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☖ Forums → Discussion Forum → A tasty maths problem for you to chew on
A tasty maths problem for you to chew on
2008-07-19, 5:48 AM #1
Okay, I know quite a few of you are mathematically inclined so I have a boggle that I've been struggling with for hours.

I need to find the real part of arcsin(z^2) where z=x+iy. This quantity describes the flow of a fluid around a corner, if you're interested.

I've tried putting everything into exponentials (that's the usual trick that makes all this easier), but I still can't separate real and imaginary parts. I've tried expanding, but that was a very long and tedious process and I'd only get a very approximate answer. I'm using a numerical approximation for now, but I really do need some analytic answer so I can see what the function looks like.

Help me Massassi, you're my only hope!
"The trouble with the world is that the stupid are cocksure and the intelligent are full of doubt. " - Bertrand Russell
The Triumph of Stupidity in Mortals and Others 1931-1935
2008-07-19, 9:26 AM #2
Unlike most of massassi, I fail profusely at math.
"They're everywhere, the little harlots."
-Martyn
2008-07-19, 9:49 AM #3
I'll pull an xkcd and suggest that you try logarithms.
And when the moment is right, I'm gonna fly a kite.
2008-07-19, 10:05 AM #4
Have you tried logarithms?
2008-07-19, 10:47 AM #5
I'll try and put it into mathematica. I'll get back to you here.
2008-07-19, 10:48 AM #6
Wouldn't a Laplace Transform work perfectly there?
"Flowers and a landscape were the only attractions here. And so, as there was no good reason for coming, nobody came."
2008-07-19, 10:59 AM #7
Hey! I have no idea in regards to this problem, but I just learned about laplace transforms. Or I was supposed to, and instead I daydreamed...but I'm supposed to know that! Cool!
Warhead[97]
2008-07-19, 12:51 PM #8
42.
2008-07-19, 1:34 PM #9
Originally posted by gbk:
I'll pull an xkcd and suggest that you try logarithms.


I can't find this xkcd :(

[Edit: never mind, wow. As soon as I posted that I did a random comic and it came up. Holy crap.

http://xkcd.com/451/

]
一个大西瓜
2008-07-19, 1:52 PM #10
Originally posted by Bobbert:
Wouldn't a Laplace Transform work perfectly there?

Uh, he is not solving a differential equation, so it might not be that useful.

Originally posted by gbk:
I'll pull an xkcd and suggest that you try logarithms.

Though this is obviously a joke, it might be worth looking at complex logarithms (see http://mathworld.wolfram.com/InverseSine.html for the derivation of the inverse sine using a complex logarithm). Polar coordinates are your friend.
[This message has been edited. Deal with it.]
2008-07-19, 3:03 PM #11
Maxima did not like it too much:

[http://i33.tinypic.com/2nh0upk.png]
[This message has been edited. Deal with it.]
2008-07-19, 3:14 PM #12
You people make me feel stupid. If I even had to look at a math problem like that for more than five seconds I'd just shoot myself. :suicide:
Democracy: rule by the stupid
2008-07-19, 5:51 PM #13
I tried for about 30 minutes to solve this damn thing...ggrr

about 10 pages of paper later and about 3-4 different approaches I gave up, it's the weekend dammit.
People of our generation should not be subjected to mornings.

Rbots
2008-07-19, 6:52 PM #14
Code: 
import cmath

def doofer(z):
    return cmath.asin(z*z)

doofer(complex(x,y))


No, I don't have a proper answer.
Detty. Professional Expert.
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2008-07-19, 7:39 PM #15
I asked a friend about this who is good with math. This is what he got.
Attachment: 19756/Answer.jpg (35,423 bytes)

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