Question

what does the "moment" in mathematics means(physically) and how does it correlate with laplace transform?

Answer 1

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.

Answer 2

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

Answer 3

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

Answer 4

"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?

Answer 5

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/

Answer 6

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?

Answer 7

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.