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Provides a mathematically rigorous, yet readily accessible treatment of applications of Laplace transforms. Includes the Dirac delta function given a completely justifiable treatment in the context of the Riemann-Stieltjes integral. The Laplace transform is a wonderful tool for solving ordinary and partial differential equations and has enjoyed much success in this realm. With its success, however, a certain casualness has been bred concerning its application, without much regard for hypotheses and when they are valid. Even proofs of theorems often lack rigor, and dubious mathematical practices are not uncommon in the literature for students