Recent content by stufletcher

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    Smarter way to solve a continuity equation?

    Hmm. To be honest I don't know where to start. For example, how to i manage the position vector? Do i replace x, y, z with r cos \theta sin \phi etc, then do the divergence? It starts to look very messy ... t^{-\frac{5}{2}}e^{-\frac{r}{4kt}} r cos \theta sin \phi for the x component for example
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    Smarter way to solve a continuity equation?

    Homework Statement The density in 3-D space of a certain kind of conserved substance is given by \[\rho (x,y,z, t) = At^{-\frac{3}{2}}e^{-\frac{r^2}{4kt}}\] where \mathbf r = x\mathbf i + y\mathbf j +z\mathbf k and r = |\mathbf r|. The corresponding flux vector is given by \mathbf...
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    Compare a series sum to it's equivelent integral

    it's always something simple isn't it.. area \frac{5}{x^{1.1}} * (x - (x-1)) < \int_{x-1}^x\frac{5}{x^{1.1}}dx for all values of positive x, so the sum must be smaller than the integral thanks for the tip stu
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    Compare a series sum to it's equivelent integral

    Homework Statement excuse my formatting. compare sum(from n=2 -> infinity) of 5/(n^1.1) to integral (from 1 -> infinity) of 5/(x^1.1) Homework Equations The Attempt at a Solution if it was sum and integrate from 2 it would be easy... the sum is a rienmann sum using...
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