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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
 one month ago
 one month 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
 one month ago
 one month ago

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

RyGuy Group TitleBest ResponseYou've already chosen the best response.0
idek why i clicked on this. im am sooooo not smart enough for this lol.
 one month ago

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

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

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

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

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

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

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

nipunmalhotra93 Group TitleBest ResponseYou've already chosen the best response.0
replace x by ziy
 one month 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)
 one month ago

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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