Engineering Analysis Fall 2009 Dan C Marinescu Office HEC 439 B Office hours Tu Th 11 00 12 00 Lecture 2 Last time Today Software packages for numerical simulation Modeling Analytical and Numerical Methods for Model Solving Example the bungee jumper More on Analytical and Numerical Methods for Model Solving Laplace Transform Next Time Overview of Matlab Lecture 2 2 Transform Methods Basic 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 representation Instead of correlation an intensive numerically problem use multiplication Lecture 2 3 Properties of the Laplace Transform Linearity Scaling Frequency shifting Time shifting Frequency differentiation Frequency integration Differentiation Integration Convolution Lecture 2 4 Lecture 2 5
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