Giving Meaning to the Circular Membrane Problem with Mathematica

Document Type

Article

Publication Date

Spring 1992

Publication Title

Mathematica in Education

Abstract

Many boundary value problems present difficulties to students of differential equations which can be alleviated through the use of Mathematica. These difficulties include computational obstacles in the method of solution as well as perceptual complications in the understanding of the solution after it is obtained. Since numerous boundary value problems lead to results that are not easily visualized or understood, very little except for an impressive formula is gained by students after hours spent on solving these complicated problems. In order to provide a better understanding of the solutions, Mathematica can be used to overcome the visual and perceptual boundaries encountered by allowing for the graphing of solutions. Also in these problems, Mathematica can be used to solve the ordinary differential equations obtained through the method of separation of variables, calculate the integrals necessary to determine coefficients, and investigate the special functions which may be involved in the solution.

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