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 3

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. 4

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Force fields 6

Electric force field (Coulomb's Law) 7

Gradient fields 8

Line integrals 9

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Application: find the center of gravity for a "wire" 12

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We will sometimes see integrals over a line with respect to x or y ... 16

WORK: We will calculate work done in moving a particle through a force field from point P to Q. 17

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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. 21

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Practice! 27

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