Laplace Transforms

I’ve been finding Laplace transforms very difficult. So finally after a lot of procrastination, I’m actually studying it. I guess there would be many people out there in same situation as me. This article is intended for such people who wants to get basic idea about it in very short time.

This is what I understood from class.

Ok this is the equation. But I never understood what it meant until today. Laplace transforms let you convert functions dependent on time to functions dependent on frequency.  Once you get the physical idea, it starts to unfold itself. Here, f(t) is the function based on time and F(s) is the function based on frequency. I used the following links to understand the concepts. Hope you also find them useful.

Khan Academy‘s video lectures on Laplace transforms further enforced the ideas [Link].

The wikipedia page for had a table of Laplace transforms which i found quite useful [Link].

There is a better table available at Interactive mathematics [Link].

The next topic which I found difficult was Laplace transforms on unit step functions [Link].

And this site helped me with Laplace transform of derivatives.

Why use Laplace transform?

I still haven’t figured out this part completely. If you have figured out this part, please comment. I think understanding this part will help develop more interest in the subject. A lil googling told me that they are used in analysing circuits. But I still didn’t understand the how part. I think Laplace transforms are used to study the effect of change in frequency of voltage or current source in circuits where current or voltage varies with time.