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The Laplace transform is a wonderful tool for solving ordinary and partial differential equations, and has enjoyed much success in this realm. But with its success, a certain casualness has been bred concerning its application, without much regard for hypotheses and when they are valid. In the present text, the author brings to the subject a certain amount of mathematical correctness and makes it accessi ble to undergraduates. To this end the text addresses a number of issues which are rarely considered. Special features of the book include a justification of the Laplace Transform method for solving linear ODEs, sufficient conditions for taking the Laplace Transform of an infinite series, steady-state solutions, and a rigorous approach to the Complex Inversion Formula, to name but a few.§
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