## Introduction to Laplace Transforms for Radio and Electronic Engineers |

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Page 100

be certain that any pre-conceived notions about functions which we hold from

, the important ideas of real theory can be carried over more or less as they are, ...

be certain that any pre-conceived notions about functions which we hold from

**real variable**theory are valid in the complex field before we use them. Fortunately, the important ideas of real theory can be carried over more or less as they are, ...

Page 105

... last expression. dz ( z ) z* The results are the same as they would have been

had z been real, and these examples are typical of an important general result.

An analytic function of a complex variable behaves like a function of a

... last expression. dz ( z ) z* The results are the same as they would have been

had z been real, and these examples are typical of an important general result.

An analytic function of a complex variable behaves like a function of a

**real****variable**, ...Page 106

of the results of

trigonometrical and hyperbolic identities, expansion in series etc., may be carried

over without alteration from

...

of the results of

**real variable**theory, including rules for differentiation,trigonometrical and hyperbolic identities, expansion in series etc., may be carried

over without alteration from

**real variable**theory. This statement could never pass...

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### Contents

The Laplace Transformation | 14 |

Properties of Transforms | 33 |

Further Theorems | 50 |

Copyright | |

6 other sections not shown

### Common terms and phrases

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