Introduction to Laplace Transforms for Radio and Electronic Engineers |
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Page 82
... ( 13 ) by the Differentiation theorem . The fact that the term involving the initial value of current appears on the ... equation for this case in the form ( Lp + R ) i = x so that the current transform appears as the system function times the ...
... ( 13 ) by the Differentiation theorem . The fact that the term involving the initial value of current appears on the ... equation for this case in the form ( Lp + R ) i = x so that the current transform appears as the system function times the ...
Page 140
... Equation 11 , and the inversion of V ( x , p ) to obtain the voltage at any point of the line , will be carried out ... ( 13 ) = Y = PVLC ( 14 ) ( 15 ) and the boundary conditions are V ( 0 , t ) = E , V ( ∞ , 0 ) finite The general solution ...
... Equation 11 , and the inversion of V ( x , p ) to obtain the voltage at any point of the line , will be carried out ... ( 13 ) = Y = PVLC ( 14 ) ( 15 ) and the boundary conditions are V ( 0 , t ) = E , V ( ∞ , 0 ) finite The general solution ...
Page 164
... mathematics . * F ( w ) is called the " complex Fourier transform " , or more simply the " Fourier transform " , of f ( t ) , defined by Equation 12 , or explicitly by F ( w ) = √∞ f ( t ) e - iwt dt S = 81 ( 13 ) so that Equation 12 ...
... mathematics . * F ( w ) is called the " complex Fourier transform " , or more simply the " Fourier transform " , of f ( t ) , defined by Equation 12 , or explicitly by F ( w ) = √∞ f ( t ) e - iwt dt S = 81 ( 13 ) so that Equation 12 ...
Contents
The Laplace Transformation | 14 |
Properties of Transforms 333 | 33 |
Further Theorems | 50 |
Copyright | |
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Common terms and phrases
a₁ amplitude analytic analytic function approaches zero branch point C₁ C₂ capacitor chapter circuit problems closed contour coefficients complex variable contour integral cosh currents and voltages definition denominator derivative differential equations e-ap e-pt Equation 13 Equation 21 error functions essential singularity Example F(jw Fourier frequency given gives Heaviside impedance impulsive response indicial response infinite input integral round inverse transform Inversion theorem Jordan's Lemma Laplace transform Laurent series limit linear mathematical method obtain Ohm's Law Operational Mathematics output pulse R+Lp R₁ reader real variable residues result SABC Shifting theorem shown in Fig simple poles singularity sinh sinusoidal solution solve steady-state system function term tion TRANSFORM OF y(t transformed equation unit step variable theory voltage y₁ z-plane δν ди дх