Calculus

Preface vii Features ix Supplements xv Acknowledgments xvii About the Authors xix 11 Vectors 1 Preview 1 11.1 Vectors in the Plane 2 11.2 Vectors in Three-Dimensional Space 12 11.3 The Dot Product and Applications 21 11.4 The Cross Product and Triple Product 32 11.5 Lines and Planes in Space 44 Summary of Key Topics 58 Genesis & Development 62 12 Vector-Valued Functions 65 Preview 65 12.1 Vector-Valued Functions-Limits, Derivatives, and Continuity 66 12.2 Velocity and Acceleration 77 12.3 Tangent Vectors and Arc Length 87 12.4 Curvature 97 12.5 Applications of Vector-Valued Functions to Motion 107 Summary of Key Topics 121 Genesis & Development 125 13 Functions of Several Variables 129 Preview 129 13.1 Functions of Several Variables 130 13.2 Cylinders and Quadric Surfaces 141 13.3 Limits and Continuity 150 13.4 Partial Derivatives 156 13.5 Differentiability and the Chain Rule 166 13.6 Gradients and Directional Derivatives 178 13.7 Tangent Planes 187 13.8 Maximum-Minimum Problems 198 13.9 Lagrange Multipliers 212 Summary of Key Topics 222 Genesis & Development 226 14 Multiple Integrals 231 Preview 231 14.1 Double Integrals over Rectangular Regions 232 14.2 Integration over More General Regions 240 14.3 Calculation of Volumes of Solids 248 14.4 Polar Coordinates 254 14.5 Integrating in Polar Coordinates 263 14.6 Triple Integrals 277 14.7 Physical Applications 283 14.8 Other Coordinate Systems 292 Summary of Key Topics 298 Genesis & Development 304 15 Vector Calculus 307 Preview 307 15.1 Vector Fields 308 15.2 Line Integrals 317 15.3 Conservative Vector Fields and Path-Independence 328 15.4 Divergence, Gradient, and Curl 340 15.5 Green's Theorem 348 15.6 Surface Integrals 358 15.7 Stokes's Theorem 369 15.8 Flux and the Divergence Theorem 383 Summary of Key Topics 392 Genesis & Development 396 Appendix Answers to Selected Exercises 399 Index