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raheen
Group Title
Find the holomorphic function f(x+iy) such that Re f(x+iy)= cosh(3y)sin(3x) and f(0)=0
 3 years ago
 3 years ago
raheen Group Title
Find the holomorphic function f(x+iy) such that Re f(x+iy)= cosh(3y)sin(3x) and f(0)=0
 3 years ago
 3 years ago

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hahd Group TitleBest ResponseYou've already chosen the best response.0
ugh i havent taken calc yet so i cant do this
 3 years ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.3
cauchy reimann yes?
 3 years ago

raheen Group TitleBest ResponseYou've already chosen the best response.0
yes satellite
 3 years ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.3
so the derivative of this wrt x must be the derivative of the imaginary part wrt y right? the derivative is \[3\cos(3x)\cosh(3y)\] integrate wrt y and get \[\cos(3x)\sinh(3y)\] i think.
 3 years ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.3
it's been a while. am i on the right track?
 3 years ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.3
you also need the partial wrt y is minus the partial wrt x of the imaginary part. if we are lucky it already is oh and you also need that f(0)=0 i forgot the +C when i integrated
 3 years ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.3
how to you like that? i miracle! it works
 3 years ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.3
so i guess unless i totally screwed this up the answer is \[f(x+iy)=\cosh(3y)\sin(3x)+\cos(3x)\sinh(3y)\]
 3 years ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.3
think we lost raheen maybe he will be back
 3 years ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.3
rather \[f(x+iy)=\cosh(3y)\sin(3x)+i\cos(3x)\sinh(3y)\]
 3 years ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.3
i forgot the i part
 3 years ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.3
@raheen look ok?
 3 years ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.3
it does not come with a money guarantee because it has been several years but i think it looks good. you can check cauchy reimann equations for this and see if they work
 3 years ago

raheen Group TitleBest ResponseYou've already chosen the best response.0
satellite you are about to reach , great work I think you did how about using the 2 conditions of CR then you need to integrate and don forget to find the constant
 3 years ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.3
well i integrated wrt y and got the answer. then i checked that the second equation and it worked. and by inspection you can see that \[f(0)=0\]
 3 years ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.3
i mean if the CR equations are going to work, then after i take the derivative wrt x and integrate wrt y , then the second condition \[\frac{\delta u}{\delta y}=\frac{\delta v}{\delta x}\] had better work or else we are screwed. both conditions must hold. but in any case i checked and they do
 3 years ago

raheen Group TitleBest ResponseYou've already chosen the best response.0
that's so great satellite, thank you.
 3 years ago

Zarkon Group TitleBest ResponseYou've already chosen the best response.2
the only thing I would add is that when you integrated with respect to y you don't get C you get some function of x
 3 years ago

raheen Group TitleBest ResponseYou've already chosen the best response.0
Zarkon, thank you, you are right it's C(x)
 3 years ago

Zarkon Group TitleBest ResponseYou've already chosen the best response.2
It doesn't look like it will change the final answer though
 3 years ago
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