Transcription of Laplace and Z Transforms - MIT
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Laplace and Z Transforms - MIT
: Signals and SystemsLaplace and Z TransformsOctober 1, 2009 Mid-term Examination #1 Wednesday, October 7, 7:30-9:30pm, Walker recitations on the day of the :DT Signals and SystemsLectures 1 5 Homeworks 1 4 Homework 4 will include practice problems for mid-term , it will not collected or graded. Solutions will be book: 1 page of notes (812 11inches; front and back).Designed as 1-hour exam; two hours to sessions during open o ce ict? Contact before Friday, October 2, TimeMany continuous-time systems can be represented with di : leaky tankr0(t)r1(t)h1(t)Di erential equation representation: r1(t) =r0(t) r1(t)Last time we considered two methods to solve di erential equations: solving homogeneous and particular equations singularity matchingSolving Di erential Equations with Laplace TransformThe Laplace transform provides a particularly powerful method ofsolving di erential equations it Transforms a di erential equationinto an algebraic (whereLrepresents the Laplace transform ):di erentialalgebraicalgebraicdi erential equation solve di erentialequationalgebraicequationalgebra icanswersolution todi erential equationL solveL 1 Laplace transform : De nitionLaplace transform maps a function of timetto a function (s) = x(t)e stdtThere are two important variants:Unilateral ( )X(s) = 0x(t)e stdtBilateral ( )X(s) = x(t)e stdtBoth share import
Last time we considered two methods to solve dierential equations: • solving homogeneous and particular equations • singularity matching. Solving Dierential Equations with Laplace Transform The Laplace transform provides a particularly powerful method of solving dierential equations — it transforms a dierential equation
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ELEMENTARY DIFFERENTIAL EQUATIONS, Methods, Laplace Transform, Laplace Transform Methods, University of North, Laplace Transform Methods Laplace transform, Laplace, Transform, Comparison of Particle Sizing Methods, Solution of the Partial Differential, Solution of the Partial Differential Equations, Understanding Digital Signal Processing, Digital Signal Processing, MATHEMATICAL MODELING AND ORDINARY, MATHEMATICAL MODELING AND ORDINARY DIFFERENTIAL EQUATIONS, Partial Differential Equations