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Calculus and Beyond Homework Help
When to use the Jacobian in spherical coordinates?
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[QUOTE="ergospherical, post: 6575487, member: 691758"] It's sort of already baked in. The surface element comes from a little parallelogram with sides ##d\boldsymbol{l}_u = \frac{\partial \boldsymbol{\sigma}}{\partial u} du## and ##d\boldsymbol{l}_v = \frac{\partial \boldsymbol{\sigma}}{\partial v} dv## and therefore area \begin{align*} dS = |d\boldsymbol{l}_u \times d\boldsymbol{l}_v| = \left| \frac{\partial \boldsymbol{\sigma}}{\partial u} \times \frac{\partial \boldsymbol{\sigma}}{\partial v} \right| du dv \end{align*}The part ##\frac{\partial \boldsymbol{\sigma}}{\partial u} \times \frac{\partial \boldsymbol{\sigma}}{\partial v}## is what your solutions denoted by the vector ##\mathbf{N}##. [/QUOTE]
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When to use the Jacobian in spherical coordinates?
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