Jacobian and area differential

[Win_odd Dhamnekar]

How to answer this question? I have posted it on math stack exchange one month ago but it still remained unanswered.

Jacobian and area differential

A transformation T (u, v) is said to be a conformal transformation if its Jacobian matrix preserves angles between tangent vectors. Consider that the vector $\langle 0,1\rangle$ is parallel to the ...

math.stackexchange.com

 

[Deleted member 4993]

That is probably because you have not shown any "work" and we do not know where to begin to help you!!

 

[topsquark]

That, and perhaps some errors such as calling [math]r = \pi[/math] and [math]r = \theta[/math] lines. (They are a circle and spiral, respectively.)

-Dan

 

[Win_odd Dhamnekar]

That, and perhaps some errors such as calling [math]r = \pi[/math] and [math]r = \theta[/math] lines. (They are a circle and spiral, respectively.)

-Dan

Hello,
But i have reproduced this question exactly the same as given on internet.

 

[topsquark]

Then it isn't your mistake. But it's still wrong and may be putting people off from answering. I'm just guessing. Unfortunately I can't help you with your question myself.

-Dan

 

[Win_odd Dhamnekar]

Then it isn't your mistake. But it's still wrong and may be putting people off from answering. I'm just guessing. Unfortunately I can't help you with your question myself.

-Dan

Hello, In my PDF, the vector parellel to the line \(\displaystyle \displaystyle r= \pi\) is \(\displaystyle \displaystyle \langle 1,0 \rangle.\) but on internet it is \(\displaystyle \langle 0,1 \rangle.\) Does it make any difference? Please visit this link The Jacobian question number 41,42 and 43.

 

[Dr.Peterson]

Please show us that internet source, and your pdf, so we can see what's really going on in the problem.

It appears that they are thinking of transforming from (r, θ) as Cartesian coordinates to (r, θ) as polar coordinates.

 

[Win_odd Dhamnekar]

Hello,
Please visit this linkThe Jacobian question number 41,42 and 43

 

[Deleted member 4993]

You have not yet shown us your work/thought and explained exactly why/where are you stuck?

 

[Deleted member 4993]

That, and perhaps some errors such as calling [math]r = \pi[/math] and [math]r = \theta[/math] lines. (They are a circle and spiral, respectively.)

-Dan

I am assuming they are referring to conglomeration of points connected in one dimension as a line (as opposed to straight-line or curve).