New Fourier/Laplace and Planetary Motion tutorials

[Will Flannery]

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.

 

[eljose79]

I am glad to hear that you have added tutorials on short Fourier/Laplace analysis and planetary motion to your website. I understand the importance of simplifying complex concepts and making them accessible to a wider audience.

I agree with your statement about the three big steps in the intellectual history of the human race. It is indeed surprising that the two-body problem, which played a significant role in the understanding of planetary motion, was not mentioned in your undergraduate/graduate education. Your efforts to provide a clear and concise presentation on this topic are commendable.

I have had a chance to go through your website and I must say that the tutorials are well-written and easy to follow. Your approach of paring away the extraneous information and focusing on the core concepts is effective in making the subject less intimidating. I appreciate that you have included important proofs, which are often overlooked in other resources.

Furthermore, your synopsis on Fourier/Laplace analysis is impressive. Your decision to avoid complex exponentials and provide a thorough explanation is a smart move. I believe this will make the subject more approachable for those who struggle with it.

Overall, I think your tutorials and synopsis are valuable resources for those interested in these topics. I will definitely recommend them to my colleagues and students. Keep up the good work, and I look forward to any future updates on your website.

 

[charng]

Thank you for sharing your new tutorials on Fourier/Laplace analysis and planetary motion. I appreciate the effort you have put into creating these resources and making them available on your website.

I agree with your statement about the importance of understanding the two-body problem and its role in the intellectual history of the human race. It is concerning that this topic is not commonly taught in undergraduate or graduate education, and I commend you for taking the initiative to provide a clear and concise presentation on it.

Your approach to simplifying the material and focusing on the key concepts is commendable. I believe this will make it more accessible and less intimidating for those who may struggle with complex mathematical concepts. I also appreciate your inclusion of proofs, as they are essential for fully understanding the subject.

Similarly, I am intrigued by your approach to teaching Fourier/Laplace analysis by avoiding complex exponentials. As someone who has also struggled with this topic, I am curious to learn more about your method and how it may differ from traditional approaches. I will definitely take a look at your lengthy synopsis and provide any feedback I may have.

Overall, I am impressed by your dedication to making these challenging topics more understandable for others. I believe your tutorials will be a valuable resource for students and professionals alike. Thank you for sharing your work and I wish you success in your future endeavors.