Teaching The Laplace Transform Using Diagrams

Teaching the Laplace Transform Using Diagrams
Authors: Ngo, V. and Ouzomgi, S.
College Mathematics Journal, Vol. 23, no. 4, pp. 309-312, 1992.

This article describes a method of teaching the Laplace Transform based upon the use of commutative diagrams. After presenting the Laplace Transforms of a few basic functions (such as eat, sin t, cos t, tn, etc.), this pedagogical technique employs the use of these diagrams to present basic theorems that can be used to find other, more complicated Laplace transforms and inverse Laplace transforms. These commutative diagrams themselves are squares with the original functions on the left two corners, the transformed functions on the right two corners and the original (basic function) function-transform pair on the upper two corners, the altered (modified, more complicated function) function-transform pair on the lower two corners. These diagrams can be stacked to represent combinations of the theorems to find ever more complicated Laplace transforms. The article very nicely provides the theorem on diagrammatic representation and some examples of using the diagrams. [Those who have not had any exposure to Laplace transforms before reading this article, will find the method presented in the article very easy to understand as well as useful in understanding the mathematics behind the Laplace transform.] (Summary by Ben Murphy, Pomona College '13)

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