Transversal vibrations in a 2D membrane

In order to develop mathematical models, it is necessary to get a basic knowledge about the implementation of high and middle programming languages. A mathematical model for transversal vibrations in a bi-dimensional membrane is proposed and explained using basic Newton's laws and by solving the resulting partial differential equation that describes the membrane's behaviour with analytical and numerical classic methods such finite differences and separation of variables. The calculation of approximations to the solution is made by using microcomputers and applying FORTRAN90-language-developed software that makes the numerical calculations. Animations of the membrane's evolution through time are shown by using Mathematica (R) high level software. This allows students, scientists or engineers, to have a better approach of the use of specifically FORTRAN90 and Mathematicac (R) software, and understanding the solution for the partial differential equation as well as of the evolution of the phenomena for a rectangular membrane. Besides solving the equation, this work develops software and provides information to be used for increasing and make faster the e-Learning of those implementations and for having a wide perspective to develop real phenomena modelling.