Transcription of 5 LAPLACE TRANSFORMS - Pennsylvania State University
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5 LAPLACE TRANSFORMS - Pennsylvania State University
CHAPTER5 LAPLACE Introduction and DefinitionIn this section we introduce the notion of the LAPLACE transform . We will usethis idea to solve differential equations, but the method also can be used tosum series or compute integrals. We begin with the definition: LAPLACE TransformLetf(t) be a function whose domain includes (0, ) then the LAPLACE trans-form off(t) is:L(f(t))(s) = 0f(t)e stdtNote that the LAPLACE transform of a function is another function whosevariable is usually denoted ass. Also note that the LAPLACE transform involvesan improper integral.
5 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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