Talk:Separation of variables
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Before:
- In mathematics, separation of variables is any of several methods of solving ordinary and partial differential equations, in which algebra allows to re-write an equation so that each of two variables occurs on only side of the equation and the other does not.
After:
- In mathematics, separation of variables is any of several methods for solving ordinary and partial differential equations, in which algebra allows one to re-write an equation so that each of two variables occurs on only one side of the equation.
I have a problem with this edit. Suppose the equation is
This trivially becomes
Then clearly each of the two variables occurs on only one side of the equation. But the variables have not been separated! Michael Hardy 02:43, 9 February 2006 (UTC)
- {{sofixit}}? I edited the copy of that sentence, not the content. It seems to me that neither the before nor the after clearly defines separation of variables. Starwiz 17:02, 18 February 2006 (UTC)
[edit] Why can solutions to PDEs be written as sums of products?
In the article it is stated that solutions to PDEs can be expressed as a sum in which each term is a product of several functions which each depend on only one variable. For example, given the equation
we are told to assume that the solution can be written
This should be explained. The explanation is really quite simple. Since any function
Ψ(x,y) can be expressed as a Fourier series (assuming a compact domain where x and y run from zero to one) we have
which is a sum of products of functions depending on x and y independently.
This explanation should be given in the article.
128.36.90.229 03:15, 24 February 2007 (UTC)
