Date of Award:


Document Type:


Degree Name:

Master of Science (MS)


Mathematics and Statistics


Joe Elich


The purpose of this paper is to present a study of different methods of solving certain boundary value problems. In particular it will be concerned with solutions by classical methods and by operational methods. Of the various operational methods that may be considered, the Laplace transformation appears to be the best be used in this paper.

In the 1951 Encyclopedia Americana Annual is this report on the activities in applied mathematics for the previous year:

Progress was made on the general problem of finding the eigenvalues of matrices and systems of differential equations. Considerable effort was also expended in seeking methods of solution for the partial differential equations of physics.

This gives an indication of the importance of this type of work at the present time. With the development of atomic energy, Jet air­planes, and guided missiles, have come many new and different boundary value problems. The solution of these problems is an important factor in the development.

The paper will include a general description of what is meant by boundary value problem, followed by some examples. These examples will be solved by classical methods and then by operational method (Laplace transformation). Then where possible, comparisons between the two methods will be made. From the study of the solutions of these examples conclusions will be drawn.