If $f(x,y) = u(x,y)+ iv(x,y)$ and $z = x+iy$ where $dz = dx+idy$, then the total derivative of $f$ wrt $z$
Clash Royale CLAN TAG#URR8PPP
up vote
0
down vote
favorite
If $f(x,y) = u(x,y)+ iv(x,y)$ and $z = x+iy$ where $dz = dx+idy$, then the total derivative of $f$ wrt $z$ is $$dfracdfdz = dfracdfdxcdot dfracdxdz+dfracdfdy cdot dfracdydz =dfrac12(dfracdfdx-idfracdfdy)$$
The first equality i understand, however how do you get the second equality?
I need to know as I need to find further for $$dfracdfdoverlinez, dfracdoverlinefdoverlinez$$
complex-analysis
add a comment |Â
up vote
0
down vote
favorite
If $f(x,y) = u(x,y)+ iv(x,y)$ and $z = x+iy$ where $dz = dx+idy$, then the total derivative of $f$ wrt $z$ is $$dfracdfdz = dfracdfdxcdot dfracdxdz+dfracdfdy cdot dfracdydz =dfrac12(dfracdfdx-idfracdfdy)$$
The first equality i understand, however how do you get the second equality?
I need to know as I need to find further for $$dfracdfdoverlinez, dfracdoverlinefdoverlinez$$
complex-analysis
$x=frac z+overset - z 2$,$y=frac z-overset - z 2i$
â Kavi Rama Murthy
Aug 24 at 9:04
Oh, so you treat $overlinez$ as a constant when you differentiate too? Thanks
â ilovewt
Aug 24 at 9:05
add a comment |Â
up vote
0
down vote
favorite
up vote
0
down vote
favorite
If $f(x,y) = u(x,y)+ iv(x,y)$ and $z = x+iy$ where $dz = dx+idy$, then the total derivative of $f$ wrt $z$ is $$dfracdfdz = dfracdfdxcdot dfracdxdz+dfracdfdy cdot dfracdydz =dfrac12(dfracdfdx-idfracdfdy)$$
The first equality i understand, however how do you get the second equality?
I need to know as I need to find further for $$dfracdfdoverlinez, dfracdoverlinefdoverlinez$$
complex-analysis
If $f(x,y) = u(x,y)+ iv(x,y)$ and $z = x+iy$ where $dz = dx+idy$, then the total derivative of $f$ wrt $z$ is $$dfracdfdz = dfracdfdxcdot dfracdxdz+dfracdfdy cdot dfracdydz =dfrac12(dfracdfdx-idfracdfdy)$$
The first equality i understand, however how do you get the second equality?
I need to know as I need to find further for $$dfracdfdoverlinez, dfracdoverlinefdoverlinez$$
complex-analysis
asked Aug 24 at 9:02
ilovewt
883316
883316
$x=frac z+overset - z 2$,$y=frac z-overset - z 2i$
â Kavi Rama Murthy
Aug 24 at 9:04
Oh, so you treat $overlinez$ as a constant when you differentiate too? Thanks
â ilovewt
Aug 24 at 9:05
add a comment |Â
$x=frac z+overset - z 2$,$y=frac z-overset - z 2i$
â Kavi Rama Murthy
Aug 24 at 9:04
Oh, so you treat $overlinez$ as a constant when you differentiate too? Thanks
â ilovewt
Aug 24 at 9:05
$x=frac z+overset - z 2$,$y=frac z-overset - z 2i$
â Kavi Rama Murthy
Aug 24 at 9:04
$x=frac z+overset - z 2$,$y=frac z-overset - z 2i$
â Kavi Rama Murthy
Aug 24 at 9:04
Oh, so you treat $overlinez$ as a constant when you differentiate too? Thanks
â ilovewt
Aug 24 at 9:05
Oh, so you treat $overlinez$ as a constant when you differentiate too? Thanks
â ilovewt
Aug 24 at 9:05
add a comment |Â
active
oldest
votes
active
oldest
votes
active
oldest
votes
active
oldest
votes
active
oldest
votes
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f2892916%2fif-fx-y-ux-y-ivx-y-and-z-xiy-where-dz-dxidy-then-the-total%23new-answer', 'question_page');
);
Post as a guest
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
$x=frac z+overset - z 2$,$y=frac z-overset - z 2i$
â Kavi Rama Murthy
Aug 24 at 9:04
Oh, so you treat $overlinez$ as a constant when you differentiate too? Thanks
â ilovewt
Aug 24 at 9:05