Initial conditions, generalized functions, and the laplace transform troubles at the origin

The unilateral Laplace transform is widely used to analyze signals, linear models, and control systems, and is consequently taught to most engineering undergraduates. In our courses at MIT in electrical engineering and computer science, mathematics, and mechanical engineering, we have found some significant pitfalls associated with teaching students to understand and apply the Laplace transform. We have independently concluded that one reason students find the Laplace transform difficult is that there is significant confusion present in many of the standard textbook presentations of this subject, in all three of our disciplines