Quote by I like Serena
Does Zeidler have a purpose in defining his transform in this slightly different way?
Does it make some calculation or concept easier to do or understand?
Or is he just blissfully unaware of current scientific conventions and making his own up as he goes along without any purpose?

My characterization of his transform in a previous post is not correct. There I implied that the transform was only applied to functions that were zero for values of t less than 0. In fact, his transform involves multiplying an arbitrary function by the Heaviside function first, and then applying the Fourier transform. There is no doubt that he wants the transform he is using. It is forced on him by the fact that he will apply this transform to functions related to forces that are turned on at time t = 0, i.e. are zero for times less than t = 0, but which formally have definitions that are not zero for times less than t = 0. As to why he calls it a Laplace transform, only the professor can say, and I can't reach him. The only issue in my mind when I started this investigation was that in order to write up the error for my errata page, I needed to know what the correct terminology was. Now I have found it. I appreciate all the help I got from you and others in this search.