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The Laplace Transform - Armstrong

185 Chapter 7 The Laplace TransformIn this chapter we will explore a method for solving linear differential equationswith constant coefficients that is widely used in electrical engineering. It involvesthe transformation of an initial-value problem into an algebraic equation, whichis easily solved, and then the inverse transformation back to the solution of theoriginal problem, thereby bypassing the need to solve for arbitrary constants inthe general solution. The technique is especially well suited for finding gener-alized solutions to systems driven by impulses or by discontinuous or periodicforcing Definition and Basic PropertiesGiven a functionf(t) defined fort 0, itsLaplace transformF(s) is definedasF(s) = 0e stf(t)dt.(1)Notice that the variablesappears as a parameter in an improper integral.

The Laplace Transform In this chapter we will explore a method for solving linear di erential equations with constant coe cients that is widely used in electrical engineering. It involves the transformation of an initial-value problem into an algebraic equation, which

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