Engineering Analysis – Fall 2009Lecture 2Transform MethodsProperties of the Laplace TransformSlide 5Engineering Analysis – Fall 2009Dan C. MarinescuOffice: HEC 439 BOffice hours: Tu-Th 11:00-12:00Lecture 2 2Lecture 2Last timeSoftware packages for numerical simulation.ModelingAnalytical and Numerical Methods for Model SolvingExample – the bungee jumperToday:More on Analytical and Numerical Methods for Model SolvingLaplace TransformNext TimeOverview of MatlabLecture 2 3 Transform MethodsBasic idea: find a convenient representation of the equations describing a physical phenomena. For example, in signal analysis rather than analyzing a function of time, s(t), study the spectrum of the signal S(f), in other words carry out the analysis in the frequency domain rather than the time domain.Advantage of Fourier (spectral analysis): More intuitive physical representationInstead of correlation (an intensive numerically problem) use multiplication.Lecture 2 4 Properties of the Laplace TransformLinearity ScalingFrequency shiftingTime shiftingFrequency differentiationFrequency integrationDifferentiationIntegrationConvolutionLecture 2
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