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Post by Admin on Jan 4, 2019 17:37:33 GMT
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Post by telemeter on Apr 2, 2020 20:00:10 GMT
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Post by Admin on Apr 6, 2020 16:56:47 GMT
telemeter
This doesn't seem right to me.
How do you justify writing
$\nabla_z=J\nabla_w$
And then I don't follow your first step:
$\displaystyle\nabla_z=J\nabla_w\Longrightarrow \nabla_z=\binom{\partial_xu}{\partial_yu}\partial_u+\binom{\partial_xv}{\partial_yv}\partial_v$
Also comparing line 1 and the last line would mean that
$\displaystyle J=\binom{\partial_xu}{-\partial_xv}$ which doesn't seem right.
Vasco
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Post by Admin on Apr 7, 2020 8:07:45 GMT
telemeter
This can be resolved by noting that your $J$ is not the same $J$ as that on page 193 but instead is
$\displaystyle J_1=\binom{\partial_xu~~\partial_xv}{\partial_yu~~\partial_yv}$
This is what you get if you use the chain rule to derive the first line of your derivation.
Vasco
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Post by telemeter on Apr 8, 2020 8:11:54 GMT
Vasco
Yes, sorry . The form of J I used (automatically) is what I am used to from other maths and physics texts. I shouldn't have referenced that Needham introduced J in the text without noting the alternative presentation. I'll amend the note accordingly.
telemeter
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