## An introduction to the Laplace transform and the Z-transform |

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### Contents

The Laplace transform and the inverse Laplace transform | 1 |

The transforms of derivatives and the application to differential equations | 7 |

Some useful theorems | 19 |

Copyright | |

12 other sections not shown

### Common terms and phrases

algebraic Appendix bg(t block diagram coefficients constant convolution integral cos(o)o defined Determine the inverse Determine the Laplace difference equations dt2 dt given dxjdt e~sr equation 8.l evaluated EXAMPLE Exercise exponential f(nT Final value theorem Flat-topped sampling following functions function f(t G(jco given that x(0 Graph of h(u graph of h(u)x(t Heaviside step function Hence Initial value theorem input inverse Laplace transform inverse z transform limit f(t limit sF(s loop currents method multiplied Note obtain operation operational amplifier original differential equations output partial fractions periodic function phase response poles of G(s pulses residue result sampled function sampled signal sampling instants shown in Figure signal simultaneous equations sin(co sinh(o)o solution Solve the differential square wave standard forms steady state error step of magnitude transfer function transformed equations Transforming the equation unit step function value theorem limit voltages Volterra integral equation zero