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# In layman's terms what is a partial differential equation? watch

1. This is just personal research; nothing to do with school. I understand what a differential equation is, but haven't got a clue as to what a partial differential equation is. The only explanations I could find online were far too complicated to me to understand. Can anyone help me understand?!
2. If you have a (differentiable) function of several variables, then its derivative with respect to one of them is called its partial derivative with respect to that variable, and usually written (for a function of some variables including ). A partial differential equation (PDE) is just like an ordinary differential equation (ODE), but using partial derivatives and multivariate functions. One key difference between them and ordinary differential equations is that where with ODEs you produce arbitrary constants, with PDEs you get arbitrary functions of the variables that you have no information about. For example, if you have :

, where is a function of two variables, and , then the solution is given by .
3. (Original post by Derp96)
This is just personal research; nothing to do with school. I understand what a differential equation is, but haven't got a clue as to what a partial differential equation is. The only explanations I could find online were far too complicated to me to understand. Can anyone help me understand?!
If you want to do a bit more research I would recommend going on wikipedia and searching:

transport equation
wave equation
heat equation

This will give you a bit of physical interpretation of not only what PDEs are but what they represent
4. (Original post by Derp96)
This is just personal research; nothing to do with school. I understand what a differential equation is, but haven't got a clue as to what a partial differential equation is. The only explanations I could find online were far too complicated to me to understand. Can anyone help me understand?!
Quite simply a partial differential equation contains partial derivatives, which are derivatives of multivariable funcitons. (Functions with two or more variables) i.e. f(x,y) ..

In comparison to the differential equations you've encountered which are called Ordinary Differential Equations, which are differential equations which contain derivatives of a single variable function i.e. f(x)

Partial Differential equations are used widely to model multi dynamic systems,with many applications in physics

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