5.5 ConvolutionandtheLaplaceTrans- form
174 CHAPTER 5. LAPLACE TRANSFORMS Perhaps this was better done with PARTS, but we wanted to illustrate the power of the Laplace transform ¤ The advantage of …
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5 LAPLACE TRANSFORMS - Pennsylvania State University
math.bd.psu.edu5 LAPLACE TRANSFORMS 5.1 Introduction and Definition In this section we introduce the notion of the Laplace transform. We will use this idea to solve differential equations, but the method also can be used to sum series or compute integrals. We begin with the definition: ... (t)]( s) = sL[y0(t)] ...
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math.bd.psu.edu5.4. UNIT STEP FUNCTIONS AND PERIODIC FUNCTIONS 157 Which implies that y(t) = t2 solves the DE. (One may easily check that, indeed y(t) = t2 does solve the DE/IVP. ¤ Exercises In 1-8, solve the ODE/IVP using the Laplace Transform
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