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# Cauchy-Riemann equation polar form

Maths and statistics discussion, revision, exam and homework help.

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1. Cauchy-Riemann equation polar form
I couldn't find any book discussing all of this.

================================ ===================
U+jV=f(x+jy) W=f(z)

Ux=Vy
Uy= -Vx
jWx=Wy <--Cauchy-Riemann equation

Uxx+Uyy=0
Vxx+Vyy=0 <--harmonic condition

================================ ===================
U+jV=f(rcjs\thetha) W=f(z)

<--Cauchy-Riemann equation

?? ??
?? ?? <--harmonic condition??

================================ ===================
RcjsB=f(x+jy) W=f(z)

RBy = Rx
RBx= -Ry
jWx=Wy <--Cauchy-Riemann equation

Rxx?? Ryy??
Byy?? Bxx?? <--harmonic condition??

================================ ===================
RcjsB=f(rcjs\theta) W=f(z)

<--Cauchy-Riemann equation

?? ??
?? ?? <--harmonic condition??
Last edited by BookInquiry; 18-05-2012 at 03:55.
2. Re: Cauchy-Riemann equation polar form
Do you have a question?
3. Re: Cauchy-Riemann equation polar form
Most harmonic conditions of them are not known.
4. Re: Cauchy-Riemann equation polar form
So you want to write the Laplace equation in polar coordinates?

5. Re: Cauchy-Riemann equation polar form
Are they related? You must have worked with some (books, lecture notes or internet materials) which make you master the topics. Could you suggest your choice to me? I want to follow your track to study.
6. Re: Cauchy-Riemann equation polar form
Any good calculus book will talk about change of variables. I don't know one to recommend off the top of my head I am afraid.

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Last updated: May 19, 2012
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