In the field of applied mathematics, one often uses the approach described below:
I) Formulate a mathematical model of the situation, for instance by finding the governing equations of the problem.
II) Solve the equations by using some suitable analytic or numeric method.
III) Go back and verify that the obtained solution is consistent with the experimental observations.
Remark: We can get further assistance in the first step by using:
a) Dimensional analysis.
We will examine these two methods in the following parts.