Define Laplace Transform

Laplace transform is a type of integral transform that are popularly used in the field of physics and engineering. In mathematical notation the concept of Laplace transform can be represented as L f(a). The above given notation can be consider as a linear operator for a function f (a). Here the value ‘a’ can be considered as a real argument, which should be greater than equal to zero. When the Laplace transform are performed on the above given function then it transform them into f(a) → f(b). Here f(b) can be consider as function with complex argument ‘b’.

Normally the concept of Laplace transform is related to the Fourier transform. But there is big difference between them. Laplace transform resolves a function into moments whereas in same aspect Fourier transform perform the task of representing a function in a series of modes. The concept of Laplace transform is formed by Great mathematician Mr. Pierre Laplace at the time when he performing his experiment on Probability theory. In the below we show you how a Laplace transforms works:

Suppose there F(a) is a function defined as [0, ∞]. Now laplace transform for F(a) can be defiend  as new function :

L(f(b)) = ⌠0∞ e-ba f(a)da = lim α→∞ ⌠0α e ba f(a)da

the basic meaning of above given mathematical notation is that there is a function f(a) on which Laplace transform are performed that gives the new function f(b) with a complex number b. The scope of integral depends on types of function of interest. The basic reason behind the use of Laplace transform is that to reduce a differential equation to an algebra problem. In mathematics, Laplace transform works well when forcing function in differentiation equation gets more complicated. The Statistical Inference is a mathematical process that perform the task of drawing conclusion from data. karnataka education board came into existence into real world in the year of 1966. The main work of karnataka education board is conducting SSLC examinations and In the next session we will discuss about How to Solve Antiderivative.