Laplace transform is an operational tool for solving constant conceits linear differential 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 solution of the given problem.
Suppose that f is a real- or complex-valued function of the (time) variable t > 0 and (s) is a real or complex parameter. We define the Laplace transform of f as:
The symbol ?? is the Laplace transformation, which acts on functions f = f (t) and generates a new function, F(s) = L f (t) whenever the limit exists (as a finite number). When it does, the integral is said to converge. If the limit does not exist, the integral is said to diverge and there is no Laplace transform defined for f .
Examples: Find the Laplace transformations for the following functions:
1. f(t) = k k = constant
F(s) = L f(t) = k . e –st dt = k e –st .dt = k ????????????0 = ?? ??
2. f(t) = e -at
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 .
|