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Unformatted text preview: 18.03 Lecture 26, April 14Laplace Transform: basic properties; functions of a complex variable;polesdiagrams; sshift law.[1] The Laplace transform connects two worlds:  The t domain t is real and positive functions f(t) are signals, perhaps nasty, with discontinuities and delta functions ODEs relating them convolution systems represented by their weight functions w(t) ^L   L^{1}v   The s domain s is complex beautiful functions F(s) , often rational = poly/poly and algebraic equations relating them  ordinary multiplication of functions systems represented by their transfer functions W(s) The use in ODEs will be to apply L to an ODE, solve the resulting verysimple algebraic equation in the s using the "inverse Laplace transform"world, and then return to realityL^{1}. [2] The definition can be motivated but it is more efficient to simplygive it and come to the motivation later. Here it is....
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 Winter '08
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