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The Laplace Transform

# The Laplace Transform - Differential Equations Second...

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Differential Equations Second Quarter SY 0506 ____________________________________________________________________________________________________________ Silva, Alviso and Llacuna – Mathematics Department, MIT 163 Lesson 32 The Laplace Transform Specific Objectives: At the end of the lesson, the students are expected to: define Laplace Transforms and its properties find the Laplace Transforms of different types of functions Let f(t) be a function of t defined for each positive values of t. Then the Laplace transform of f(t), donated by ( ) { } L f t , is defined by ( ) { } dt t f e t f L st ) ( 0 = ––––––– (1) provided that the integral exists. s is a parameter, which may be a real or complex number. ( ) { } L f t being clearly a function of s is briefly written as F(s). That is, ( ) { } ( ) s F dt e t f L st = = 0 where ( ) { } L f t or ( ) F s – Laplace Transform of f(t). Transforms of Elementary Functions

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The Laplace Transform - Differential Equations Second...

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