Calculus Multivariable, with Access Code Student Package, Debut Edition

by Brian E. Blank (Washington University in St. Louis); Steven G. Krantz (Washington University in St. Louis)

• ISBN13: 9780470413180
• ISBN10: 0470413182
• Edition: Student
• Format: Paperback
• Copyright: 2008-06-01
• Publisher: WILEY

Summary

Blank and Krantz's Calculus brings together time-tested methods and innovative thinking to address the needs of today's readers, who come from a wide range of backgrounds and look ahead to a variety of futures. Some study the subject because it is required, others because it will widen their career options. Mathematics majors go into law, medicine, genome research, the technology sector, and many other professions. Blank and Krantz's Calculus strives to empower these readers, enhance their critical thinking skills, and equip them with the knowledge and skills to succeed in the discipline they ultimately choose to study.

Table of Contents

Preface	p. vii
Features	p. ix
Supplements	p. xv
Acknowledgments	p. xvii
About the Authors	p. xix
Vectors	p. 1
Preview	p. 1
Vectors in the Plane	p. 2
Vectors in Three-Dimensional Space	p. 12
The Dot Product and Applications	p. 21
The Cross Product and Triple Product	p. 32
Lines and Planes in Space	p. 44
Summary of Key Topics	p. 58
Genesis & Development	p. 62
Vector-Valued Functions	p. 65
Preview	p. 65
Vector-Valued Functions-Limits, Derivatives, and Continuity	p. 66
Velocity and Acceleration	p. 77
Tangent Vectors and Arc Length	p. 87
Curvature	p. 97
Applications of Vector-Valued Functions to Motion	p. 107
Summary of Key Topics	p. 121
Genesis & Development	p. 125
Functions of Several Variables	p. 129
Preview	p. 129
Functions of Several Variables	p. 130
Cylinders and Quadric Surfaces	p. 141
Limits and Continuity	p. 150
Partial Derivatives	p. 156
Differentiability and the Chain Rule	p. 166
Gradients and Directional Derivatives	p. 178
Tangent Planes	p. 187
Maximum-Minimum Problems	p. 198
Lagrange Multipliers	p. 212
Summary of Key Topics	p. 222
Genesis & Development	p. 226
Multiple Integrals	p. 231
Preview	p. 231
Double Integrals over Rectangular Regions	p. 232
Integration over More General Regions	p. 240
Calculation of Volumes of Solids	p. 248
Polar Coordinates	p. 254
Integrating in Polar Coordinates	p. 263
Triple Integrals	p. 277
Physical Applications	p. 283
Other Coordinate Systems	p. 292
Summary of Key Topics	p. 298
Genesis & Development	p. 304
Vector Calculus	p. 307
Preview	p. 307
Vector Fields	p. 308
Line Integrals	p. 317
Conservative Vector Fields and Path-Independence	p. 328
Divergence, Gradient, and Curl	p. 340
Green's Theorem	p. 348
Surface Integrals	p. 358
Stokes's Theorem	p. 369
Flux and the Divergence Theorem	p. 383
Summary of Key Topics	p. 392
Genesis & Development	p. 396
Appendix Answers to Selected Exercises	p. 399
Index
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