Definition Of Partial Differential EquationsThis section presents some basic definitions regarding Partial Differential Equations.
The partial derivative of a function f with respect to the variable x is usually denoted by
Partial Differential Equations
If a function is solution for
Example - Simple example
The Solution Of Partial Differential Equations
- It will be clear from these examples that the methods used for the solution of ordinary differential equations will not apply to Partial Differential Equations without considerable modification. A general discussion of partial differential equations is both difficult and lengthy. The objective in the following examples is to show some of the substitutions which may be used in the solution of the types of equation which occur in Scientific and engineering applications.
Example - Exponential Solution
In the treatment of ordinary linear equations it was found that the use of exponentials was useful. This suggests as a trial solution. Substituting in the differential equation:
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