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 9 months ago
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
 9 months ago
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

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hartnn
 9 months ago
Best ResponseYou've already chosen the best response.1Milne Thompson Method ?

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

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

hartnn
 9 months ago
Best ResponseYou've already chosen the best response.1because 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 ?

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

Miracrown
 9 months ago
Best ResponseYou've already chosen the best response.2Have you tried the partial derivatives ?

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

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

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

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

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

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

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

nipunmalhotra93
 9 months ago
Best ResponseYou've already chosen the best response.0replace x by ziy

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

nipunmalhotra93
 9 months ago
Best ResponseYou've already chosen the best response.0do that in df/dx

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

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

nipunmalhotra93
 9 months ago
Best 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,

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

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

nipunmalhotra93
 9 months ago
Best 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?

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

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

Miracrown
 9 months ago
Best ResponseYou've already chosen the best response.23x^2 y  x^2 + y^2  y^3 is written as v(x,y)

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

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

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

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

nipunmalhotra93
 9 months ago
Best ResponseYou've already chosen the best response.0See 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)

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

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

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

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

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

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

nipunmalhotra93
 9 months ago
Best 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

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

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

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

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

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

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

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