Introduction to Laplace Transforms for Radio and Electronic Engineers |
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Page 107
... integration , and because this path , or contour , is always involved in the definition of an integral , the process is usually called " contour integration " . Fig . 6.6.1 shows a path ABC between two points zo and z , in the z - plane ...
... integration , and because this path , or contour , is always involved in the definition of an integral , the process is usually called " contour integration " . Fig . 6.6.1 shows a path ABC between two points zo and z , in the z - plane ...
Page 123
... contour integral Let us integrate the function ept P ( 1 ) with respect to p over the full - line contour shown in Fig . 7.1.1 , assuming that t is positive . The contour consists of a straight line parallel to the imaginary axis and y ...
... contour integral Let us integrate the function ept P ( 1 ) with respect to p over the full - line contour shown in Fig . 7.1.1 , assuming that t is positive . The contour consists of a straight line parallel to the imaginary axis and y ...
Page 125
... contour integral . In this brief derivation , we have deliberately avoided a rather tricky mathematical discussion by the use of the very convenient phrase " it can be shown " . For those who dislike taking anything on trust , but who ...
... contour integral . In this brief derivation , we have deliberately avoided a rather tricky mathematical discussion by the use of the very convenient phrase " it can be shown " . For those who dislike taking anything on trust , but who ...
Contents
The Laplace Transformation | 14 |
Properties of Transforms 333 | 33 |
Further Theorems | 50 |
Copyright | |
6 other sections not shown
Common terms and phrases
a₁ algebraic 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 diagram differential equations e-ap e-Kat e-pt Equation 13 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 partial fractions pulse R₁ reader real variable residues result SABC Shifting theorem shown in Fig simple poles singularity sinh sinusoidal solution solve steady-state system function Table term tion TRANSFORM OF y(t transformed equation unit step variable theory voltage z-plane δν ди