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Full Description
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.
Contents
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
