Calculus: Multivariable, Volume 2

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Springer Science & Business Media, 2006 - Mathematics - 439 pages
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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
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About the author (2006)

Steven Krantz, Ph.D., is Chairman of the Mathematics Department at Washington University in St. Louis. An award-winning teacher and author, Dr. Krantz has written more than 45 books on mathematics, including "Calculus Demystified," another popular title in this series. He lives in St. Louis, Missouri.

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