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Application to networks
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applicable to f(t asymptotic expansion behaviour of h(t boundary condition circuit class of functions coefficients condenser consider tho consists constant converges converges absolutely defined definition denotes derivative differential equation differentiation and integration Duhamel's integral e"at eat f(t eouation evaluate expression free line function f(t fundamental function h(t Furthermore Heaviside Hence induction infinity initial conditions initial value problems introduce inverse Laplace transform Lemma Let H(z line integral mathematical neighborhood o"zt obtain Ohm's law ooerator operational calculus operator H(p oporator origin partial fractions polynomial problem Proof prove rational operator receiving end regular operator relation resistance respect to powers result rosulting rzt h(t shifting theorem superposition tho function tho operator tion transform G(z transmission transmitting end unit function valid vanish variable wave x-axis zero