Student Solutions Manual to accompany Calculus: Multivariable 2e

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.

• 9 Vectors 1 9.1 Vectors in the Plane 19.2 Vectors in Three-Dimensional Space 79.3 The Dot Product and Applications  129.4 The Cross Product and Triple Product 169.5 Lines and Planes in Space  2210 Vector-Valued Functions 3410.1 Vector-Valued Functions|Limits, Derivatives, and Continuity  3410.2 Velocity and Acceleration  4310.3 Tangent Vectors and Arc Length 5310.4 Curvature  6410.5 Applications of Vector-Valued Functions  7411 Functions of Several Variables 8611.1 Functions of Several Variables  8611.2 Cylinders and Quadratic Surfaces  9511.3 Limits and Continuity 10311.4 Partial Derivatives 10611.5 Dierentiability and the Chain Rule  11411.6 Gradients and Directional Derivatives  12311.7 Tangent Planes  12911.8 Maximum-Minimum Problems  13411.9 Lagrange Multipliers  14412 Multiple Integrals 15612.1 Double Integrals over Rectangular Regions 15612.2 Integration over More General Regions  16012.3 Calculation of Volumes of Solids  17112.4 Polar Coordinates  17912.5 Integrating in Polar Coordinates  18812.6 Triple Integrals  20012.7 Physical Applications  20912.8 Other Coordinate Systems  21513 Vector Calculus 22213.1 Vector Fields  22213.2 Line Integrals  22813.3 Conservative Vector Fields and Path-Independence 23613.4 Divergence, Gradient, and Curl  24113.5 Green's Theorem  24513.6 Surface Integrals  25313.7 Stokes's Theorem  26213.8 Flux and the Divergence Theorem  277