I've added short Fourier/Laplace analysis and planetary motion tutorials to my web page.
First, the planetary motion page - my thinking is that the three big steps in the intellectual history of the human race are -
1. when we came down out of the trees,
2. when Newton solved the two-body problem and explained planetary motion, and
3. we're waiting for the third step
And yet, I'd never seen even a mention of the two-body problem in my undergraduate/graduate math/engineering education. So I wanted to give as painless a presentation as possible.
I found a clear presentation in the on line notes for a mechanical engineering course by R. Fitzpatrick of Univ. of Texas, and pretty much just pared away all the extraneous (to my purposes) stuff. The result is at
www.berkeleyscience.com/pm.htm
The Fourier/Laplace page is not exactly a tutorial, it is a synopsis for a book on the subject I've written, but I wrote the synopsis first as a guide to myself. I realized from working as an engineer that knowledge of Fourier methods is essential, and yet I knew my understanding of the fundamentals was non-existent, and when I started I was only hoping that an easy way through this theory could be found. I think I found one. First, I included the important proofs because they are essential, incredible, and as it turns out, not difficult. Second, I realized that my brain always flinched and froze when it came across a complex exponential, and I wanted to fully elucidate this subject. Turns out it's better to avoid them altogether, which is what I did, and the result is, I think, my book is MUCH clearer than anything else on the subject (IMO). The lengthy synopsis is at
www.berkeleyscience.com/synopsis4.htm
I welcome any feedback.
