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

hartnn
 one year 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
 one year 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
 one year 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
 one year 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
 one year ago
Best ResponseYou've already chosen the best response.2Have you tried the partial derivatives ?

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

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

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

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

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

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

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

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

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

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

nipunmalhotra93
 one year 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
 one year 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
 one year ago
Best ResponseYou've already chosen the best response.1"replace x by ziy" what would df/dx convert to ??

Miracrown
 one year 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
 one year ago
Best ResponseYou've already chosen the best response.0df/dx=3z^2i2z

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

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

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

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

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

hartnn
 one year 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
 one year ago
Best ResponseYou've already chosen the best response.0@hartnn yea yea that'll work too...

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

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

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

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

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