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Using differential operators to get approximate or exact solutions to linear differential equations, an example with RC circuits

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\*Sigh\* have people forgotten about Laplace transforms now ... you use them even in infinite dimensional settings properly study operator semigroups for partial differential operators to provide a proper framework.
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I don't really see why anyone would use this when we have a pretty complete theory of linear ODEs / linear DAEs. If you want to solve f(t) + af'(t)=g(t) just use the matrix exponential formula...
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Interestingly enough, this is basically identical to work Oliver Heaviside did in electrical circuits, or at least very close. The result was basically identical to using the Laplace transform for circuits.
by

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