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hartnn
Group Title
f(z)=(x^33xy^2+2xy)+ i(3x^2 yx^2+y^2y^3) is analytic, find \(f^' (z)\) & f(z) in terms of z
 4 months ago
 4 months ago
hartnn Group Title
f(z)=(x^33xy^2+2xy)+ i(3x^2 yx^2+y^2y^3) is analytic, find \(f^' (z)\) & f(z) in terms of z
 4 months ago
 4 months ago

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hartnn Group TitleBest ResponseYou've already chosen the best response.1
Milne Thompson Method ?
 4 months ago

hartnn Group TitleBest ResponseYou've already chosen the best response.1
w=(x^33xy^2+2xy)+ i(3x^2 yx^2+y^2y^3 ) what next ? would i find dw/dx or dw/dy ?
 4 months ago

hartnn Group TitleBest ResponseYou've already chosen the best response.1
i had done similar problem, where i found dw/dx and then plugged in x= z, y= 0 will this work here ?
 4 months ago

hartnn Group TitleBest ResponseYou've already chosen the best response.1
because with that i am getting the complex term too, with the 'i' ...... and if i try x=0, y=z (can i do this ?) then i get f'(z) as z^2 z^3 correct or not ?
 4 months ago

RyGuy Group TitleBest ResponseYou've already chosen the best response.1
idek why i clicked on this. im am sooooo not smart enough for this lol.
 4 months ago

Miracrown Group TitleBest ResponseYou've already chosen the best response.2
Have you tried the partial derivatives ?
 4 months ago

hartnn Group TitleBest ResponseYou've already chosen the best response.1
dw/dx or dw/dy are partial derivatives only....
 4 months ago

hartnn Group TitleBest ResponseYou've already chosen the best response.1
what next after i find dw/dx (or dw/dy) ?
 4 months ago

nipunmalhotra93 Group TitleBest ResponseYou've already chosen the best response.0
find partial derivative of f wrt x
 4 months ago

Miracrown Group TitleBest ResponseYou've already chosen the best response.2
right, we need to find both of those first
 4 months ago

Miracrown Group TitleBest ResponseYou've already chosen the best response.2
What would df/dx be ?
 4 months ago

hartnn Group TitleBest ResponseYou've already chosen the best response.1
f(z)=(x^33xy^2+2xy)+ i(3x^2 yx^2+y^2y^3) df/dx = (3x^2 3y^2 +2y) + i (6xy 2x)
 4 months ago

hartnn Group TitleBest ResponseYou've already chosen the best response.1
df/dy = (6xy +2x) + i(3x^2 +2y3y^2)
 4 months ago

nipunmalhotra93 Group TitleBest ResponseYou've already chosen the best response.0
replace x by ziy
 4 months ago

nipunmalhotra93 Group TitleBest ResponseYou've already chosen the best response.0
and all the y terms will cancel out... leaving only z terms (as it is analytic)
 4 months ago

Miracrown Group TitleBest ResponseYou've already chosen the best response.2
df/dx is good :)
 4 months ago

nipunmalhotra93 Group TitleBest ResponseYou've already chosen the best response.0
do that in df/dx
 4 months ago

hartnn Group TitleBest ResponseYou've already chosen the best response.1
i used milne thompson method for similar type of problem before...i would like to try same thing...
 4 months ago

Miracrown Group TitleBest ResponseYou've already chosen the best response.2
df/dy is good also
 4 months ago

hartnn Group TitleBest ResponseYou've already chosen the best response.1
basically i plugged in x=z and y=0 and things sorted out....in this problem, it doesn't..
 4 months ago

nipunmalhotra93 Group TitleBest ResponseYou've already chosen the best response.0
@Miracrown it is, but it'll make it a little more complicated. using f'(z)=df/dx is more straightforward,
 4 months ago

hartnn Group TitleBest ResponseYou've already chosen the best response.1
so my final answer should be z^2 (zi) ?
 4 months ago

