

Heaviside’s Operator Calculus - Rod
http://myreckonings.com/wordpress/2007/12/07/heavisides-operator-calculus

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jibiki
Is there a way to make the operator calculus rigorous? Because it's not at all
clear which operations are allowed. If we naively used the sort of operations
Heaviside used, we could conclude (where p is the operator d/dt) that:

    
    
      x = 1
      =>
      x = pt
      =>
      1/x = (1/p) (1/t)
      =>
      1/x = ln(t)
      =>
      x = 1/ln(t)
    

Which is ridiculous...

~~~
Rod
If _x_ is a function, what does _1/x_ mean? The inverse of operator _p_ is
indeed _1/p_ (assuming that the integrator has zero initial condition) but let
us not start inverting everything at will ;-)

~~~
jibiki
But clearly some spooky inversion is allowed, e.g., writing:

    
    
      v = Lpi
      =>
      v/i = Lp
    

I don't even know what that means!

~~~
Rod
Uhmmm, shouldn't the operator _p_ be operating on some function? I don't know
what _v/i_ means either, but it looks like an operator to me: you apply it to
function _i_ and you obtain _v_ , LOL.

This stuff is trippy!

