Talk:Advanced Mathematics for Engineers and Scientists/Introduction to Partial Differential Equations

Why not introduce with simple mathmatical notions: ODE's reverse ordinary differential operators, PDE's reverse partial differential operators? Fephisto 11:07, 18 December 2006 (UTC)

I'm not entirely sure what you mean by that. I have seen concepts of operators but they're rarely taught, and only for linear equations.

Ben pcc 17:20, 5 January 2007 (UTC)

To put it bluntly, this article is wrong. It confuses the distinction between PDEs and ODEs with some very specific usage of them. Whether the variables themselves are actually discrete or not in the real world, they are modelled as continuous before ANY derivative is taken (whether partial or not). When the dynamics of real world phenomena are simulated on a computer, they are made to be discrete in various ways no matter whether they are based on PDE theory or ODE theory. ODEs have no such connection to discrete entities and the real world media need not be continuous for it to have variables that can be described by a PDE.

One way in which ODEs and PDEs DO differ is that ODEs only have one independent variable and PDEs have many. You use PDEs to effectively turn multivariate systems into multiple ODEs each of which treats all variables, except one, as constant. 86.5.179.220 (discuss) 20:17, 27 January 2012 (UTC)