Student Solutions Manual to accompany Calculus: Multivariable 2e

Spis treści:
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