xorbie

int(xe^(x^2))? that's not so tough.. F(x)=[e^(x^2)]/2

Perhaps you meant int(e^(x^2))?

Anyway, I'm shipping this off to S&S.

nermal

The trick is, Laplace is a Linear transform. Addition and scaling are maintained in the mapping--so you can transform the function, then inverse transform it and get the original function back. It's kind of like blowing up the picture in MS-Paint, tweaking it in big scale, and then shrinking it back to the original size.

Any linear transform can be used to solve a differential equation in another space, Fourier, Laplace, etc. but Laplace happens to be real easy in a lot of applications.

Think of it as folding the paper in half when you cut the snowflake. That's a transform.

Ed

MBS

I think there should be a table in your book that tells what the Laplace and inverse Laplace transforms of various functions and derivatives are. The book usually derives the basic transform and inverse transform formulas by evaluating the integral in the definition. I don't remember the formulas off hand though. I wasn't required to memorize the formulas. They were given on a hand out during the exam.

AdamWho

I typed laplace cosine transform into google and I got a suitable result.

nermal

If you're really interested in getting your brain around the theory, take an intro course in topology.

Ed

Demosthenes

I'm taking an intro course in topology next semester and I can't wait! Topology is one of my favorite mathematics fields.

Quantum Ninja

Speaking of which, I just took the final for my intro topology course today. It's definitely interesting stuff if you're looking to think in an even more abstract sense than, say, an introductory analysis course covering basic calculus. I actually was also signed up for such an analysis course this semester and found the two complemented each quite well, at least while we concentrated on metric spaces at the start of topology.

Once we moved on to general topological spaces, it was a shift into more "meta-mathematical" territory. The real-world uses of the general topological space seem less apparent than a metric space, but I can see how they are convenient for proving general results in mathematics. It's not necessarily useful to say, an experimental physicist or an engineer, but I believe theoretical physicists (particularly in string theory and cosmology) rely on it, as well as mathematicians, obviously.

Anyway, good luck with topology next semester and enjoy it! It's good stuff.