Got Homework?
Connect with other students for help. It's a free community.
Here's the question you clicked on:
 0 viewing
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
 5 months ago
 5 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
 5 months ago
 5 months ago

This Question is Closed

hartnn Group TitleBest ResponseYou've already chosen the best response.1
Milne Thompson Method ?
 5 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 ?
 5 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 ?
 5 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 ?
 5 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.
 5 months ago

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

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

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

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

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

Miracrown Group TitleBest ResponseYou've already chosen the best response.2
What would df/dx be ?
 5 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)
 5 months ago

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

nipunmalhotra93 Group TitleBest ResponseYou've already chosen the best response.0
replace x by ziy
 5 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)
 5 months ago

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

nipunmalhotra93 Group TitleBest ResponseYou've already chosen the best response.0
do that in df/dx
 5 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...
 5 months ago

Miracrown Group TitleBest ResponseYou've already chosen the best response.2
df/dy is good also
 5 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..
 5 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,
 5 months ago

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

Miracrown Group TitleBest ResponseYou've already chosen the best response.2
looks like for df/dy , the "i" component is minus
 5 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?
 5 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)
 5 months ago

hartnn Group TitleBest ResponseYou've already chosen the best response.1
"replace x by ziy" what would df/dx convert to ??
 5 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)
 5 months ago

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

nipunmalhotra93 Group TitleBest ResponseYou've already chosen the best response.0
df/dx=3z^2i2z
 5 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 ?
 5 months ago

Miracrown Group TitleBest ResponseYou've already chosen the best response.2
df/dz = ux(x,y) + ivx(x,y) , where
 5 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
 5 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)
 5 months ago

Miracrown Group TitleBest ResponseYou've already chosen the best response.2
then, vx(x,y) =  uy(x,y)
 5 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
 5 months ago

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

Miracrown Group TitleBest ResponseYou've already chosen the best response.2
http://www.sciencedirect.com/science/article/pii/B9780080169392500214
 5 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
 5 months ago

nipunmalhotra93 Group TitleBest ResponseYou've already chosen the best response.0
@hartnn yea yea that'll work too...
 5 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 .
 5 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
 5 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 ???
 5 months ago

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

klimenkov Group TitleBest ResponseYou've already chosen the best response.1
Did you try to divide \(f(z)\) by \(x+ iy\) ?
 5 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 ?
 5 months ago

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

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

hartnn Group TitleBest ResponseYou've already chosen the best response.1
Thanks all :) @klimenkov @nipunmalhotra93 @Miracrown
 5 months ago
See more questions >>>
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.