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Unformatted text preview: Ch 6.1: Definition of Laplace Transform Many practical engineering problems involve mechanical or electrical systems acted upon by discontinuous or impulsive forcing terms. For such problems the methods described in Chapter 3 are difficult to apply. In this chapter we use the Laplace transform to convert a problem for an unknown function f into a simpler problem for F , solve for F , and then recover f from its transform F . Given a known function K ( s , t ), an integral transform of a function f is a relation of the form < = , ) ( ) , ( ) ( dt t f t s K s F The Laplace Transform Let f be a function defined for t 0, and satisfies certain conditions to be named later. The Laplace Transform of f is defined as Thus the kernel function is K ( s , t ) = e- st . Since solutions of linear differential equations with constant coefficients are based on the exponential function, the Laplace transform is particularly useful for such equations. Note that the Laplace Transform is defined by an improper integral, and thus must be checked for convergence....
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This note was uploaded on 08/13/2009 for the course DIFF 2343632 taught by Professor Csar during the Fall '09 term at Middle East Technical University.
- Fall '09