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24 Cards in this Set
- Front
- Back
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work
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S <F(r(t)),r'(t)>dt
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differential line integral?
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Sc Pdx+Qdy+Rdz
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when F=grad.f
ScFdr=? |
f(b)-f(a)
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If F=(F1,F2,F3) what is the div. of F?
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F1x+F2y+F3z
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What does x equal in spherical coordinates?
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psin%cos@
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What does y equal in spherical coordinates?
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psin%sin@
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What does r equal in spherical coordinates?
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Psin%
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What is the Laplacian?
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the divergence of the gradient.
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curl of F=
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l i j k l
l dx dy dz l l F1 F2 F3 l |
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What two curl identities equal zero?
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the div. of the curl
the curl of the grad. |
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Green's Thrm
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Sbu Pdx+Qdy = Su Qx-Py dA
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Sbu Pdx+Qdy =
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Su Qx-Py dA
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Su Qx-Py dA =
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Sbu Pdx+Qdy
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Area of U = Sc Pdx+Qdy if...
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Qx-Py = 1
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area of ellipse
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abpi
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Flux =
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Ss <F,n> ds
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Stoke's Thrm
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Sbu <F,dr> = Ss <curl F, n>ds
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Sbu <F,dr> =
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Ss <curl F, n>ds
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Ss <curl F, n>ds=
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Sbu <F,dr>
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In polar coordinates, dV = ?
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p^2sin%dpd%d@
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Divergence Theorem
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Sv div.FdV = Sbv <F,n> ds
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Sv div.FdV =
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Sbv <F,n> ds
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Sbv <F,n> ds =
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Sv div.FdV
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in spherical coordinates, z=?
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pcos%
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