Includes index

TABLE OF CONTENTS
Preface xi
CHAPTER 9 PARAMETRIC EQUATIONS AND POLAR COORDINATES
9.1 Plane Curves and Parametric Equations
9.2 Calculus and Parametric Equations
9.3 Arc Length and Surface Area in Parametric Equations
9.4 Polar Coordinates
9.5 Calculus and Polar Coordinates
9.6 Conic Sections
9.7 Conic Sections in Polar Coordinates
Chapter 10 VECTORS AND THE GEOMETRYOF SPACE 1
10.1 Vectors in the Plane 2
10.2 Vectors in Space 12
10.3 The Dot Product 19
Components and Projections
10.4 The Cross Product 28
10.5 Lines and Planes in Space 41
10.6 Surfaces in Space 50
CHAPTER 11 VECTOR-VALUED FUNCTIONS 65
11.1 Vector-Valued Functions 66
11.2 The Calculus of Vector-Valued Functions 75
11.3 Motion in Space 86
11.4 Curvature 96
11.5 Tangent and Normal Vectors 104
Tangential and Normal Components of Acceleration - Kepler?s Laws
CHAPTER 12 FUNCTIONS OF SEVERAL VARIABLES AND PARTIAL DIFFERENTIATION
121
12.1 Functions of Several Variables 122
12.2 Limits and Continuity 138
12.3 Partial Derivatives 150
12.4 Tangent Planes and Linear Approximations 162
Increments and Differentials
12.5 The Chain Rule 174
12.6 The Gradient and Directional Derivatives 181
12.7 Extrema of Functions of Several Variables 193
12.8 Constrained Optimization and Lagrange Multipliers 208
CHAPTER 13 MULTIPLE INTEGRALS 225
13.1 Double Integrals 226
13.2 Area, Volume and Center of Mass 242
13.3 Double Integrals in Polar Coordinates 253
13.4 Surface Area 260
13.5 Triple Integrals 266 Mass and Center of Mass
13.6 Cylindrical Coordinates 278
13.7 Spherical Coordinates 285
13.8 Change of Variables in Multiple Integrals 293
CHAPTER 14 VECTOR CALCULUS 309
14.1 Vector Fields 310
14.2 Line Integrals 322
14.3 Independence of Path and Conservative Vector Fields 337
14.4 Green?s Theorem 348
14.5 Curl and Divergence 357
14.6 Surface Integrals 367
Parametric Representation of Surfaces
14.7 The Divergence Theorem 381
14.8 Stokes? Theorem 389
APPENDIX A ANSWERS TO ODD-NUMBERED EXERCISES 403
BIBLIOGRAPHY 419
CREDITS 421
INDEX 423