Student Solutions Manual to accompany Calculus: Multivariable 2e

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. 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

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.