What Heaviside did was the sort of fast-and-loose syntactic manipulation that makes mathematicians queasy and/or indignant . He treats the derivative operator just like it were an ordinary number X. And then he infers that 1/X must mean integration.
Compare to the naive argument for the positive integers 1+2+3+... summing to -1/12 that gets mathbabe's panties in a twist .
More details in Ch. 10 of Nahin's book.
The book doesn't pull any punches with the math nor the physics because equations are provided for the discerning reader whenever the discussion turns technical, which is every other page. But also on every other page is a picture of 19th century people and placesthat helps flesh out the dramatic race for electrical power.
Worth mentioning is the whole chapter given to dramatizing Heaviside's arch-nemesis, a Mr. William Henry Preece who's Chief Engineer at the British Post Office. At the end of the chapter, Nahin repeats Preece's analysis of the viability of residential electrical lighting, a problem then known as 'subdivision of light', and his conclusion that Edison is doomed to fail. The error turns out to be taking the wrong limits.
I can't resist including this excerpt: "It is almost impossible to understand why the 'subdivision of light' was so difficult to understand a mere century ago. Perhaps a century hence somebody will write the same about our present confusion over time-travel!"
Does Prof. Nahin's biography mention PC Brock?
A good library should have the biography.
Like luos (https://news.ycombinator.com/item?id=8798638), I've always liked to pretend to my students that it is so named because there is a heavy side and a light side. (Of course, I do tell them it's a joke!)
EDIT: Actually, I realise that I'm not sure why it is so kick-ass. Is it the idea of having a simple concept named after you? If so, then I have respectfully to assert that nothing beats the Kronecker delta (https://en.wikipedia.org/wiki/Kronecker_delta). (Perhaps Abelian groups (https://en.wikipedia.org/wiki/Abelian_group) come close.)
If anyone can confirm this it would be extremely interesting.
definitions do not come first, but later is a great quote, well-put.
Yeah, looks like his biography is a crash course in electrical engineering
I didn't know this by that name http://en.wikipedia.org/wiki/Telegrapher%27s_equations (just "transmission line equation" I guess the name is an anachronism)