Laplace transform is yet another operational tool for solving constant coe-
cients linear di erential equations. The process of solution consists of three
main steps:
The given \hard" problem is transformed into a \simple" equation.
This simple equation is solved by purely algebraic manipulations.
The solution of the simple equation is transformed back to obtain the so-
lution of the given problem.
In this way the Laplace transformation reduces the problem of solving a dif-
ferential equation to an algebraic problem. The third step is made easier by
tables, whose role is similar to that of integral tables in integration.
The above procedure can be summarized by
In this section we introduce the concept of Laplace transform and discuss
some of its properties.
The Laplace transform is de ned in the following way. Let f(t) be de ned
for t 0: Then the Laplace transform of f; which is denoted by L[f(t)]
or by F(s), is de ned by the following equation
The integral which de ned a Laplace transform is an improper integral. An
improper integral may converge or diverge, depending on the integrand.
When the improper integral in convergent then we say that the function f(t)
possesses a Laplace transform. So what types of functions possess Laplace
transforms, that is, what type of functions guarantees a convergent improper
integral.
المادة المعروضة اعلاه هي مدخل الى المحاضرة المرفوعة بواسطة استاذ(ة) المادة . وقد تبدو لك غير متكاملة . حيث يضع استاذ المادة في بعض الاحيان فقط الجزء الاول من المحاضرة من اجل الاطلاع على ما ستقوم بتحميله لاحقا . في نظام التعليم الالكتروني نوفر هذه الخدمة لكي نبقيك على اطلاع حول محتوى الملف الذي ستقوم بتحميله .
الرجوع الى لوحة التحكم
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