Miracrown Group TitleBest ResponseYou've already chosen the best response.2
looks like for df/dy , the "i" component is minus
 4 months ago

nipunmalhotra93 Group TitleBest ResponseYou've already chosen the best response.0
@hartnn I'm not really familiar with that method. But I think using the substitution x=ziy in df/dx is fine too isn't it?
 4 months ago

Miracrown Group TitleBest ResponseYou've already chosen the best response.2
The document I am looking at for this method, writes x^3  3xy^2 + 2xy as u(x,y)
 4 months ago

hartnn Group TitleBest ResponseYou've already chosen the best response.1
"replace x by ziy" what would df/dx convert to ??
 4 months ago

Miracrown Group TitleBest ResponseYou've already chosen the best response.2
3x^2 y  x^2 + y^2  y^3 is written as v(x,y)
 4 months ago

hartnn Group TitleBest ResponseYou've already chosen the best response.1
share the doc please ?
 4 months ago

nipunmalhotra93 Group TitleBest ResponseYou've already chosen the best response.0
df/dx=3z^2i2z
 4 months ago

hartnn Group TitleBest ResponseYou've already chosen the best response.1
wot? you can't just plug in that on right side only ? can u ?
 4 months ago

Miracrown Group TitleBest ResponseYou've already chosen the best response.2
df/dz = ux(x,y) + ivx(x,y) , where
 4 months ago

Miracrown Group TitleBest ResponseYou've already chosen the best response.2
ux is the partial derivative of u with respect to x and v is the partial derivative of v with respect to x
 4 months ago

nipunmalhotra93 Group TitleBest ResponseYou've already chosen the best response.0
See we know that df/dz=df/dx right? (the one on the right is a partial one) So, once you've found the one on the right (using partial differentiation, just replace x by ziy as x+iy=z is already known)
 4 months ago

Miracrown Group TitleBest ResponseYou've already chosen the best response.2
then, vx(x,y) =  uy(x,y)
 4 months ago

nipunmalhotra93 Group TitleBest ResponseYou've already chosen the best response.0
I just checked it the answer is f'(z)=df/dx=3z^2i2z
 4 months ago

hartnn Group TitleBest ResponseYou've already chosen the best response.1
please wait
 4 months ago

Miracrown Group TitleBest ResponseYou've already chosen the best response.2
http://www.sciencedirect.com/science/article/pii/B9780080169392500214
 4 months ago

hartnn Group TitleBest ResponseYou've already chosen the best response.1
i didn't know the answer, but after @klimenkov posted that screenshot, i tried plugging in x=z and y=0
 4 months ago

nipunmalhotra93 Group TitleBest ResponseYou've already chosen the best response.0
@hartnn yea yea that'll work too...
 4 months ago

Miracrown Group TitleBest ResponseYou've already chosen the best response.2
so, basically, where we have df/dx , we input z for "x" and 0 for "y" , as you mentioned nd, that should work out .
 4 months ago

nipunmalhotra93 Group TitleBest ResponseYou've already chosen the best response.0
@hartnn It's essentially the same thing I just made it more complicated lol sorry about that :P
 4 months ago

hartnn Group TitleBest ResponseYou've already chosen the best response.1
sorry, my internet got disconnected.... did i do it correctly ?? or i integrated it one more time unnecessarily ???
 4 months ago

hartnn Group TitleBest ResponseYou've already chosen the best response.1
i should get f(z) as z^2(zi) right ?
 4 months ago

klimenkov Group TitleBest ResponseYou've already chosen the best response.1
Did you try to divide \(f(z)\) by \(x+ iy\) ?
 4 months ago

hartnn Group TitleBest ResponseYou've already chosen the best response.1
thats dw/dx is same as f'(z) and after i integrate it i directly get f(z) right ?
 4 months ago

hartnn Group TitleBest ResponseYou've already chosen the best response.1
why would i do that division ?
 4 months ago

nipunmalhotra93 Group TitleBest ResponseYou've already chosen the best response.0
@hartnn yes f(z)=z^3i z^2.
 4 months ago

hartnn Group TitleBest ResponseYou've already chosen the best response.1
Thanks all :) @klimenkov @nipunmalhotra93 @Miracrown
 4 months ago
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