In this chapter we introduce the Laplace transformation as a tool for handling several types of problems. It also serves as a model for the development of other integral transformations. The technique is introduced by first treating a problem in ordinary differential equations. This is followed by a problem in partial differential equations. Next, some of the basic elementary properties of the transformation are developed. A number of examples are included in order to illustrate the applications of these working tools. In particular, these tools are applied to various problems in ordinary differential equations, partial differential equations, and integral equations, as well as in other situations.
KeywordsPartial Differential Equation Partial Fraction Laplace Transformation Inversion Formula Unit Step Function
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