IntroLaplaceTransform

# IntroLaplaceTransform - The Laplace Transform Among the...

This preview shows pages 1–2. Sign up to view the full content.

The Laplace Transform Among the tools are useful for solving differential linear equations are integral transforms. Definition : An integral transform is a relation of the form F(s) = K(s,t)f(t)dt a b ! where K(s,t) is a given function of the variables s and t, called the kernel of the transformation and the limits of integration a and b are given and it is possible that a = - and b = . The relation transforms the function f(t) into another function F(s), which is called the transform of f. The general idea of using an integral transform to solve a linear differential equation is to transform a problem for an unknown function f into a simpler problem for the function F. Then, solve the simpler problem to find F and then recover the function f from its transform F. This last step is known as inverting the transform. There are several integral transform that are useful to solve differential equation, but in this chapter we will use the Laplace transform. Definition : Let f(t) be given for t 0 and assume the function satisfy certain conditions to be stated later on. The Laplace transform of f(t), that it is denoted by L {f(t)} or F(s), is defined by the equation L {f(t)} = F(s) = e ! st f(t)dt 0 " # whenever the improper integral converges. Remark

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 3

IntroLaplaceTransform - The Laplace Transform Among the...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online