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Grad div and curl in the first lecture of the second part of this course we move more to consider properties of fields.
Div grad f. We introduce three field operators which reveal interesting collective field properties viz. Div grad f extended keyboard. Divergence of a vector field. The gradient of a scalar field the divergence of a vector field and the curl of a vector field.
Compute answers using wolfram s breakthrough technology knowledgebase relied on by millions of students professionals. For math science. Then the divergence of f is defined by. The gradient of a scalar field is a vector field.
δ a 2 a a displaystyle delta mathbf a nabla 2 mathbf a nabla cdot nabla mathbf a and is a tensor field of the same order. For math science. Compute answers using wolfram s breakthrough technology knowledgebase relied on by millions of students professionals. Let f x y z be a vector field continuously differentiable with respect to x y and z.
The divergence of a vector field is a number that can be thought of as a measure of the rate of change of the density of the flu id at a point. When the laplacian is equal to 0 the function is called a harmonic function. It is the derivative of f in each direction. The of a vector field is the flux per udivergencenit volume.
That is δ f 0 displaystyle delta f 0.
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