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Informationen zum Autor Brian Erf Blank is an associate professor of mathematics at Washington University in St. Louis. He received his Ph.D. in 1980 at Cornell University, with Anthony Knapp as advisor. His 20th century work involved harmonic analysis. Steven George Krantz is an American scholar, mathematician, and writer. He has authored more than 235 research papers and more than 125 books. Additionally, Krantz has edited journals such as the Notices of the American Mathematical Society and The Journal of Geometric Analysis. Klappentext A student manual for multivariable calculus practice and improved understanding of the subject Calculus: Multivariable Student Solutions Manual provides problems for practice, organized by specific topics, such as Vectors and Functions of Several Variables. Solutions and the steps to reach them are available for specific problems. The manual is designed to accompany the Multivariable: Calculus textbook, which was published to enhance students' critical thinking skills and make the language of mathematics more accessible. Inhaltsverzeichnis 9 Vectors 1 9.1 Vectors in the Plane 1 9.2 Vectors in Three-Dimensional Space 7 9.3 The Dot Product and Applications 12 9.4 The Cross Product and Triple Product 16 9.5 Lines and Planes in Space 22 10 Vector-Valued Functions 34 10.1 Vector-Valued Functions|Limits, Derivatives, and Continuity 34 10.2 Velocity and Acceleration 43 10.3 Tangent Vectors and Arc Length 53 10.4 Curvature 64 10.5 Applications of Vector-Valued Functions 74 11 Functions of Several Variables 86 11.1 Functions of Several Variables 86 11.2 Cylinders and Quadratic Surfaces 95 11.3 Limits and Continuity 103 11.4 Partial Derivatives 106 11.5 Dierentiability and the Chain Rule 114 11.6 Gradients and Directional Derivatives 123 11.7 Tangent Planes 129 11.8 Maximum-Minimum Problems 134 11.9 Lagrange Multipliers 144 12 Multiple Integrals 156 12.1 Double Integrals over Rectangular Regions 156 12.2 Integration over More General Regions 160 12.3 Calculation of Volumes of Solids 171 12.4 Polar Coordinates 179 12.5 Integrating in Polar Coordinates 188 12.6 Triple Integrals 200 12.7 Physical Applications 209 12.8 Other Coordinate Systems 215 13 Vector Calculus 222 13.1 Vector Fields 222 13.2 Line Integrals 228 13.3 Conservative Vector Fields and Path-Independence 236 13.4 Divergence, Gradient, and Curl 241 13.5 Green's Theorem 245 13.6 Surface Integrals 253 13.7 Stokes's Theorem 262 13.8 Flux and the Divergence Theorem 277 ...
Sommario
9 Vectors 1
9.1 Vectors in the Plane 1
9.2 Vectors in Three-Dimensional Space 7
9.3 The Dot Product and Applications 12
9.4 The Cross Product and Triple Product 16
9.5 Lines and Planes in Space 22
10 Vector-Valued Functions 34
10.1 Vector-Valued Functions Limits, Derivatives, and Continuity 34
10.2 Velocity and Acceleration 43
10.3 Tangent Vectors and Arc Length 53
10.4 Curvature 64
10.5 Applications of Vector-Valued Functions 74
11 Functions of Several Variables 86
11.1 Functions of Several Variables 86
11.2 Cylinders and Quadratic Surfaces 95
11.3 Limits and Continuity 103
11.4 Partial Derivatives 106
11.5 Dierentiability and the Chain Rule 114
11.6 Gradients and Directional Derivatives 123
11.7 Tangent Planes 129
11.8 Maximum-Minimum Problems 134
11.9 Lagrange Multipliers 144
12 Multiple Integrals 156
12.1 Double Integrals over Rectangular Regions 156
12.2 Integration over More General Regions 160
12.3 Calculation of Volumes of Solids 171
12.4 Polar Coordinates 179
12.5 Integrating in Polar Coordinates 188
12.6 Triple Integrals 200
12.7 Physical Applications 209
12.8 Other Coordinate Systems 215
13 Vector Calculus 222
13.1 Vector Fields 222
13.2 Line Integrals 228
13.3 Conservative Vector Fields and Path-Independence 236
13.4 Divergence, Gradient, and Curl 241
13.5 Green s Theorem 245
13.6 Surface Integrals 253
13.7 Stokes s Theorem 262
13.8 Flux and the Divergence Theorem 277
