Differential Equations

[peacecalc]

Hello friends,

what is a differential equation?

Maybe it is a good idea to explain the mathematical idea of this with an comparison of "normal" equation.

An equation is an expression which can be evaluated as true or false. If there is a variable situated in the equation, you have to assign a value to that variable and then you can evaluate wether it's true or not.

In a differential equation you are not looking for one value (or a lot of values) which satisfies your equation, you are looking for a function, which satisfies the equation. That is a more complicate situation.

An example: f'(x) = g(x), you are looking for a function where f : x |--> f(x) with the condition f'(x) = g(x). So with a differential equation you are looking not only for values, your are looking for every x value a corresponding value f(x) with the condition of a defined change "rate" f'(x).

If there exist no analytical solution for such an equation, you can "solve" (means here finding for every x value a corresponding value f(x) with the condition of a defined change "rate" f'(x) ) it by numerical calculation in little steps.

The analytical or numerical way of finding that function f is the integration.
I hope that helps to get the main idea of the fascinating topic in mathematics.

Sincerely peacecalc