## anonymous 5 years ago what does the "moment" in mathematics means(physically) and how does it correlate with laplace transform?

1. JamesJ

What's your definition of moment? I can think of at least two things it could mean, but I need you to be more precise.

2. anonymous

http://en.wikipedia.org/wiki/Moment_%28mathematics%29 i am trying to figure out what connection does it have with laplace transform

3. JamesJ

Very little if you ask me. This concept of moment has to do mostly with probability theory and the characterization of distributions.

4. anonymous

"The Laplace transform is related to the Fourier transform, but whereas the Fourier transform resolves a function or signal into its modes of vibration, the Laplace transform resolves a function into its moments" - from wiki. I am trying to figure out what does "resolve a function into its moments" means. And btw, why is s variable complex in laplace transform?

5. JamesJ

I think this phrase ""resolve a function into its moments" isn't very unhelpful. If you want to begin to get a sense of what the Laplace transform is doing, the beginning of this lecture does a good job: http://ocw.mit.edu/courses/mathematics/18-03-differential-equations-spring-2010/video-lectures/lecture-19-introduction-to-the-laplace-transform/

6. anonymous

I have just watched the lecture one hour ago and i understand that laplace transform is continous analogue of the power series of the, for example $\sum_{0}^{\infty} a_n*x^n$. But why is s a complex number?

7. JamesJ

We might use complex numbers as a convenience in calculation, just as we do in ODEs. But the Laplace transform of a real-valued function is always a real valued function.