Hey can any one help me , i want to learn about the laplace transforms but ,i am not getting good guidance so please any one can help me ,for that purpose so please tell me that where i can find good tutorials of the laplace transform.
Hey can any one help me , i want to learn about the laplace transforms but ,i am not getting good guidance so please any one can help me ,for that purpose so please tell me that where i can find good tutorials of the laplace transform.
Short Introduction:
A Laplace transform takes a function of a time and transforms it into a function of $\displaystyle s$, which is the laplace frequency variable. This is simply a complex number. Hence, we take a problem in the time domain into the frequency domain!
The way we transfer a function of time, $\displaystyle f(t)$ into a function of the laplace frequency $\displaystyle F(s)$ is using the Laplace transform integral, which is as follows:
$\displaystyle F(s) = \int_{0}^{\infty} f(t)\times e^{-st} dt $
For example, the function $\displaystyle f(t) = e^{t} $ is transformed as such:
$\displaystyle F(s) = \int_{0}^{\infty} e^{t}\times e^{-st} dt $
$\displaystyle = \int_{0}^{\infty} e^{t-st} dt $
$\displaystyle = \int_{0}^{\infty} e^{t(1-s)} dt $
$\displaystyle = [\frac{e^{t(1-s)}}{1-s}]_{0}^{\infty} $
A use for these transforms is to make differential equations much easier to solve!
If you add me to MSN I can send you some introductory notes from my university course. Mushet@hotmail.co.uk
For Laplace transforms, it is a good idea to brush up on "integration by parts". The form of the Laplace transform:
$\displaystyle L(s)= \int_0^{\infty} f(t)e^{-st} dt$
and the fact that $\displaystyle e^{-st}$ is easy to integrate makes integration by parts very useful.
Hey I keen to know that you people replied me but right now I'm passing with a very huge problem and that is I am engineering student and pursuing my engineering in the electronics ,I have a subject Mathematics as well as a signal system also ,now signal and system also contents some problems regarding the fourier transforms and laplace transform so can any one tell me that why we use that topics in the field of the mathematics as well as in the signal and system ....
one problem regarding to the Laplace transforms also that what is a "ROC" ,can any one explain me ,
"The subset of values of s for which the Laplace transform exists is called the region of convergence (ROC) or the domain of convergence." (Quoted from Laplace transform - Wikipedia, the free encyclopedia)