# Calculus: Multivariable, Volume 2

Springer Science & Business Media, 2006 - Mathematics - 439 pages
Calculus is one of the milestones of human thought. Every well-educated person should be acquainted with the basic ideas of the subject. In todaya??s technological world, in which more and more ideas are being quantified, knowledge of calculus has become essential to a broader cross-section of the population. This Debut Edition of Calculus by Brian Blank and Steven G. Krantz is published in two volumes, Single Variable and Multivariable. Teaching and writing from the traditional point of view, these authors have distilled the lessons of reform and bring you a calculus book focusing on todaya??s best practices in calculus teaching.

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### Contents

 Vectors 1 111 Vectors in the Plane 2 112 Vectors in ThreeDimensional Space 12 113 The Dot Product and Applications 21 114 The Cross Product and Triple Product 32 115 Lines and Planes in Space 44 Summary of Key Topics 58 Genesis Development 62
 Genesis Development 226 Multiple Integrals 231 141 Double Integrals over Rectangular Regions 232 142 Integration over More General Regions 240 143 Calculation of Volumes of Solids 248 144 Polar Coordinates 254 145 Integrating in Polar Coordinates 263 146 Triple Integrals 277

 VectorValued Functions 65 121 VectorValued Functions Limits Derivatives and Continuity 66 122 Velocity and Acceleration 77 123 Tangent Vectors and Arc Length 87 124 Curvature 97 125 Applications of VectorValued Functions to Motion 107 Summary of Key Topics 121 Genesis Development 125 Functions of Several Variables 129 131 Functions of Several Variables 130 132 Cylinders and Quadric Surfaces 141 133 Limits and Continuity 150 134 Partial Derivatives 156 135 Differentiability and the Chain Rule 166 136 Gradients and Directional Derivatives 178 137 Tangent Planes 187 138 MaximumMinimum Problems 198 139 Lagrange Multipliers 212 Summary of Key Topics 222
 147 Physical Applications 283 148 Other Coordinate Systems 292 Summary of Key Topics 298 Genesis Development 304 Vector Calculus 307 151 Vector Fields 308 152 Line Integrals 317 153 Conservative Vector Fields and PathIndependence 328 154 Divergence Gradient and Curl 340 155 Greens Theorem 348 156 Surface Integrals 358 157 Stokess Theorem 369 158 Flux and the Divergence Theorem 383 Summary of Key Topics 392 Genesis Development 396 ANSWERS TO SELECTED EXERCISES 399 Index 423 Copyright