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?
It is given w=f(x,y), x=rcosθ and y=rsinθ
and you are asked to show
Character is who you are when no one is looking.
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.
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)
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?