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some problem about the integral

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Old   July 12, 2006, 07:58
Default some problem about the integral
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I have some problem about the integral. if i have a function F(kexi,eta), now, the inverse problem algorithm need the integral of the F over the whold spacedomain, so i expressed it as

int(F)dkexi deta but it should expressed as

int(F) J dkexi deta where J is the Jacobian coefficient. so why should i include the J in the integral

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Old   July 12, 2006, 08:54
Default Re: some problem about the integral
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the jacobian relates the absolute coordinate system (say x, y, z) to the local coordinate system (say xi, eta, zeta). what you really want to do is to integrate over the absolute space, so your local "dxi, deta, dzeta" vector has to be multiplied by the jacobian matrix to get "dx, dy, dz". absolute and local coordinates may differ in direction (e.g. with a local curvilinear system) and/or may have different scales (normalized local coordinates).

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Old   July 13, 2006, 11:50
Default some problem about the integral
m. malik
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Just because J=J(exi,eta).
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