vector_fields

# vector_fields - MIT OpenCourseWare http:/ocw.mit.edu 18.02...

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V8. Vector Fields in Space Just as in Section V1 we considered vector fields in the plane, so now we consider vector fields in three-space. These are fields given by a vector function of the type Such a function assigns the vector F(xo, yo, zo) to a point (so, yo, zo) where M, N, and P are all defined. We place the vector so its tail is at (so, yo, zo), and in this way get the vector field. Such a field in space looks a little like the interior of a haystack. As before, we say F is continuous in some domain D of 3-space (we will usually use LLdomain" rather than "region" , when referring to a portion of 3-space) if M, N, and P are continuous in that domain. We say F is continuously differentiable in the domain D if all nine first partial derivatives Mz, My, Mz; Nx, Ny, Nz; Px,PY, pz exist and are continuous in D. Again as before, we give two physical interpretations for such a vector field. The three-dimensional
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## This note was uploaded on 05/04/2011 for the course MATH 18.02 taught by Professor Auroux during the Spring '08 term at MIT.

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vector_fields - MIT OpenCourseWare http:/ocw.mit.edu 18.02...

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