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#1 2006-05-12 21:45:16
- renjer
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- Registered: 2006-04-29
- Posts: 50
Proving an Equation when the function is unknown
Now here's a problem I have, it's often that I know the function of f but in this particular question, I do not know what f is at all. Is it okay if I let f be a function of my choice and prove it from there?
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#2 2006-05-12 22:01:57
- Jai Ganesh
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- Registered: 2005-06-28
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Re: Proving an Equation when the function is unknown
renjer,
It is given w=f(x,y), x=rcosθ and y=rsinθ
and you are asked to show
You are right, w is given as a function of x and y, but the function is not defined
It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.
Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.
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#3 2006-05-12 23:25:50
- George,Y
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- Registered: 2006-03-12
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Re: Proving an Equation when the function is unknown
IT IS A GOOD QUESTION!!!
It's a question about coords, combination of derivatives, and vector calculus altogether.
It's about expressing the original combination of derivatives in another co-ords, usually orthogonal curvy ones. For example, polar co-ords are curvy, and dr and dθ at any given point are orthogonal to each other.
It's usually explained in a vector calculus book or a calculus book for physicians. Untill now, I haven't got a satisfactory explaination for this kind of transfer in any books.
However, I do find a particular solution for your coords and your case.
Define
After substition,
According to Chain Rule
Thus you can compute the right of your equation and use cos²θ+sin²θ=1 to prove it equates the left.
Last edited by George,Y (2006-05-12 23:39:22)
X'(y-Xβ)=0
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#4 2006-05-13 01:33:32
- renjer
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- Registered: 2006-04-29
- Posts: 50
Re: Proving an Equation when the function is unknown
I remember the chain rule telling me this:
So I'm quite unsure about your method from the chain rule onwards. Can you please explain further?
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#5 2006-05-13 01:59:16
- Jai Ganesh
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- Registered: 2005-06-28
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Re: Proving an Equation when the function is unknown
renjer,
In this link, at the bottom of the page, you would find the chain rule for partial derivatives, which I think, George has referred.
It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.
Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.
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