple Integrals in Cylindrical Coordinates Triple Integrals in Spherical Coordinates SECTION PROJECT: Wrinkled and Bumpy Spheres 14.8 Change of Variables: Jacobians Jacobians Change of Variables for Double Integrals Review Exercises Problem Solving CHAPTER 15 Vector Analysis 15.1 Vector Fields Vector Fields Conservative Vector Fields Curl of a Vector Field Divergence of a Vector Field 15.2 Line Integrals Piecewise Smooth Curves Line Integrals Line Integrals of Vector Fields Line Integrals in Differential Form 15.3 Conservative Vector Fields and Independence of Path Fundamental Theorem of Line Integrals Independence of Path Conservation of Energy 15.4 Green’s Theorem Green’s Theorem Alternative Forms of Green’s Theorem SECTION PROJECT: Hyperbolic and Trigonometric Functions 15.5 Parametric Surfaces Parametric Surfaces Finding Parametric Equations for Surfaces Normal Vectors and Tangent Planes Area of a Parametric Surface SECTION PROJECT: Hyperboloid of One Sheet 15.6 Surface Integrals Surface Integrals Parametric Surfaces and Surface Integrals Orientation of a Surface Flux Integrals 15.7 Divergence Theorem Divergence Theorem Flux and the Divergence Theorem 15.8 Stokes’s Theorem Stokes’s Theorem Physical Interpretation of Curl Review Exercises SECTION PROJECT: The Planimeter Problem Solving CHAPTER 16 Additional Topics in Differential Equations 16.1 Exact First-Order Equations Exact Differential Equations Integrating Factors 16.2 Second-Order Homogeneous Linear Equations Second-Order Linear Differential Equations Higher-Order Linear Differential Equations Application 16.3 Second-Order Nonhomogeneous Linear Equations Nonhomogeneous Equations Method of Undetermined Coefficients Variation of Parameters SECTION PROJECT: Parachute Jump 16.4 Series Solutions of Differential Equations Power Series Solution of a Differential Equation Approximation by Taylor Series Review Exercises Problem Solving Appendix A: Proofs of Selected Theorems Appendix B: Integration Tables Answers to Odd-Numbered Exercises Index