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The Laplace Transformation
Properties of Transforms
6 other sections not shown
algebraic amplifier amplitude analytic analytic function anode applied voltage approaches infinity approaches zero branch point capacitance capacitor chapter circle circuit of Fig circuit problems coefficients constant contour integral convergence convolution cosh currents and voltages definition denominator derivative diagram Differentiation theorem discussion e_ap engineering Equation 13 Equation 21 error functions essential singularity Example frequency given gives graph Heaviside Heaviside's impedance impulsive response indicial response inductance initial value input integral round inverse transform Inversion theorem involves Jordan's Lemma Laplace transform Laurent series limit mathematical multiply notation obtain Ohm's Law Operational Mathematics origin output partial fractions pulse reader real variable Residue theorem residues result Shifting theorem shown in Fig simple poles sine sinh sinusoidal solution solve steady-state system function term tion trans transformed equation unit impulse unit step voltage write z-plane zero initial conditions