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 "Blank and Krantz's Calculus 2e brings together time-tested methods and innovative thinking to address the needs of today's students, who come from a wide range of backgrounds and look ahead to a variety of futures. Using meaningful examples, credible applications, and incisive technology, Blank and Krantz's Calculus 2e strives to empower students, enhance their critical thinking skills, and equip them with the knowledge and skills to succeed in the major or discipline they ultimately choose to study. Blank and Krantz's engaging style and clear writing make the language of mathematics accessible, understandable and enjoyable, while maintaining high standards for mathematical rigor." -- Publisher's website "Calculus is one of the milestones of human thought. Every well-educated person should be acquainted with the basic ideas of the subject. As our world has become more quantified and technological, knowledge of calculus has become essential to a broader cross-section of the population." "This Debut Edition of Calculus by Brian E. Blank and Steven G. Krantz, both of Washington University in St. Louis, is published in two volumes, Single Variable and Multivariable. These respected authors bring together time tested as well as innovative pedagogy and exposition in this book, focusing on today's best practices in calculus teaching. Book jacket." -- BOOK JACKET