Calculus : Multivariable / Edition 1

Calculus : Multivariable / Edition 1

by Brian E. Blank, Steven G. Krantz
     
 

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ISBN-10: 0470412712

ISBN-13: 9780470412718

Pub. Date: 06/10/2008

Publisher: Wiley

Product Details

ISBN-13:
9780470412718
Publisher:
Wiley
Publication date:
06/10/2008
Series:
Key Curriculum Press Series
Edition description:
Debut Edition
Pages:
439
Product dimensions:
8.40(w) x 9.90(h) x 0.90(d)

Related Subjects

Table of Contents

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

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