I've read that book, it is very good. A fantastic story/subject, though probably not for a general audience, just those interested in a detailed history of Heaviside and his work. It's nice to see a well-written 'technical' history book - so often such books are written by someone who doesn't really understand the subject - this is an exception.

You are mistaken about Laplace Transforms - Heaviside used a different method which was rather ad-hoc - sometimes it works, sometimes not. For the same problems, we now use Laplace Transforms instead, because they are better/cleaner.