My Math Forum how can i show all analytic functions such that

 Complex Analysis Complex Analysis Math Forum

 November 29th, 2013, 10:58 AM #1 Member   Joined: Oct 2011 Posts: 40 Thanks: 0 how can i show all analytic functions such that How can I find all analytic functions f=u+iv with u(x,y)=(x^2)+(y^2) Thanks for the help. I appreciate it.
 November 29th, 2013, 11:08 AM #2 Member   Joined: Oct 2011 Posts: 40 Thanks: 0 Re: how can i show all analytic functions such that i'm asking this question.
 December 2nd, 2013, 08:47 AM #3 Math Team   Joined: Sep 2007 Posts: 2,409 Thanks: 6 Re: how can i show all analytic functions such that If you know what an analytic function is, you should know the "Cauchy-Riemann" equations. With f(z)= u(x, y)+ Iv(x, y), z= x+ iy $\dfrac{\partial u}{\partial x}= \dfrac{\partial v}{\partial y}$ $\dfrac{\partial u}{\partial y}= -\dfrac{\partial v}{\partial x}$ Since $u(x, y)= x^2+ y^2$, $\dfrac{\partial u}{\partial x}= 2x$ and $\dfrac{\partial y}{\partial v}= 2y$ so $\dfrac{\partial v}{\partial x}= -2y$ and $\dfrac{\partial v}{\partial y}= 2x$.

 Tags analytic, functions, show

 Thread Tools Display Modes Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post WWRtelescoping Complex Analysis 1 February 25th, 2014 07:53 PM mami Complex Analysis 1 November 29th, 2013 11:03 AM Juliayaho Complex Analysis 1 November 9th, 2012 08:16 AM zeraoulia Complex Analysis 3 August 26th, 2012 08:09 AM eric3353 Calculus 1 December 22nd, 2008 08:26 AM

 Contact - Home - Forums - Cryptocurrency Forum - Top