difference in differential and partial differential

bassplayer142

How much of a difference is there in between partial and regular differential equations. I took differentials but not the partial and I was wondering how much this restricts understanding in physics. Our physics class doesn't solve the differential equations (though some I can). Does normal first order and higher order techniques work. (cauchy euler, substitution, integrating factor)...

John Creighto

Well, an obvious difference is usually differential equations have a finite number of states while partial differential equations have an infinite number of states.

bassplayer142

That makes sense to me. I'm really interested in the mathmatical techniques to solve them. But what you said does make sense.

John Creighto

Well, the wave equation can be solved via separation of variables:

http://en.wikipedia.org/wiki/Separab...ntial_equation
http://www.math.ubc.ca/~feldman/m267/separation.pdf

bassplayer142

Can all equations be solved using regular diffeq if and only if the derivative is only of one variable. Say that there isn't two seperate variables being differentiated?

John Creighto

There are conditions that must be satisfied for the existence of differential equations.
http://en.wikipedia.org/wiki/Picard-...C3%B6f_theorem

Now if a solution exists, solving it is another matter. Some systems such as discrete systems are more practical to represented in terms of difference equations then differential equations.