Multivariable Calculus

Cover......Page 1
CONTENTS......Page 9
Preface......Page 11
Preview......Page 19
Vectors in the Plane......Page 20
Vectors in Three-Dimensional Space......Page 30
The Dot Product and Applications......Page 39
The Cross Product and Triple Product......Page 51
Lines and Planes in Space......Page 64
Summary of Key Topics......Page 80
Review Exercises......Page 83
Genesis & Development......Page 85
Preview......Page 89
Vector-Valued Functions„Limits, Derivatives, and Continuity......Page 90
Velocity and Acceleration......Page 101
Tangent Vectors and Arc Length......Page 111
Curvature......Page 122
Applications of Vector-Valued Functions to Motion......Page 132
Summary of Key Topics......Page 148
Review Exercises......Page 151
Genesis & Development......Page 154
Preview......Page 159
Functions of Several Variables......Page 161
Cylinders and Quadric Surfaces......Page 172
Limits and Continuity......Page 180
Partial Derivatives......Page 188
Differentiability and the Chain Rule......Page 198
Gradients and Directional Derivatives......Page 211
Tangent Planes......Page 219
Maximum-Minimum Problems......Page 230
Lagrange Multipliers......Page 244
Summary of Key Topics......Page 255
Review Exercises......Page 258
Genesis & Development......Page 261
Preview......Page 265
Double Integrals Over Rectangular Regions......Page 266
Integration Over More General Regions......Page 274
Calculation of Volumes of Solids......Page 282
Polar Coordinates......Page 288
Integrating in Polar Coordinates......Page 297
Triple Integrals......Page 312
Physical Applications......Page 318
Other Coordinate Systems......Page 327
Summary of Key Topics......Page 335
Review Exercises......Page 340
Genesis & Development......Page 343
Preview......Page 347
Vector Fields......Page 348
Line Integrals......Page 359
Conservative Vector Fields and Path Independence......Page 369
Divergence, Gradient, and Curl......Page 383
Green's Theorem......Page 392
Surface Integrals......Page 402
Stokes's Theorem......Page 414
The Divergence Theorem......Page 429
Summary of Key Topics......Page 437
Review Exercises......Page 441
Genesis & Development......Page 444
Table of Integrals......Page 449
Formulas from Calculus: Single Variable......Page 462
Answers to Selected Exercises......Page 463
Index......Page 495