Heavyside’s operational calculus vs. transforms

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Frabjous
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Are there features of operational calculus (or operator methods) that are advantageous over transforms for DE? I know that the techniques are closely related.
 
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I’ve been poking around all day. I think I have convinced myself that there are situations where operation calculus would be useful.

I even found a great quote:
“Even Cambridge mathematicians deserve justice” -O. Heavyside
 

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