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Difference in differential and partial differential 
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#1
Feb1508, 04:04 PM

P: 422

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)...



#2
Feb1508, 04:26 PM

P: 813

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



#3
Feb1508, 04:35 PM

P: 422

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



#4
Feb1508, 04:46 PM

P: 813

Difference in differential and partial differential
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 


#5
Feb1608, 09:16 AM

P: 422

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?



#6
Feb1608, 01:48 PM

P: 813

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. 


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