Difference in differential and partial differential

In summary, there is a clear difference between partial and regular differential equations, with partial differential equations having an infinite number of states while regular differential equations have a finite number of states. This can restrict understanding in physics, as some equations may require partial differential equations to solve. However, some techniques such as Cauchy-Euler, substitution, and integrating factor may still work for both types of equations. The wave equation can be solved using separation of variables, but not all equations can be solved using regular differential equations, as there are conditions that must be satisfied for their existence. Some systems may be better represented using difference equations instead of differential equations.
  • #1
bassplayer142
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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)...
 
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  • #2
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
That makes sense to me. I'm really interested in the mathmatical techniques to solve them. But what you said does make sense.
 
  • #5
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?
 
  • #6
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.
 

FAQ: Difference in differential and partial differential

What is the difference between differential and partial differential equations?

Differential equations involve functions of one or more independent variables and their derivatives, while partial differential equations involve functions of multiple independent variables and their partial derivatives.

What are some real-life applications of differential and partial differential equations?

Differential and partial differential equations are used in many fields of science and engineering to model and analyze various phenomena, such as population growth, heat transfer, and fluid dynamics.

How are differential and partial differential equations solved?

There are various techniques for solving differential and partial differential equations, including separation of variables, the method of characteristics, and numerical methods such as finite differences or finite elements.

What is the role of initial and boundary conditions in solving differential and partial differential equations?

Initial conditions specify the values of the dependent variable and its derivatives at a given starting point, while boundary conditions specify the behavior of the dependent variable at the boundaries of the domain. These conditions are essential for finding a unique solution to a differential or partial differential equation.

Can differential and partial differential equations be used to predict the future?

Yes, differential and partial differential equations can be used to make predictions about the behavior of a system over time. However, the accuracy of these predictions depends on the accuracy of the model and the quality of the initial and boundary conditions provided.

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