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Curl (Mathematics): Vector calculus identities, Del, Divergence, Gradient, Del in cylindrical and spherical coordinates, Vorticity, Helmholtz decomposition, Cross product, Vector operator - Softcover

 
9786130213336: Curl (Mathematics): Vector calculus identities, Del, Divergence, Gradient, Del in cylindrical and spherical coordinates, Vorticity, Helmholtz decomposition, Cross product, Vector operator

Inhaltsangabe

Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In vector calculus, the curl (or rotor ) is a vector operator that describes the rotation of a vector field. At every point in the field, the curl is represented by a vector. The attributes of this vector (length and direction) characterize the rotation at that point. The direction of the curl is the axis of rotation, as determined by the right-hand rule, and the magnitude of the curl is the magnitude of rotation. If the vector field represents the flow velocity of a moving fluid, then the curl is the circulation density of the fluid. A vector field whose curl is zero is called irrotational. The curl is a form of differentiation for vector fields. The corresponding form of the fundamental theorem of calculus is Stokes' theorem, which relates the surface integral of the curl of a vector field to the line integral of the vector field around the boundary curve.

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Reseña del editor

Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In vector calculus, the curl (or rotor ) is a vector operator that describes the rotation of a vector field. At every point in the field, the curl is represented by a vector. The attributes of this vector (length and direction) characterize the rotation at that point. The direction of the curl is the axis of rotation, as determined by the right-hand rule, and the magnitude of the curl is the magnitude of rotation. If the vector field represents the flow velocity of a moving fluid, then the curl is the circulation density of the fluid. A vector field whose curl is zero is called irrotational. The curl is a form of differentiation for vector fields. The corresponding form of the fundamental theorem of calculus is Stokes' theorem, which relates the surface integral of the curl of a vector field to the line integral of the vector field around the boundary curve.

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