This link still works: <a href="https://web.archive.org/web/20080201075132/http://myreckonings.com/wordpress/2007/12/07/heavisides-operator-calculus/" rel="nofollow">https://web.archive.org/web/20080201075132/http://myreckonin...</a>
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:<p><pre><code> x = 1
=>
x = pt
=>
1/x = (1/p) (1/t)
=>
1/x = ln(t)
=>
x = 1/ln(t)
</code></pre>
Which is ridiculous...