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/Separable_partial_differential_equation
http://www.math.ubc.ca/~feldman/m267/separation.pdf

 

[bassplayer142]

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

 

[John Creighto]

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