[PDF] find the laplace transform of the given function

Overview

The Laplace transform is an integral transform used in solving differential equations of constant coefficients. This transform is also extremely useful in physics and engineering.

The Basics

Substitute the function into the definition of the Laplace transform. Conceptually, calculating a Laplace transform of a function is extremely easy. We will use the example function where is a (complex) constant such that

Properties of the Laplace Transform

Determine the Laplace transform of a function multiplied by . The results in the previous section have allowed us to take a glimpse at some interesting properties of the Laplace transform. The Laplace transform of functions like cosine, sine, and the exponential function seem to be simpler than the transform of the power function. We will see that multiplication by in the t-domain corresponds to a shift in the s-domain.

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What does the Laplace transform really tell us?

The Laplace transform is a well established mathematical technique for solving a differential equation. Many mathematical problems are solved using transformations. The idea is to transform the problem into another problem that is easier to solve. On the other side, the inverse transform is helpful to calculate the solution to the given problem.

Why is Laplace transform so useful?

Why is Laplace transformation useful in engineering mathematics? The Laplace transform is a powerful tool to solve differential equations. It transforms an Initial Value Problem in Ordinary Differential Equation to algebraic equations. One important feature of the Laplace Transform is that it can transform analytic problems to algebraic.

What does the Laplace transform do?

The purpose of the Laplace Transform is to transform ordinary differential equations (ODEs) into algebraic equations, which makes it easier to solve ODEs. The Laplace Transform is a generalized Fourier Transform, since it allows one to obtain transforms of functions that have no Fourier Transforms. Beside above, how do you use Laplace Transform?

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