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Vector fields we describe these as vector valued functions that (1) - - PDF document
Vector fields we describe these as vector valued functions that (1) - - PDF document
Vector fields we describe these as vector valued functions that (1) depend on n variables and (2) have n components. 1 At each point (x,y) there is a vector. Nearbottom currents in Long Island Sound 2 Hurricanetype wind pattern in 3D
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Hurricanetype wind pattern in 3D
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Representations: 1) 2) Sketching: 1) Pick some points in the domain. 2) Calculate the corresponding vector at each point. 3) Plot each vector with it's tail at that point.
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Force fields
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Electric force field (Coulomb's Law)
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Gradient fields
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Line integrals
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Application: find the center of gravity for a "wire"
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We will sometimes see integrals over a line with respect to x or y ...
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WORK: We will calculate work done in moving a particle through a force field from point P to Q.
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Two comments: 1) If a curve has "kinks", break the integral up into multiple integrals over the smooth parts. 2) Direction of motion/"orientation" of a parameterization matters.
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Practice!
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