Recent content by axsvl77

It has been six or so month since I posted this, so I'll answer my own question. I started with "Introduction to Wave Phenomena" by Akira Hirose Continued with "Vibrations and Waves in Physics" by Ian Main After that, "Nonlinear vibrations in mechanical and electrical systems" by J. J Stoker...

I recently looked at the reference in an article I am reading, and subsequently checked "Oscillations and Waves in Linear and Nonlinear Systems" my Rabinovihc and Trubetskov from the local library. https://www.amazon.com/dp/0792304454/?tag=pfamazon01-20 Great book, but unfortunately as a...

Here is what I've found as my answer, but had trouble formulating a question: ∇^{2}(\frac{1}{r}) = \frac{1}{r^{2}}\frac{∂}{∂r}[r^{2}\frac{∂}{∂r}(\frac{1}{r})] = \frac{1}{r^{2}}\frac{∂}{∂r}[r^{2}\frac{-1}{r^{2}}] = \frac{1}{r^{2}}\frac{∂}{∂r}(-1) =0 However, \int_V ∇^{2}(\frac{1}{r})dV...

I really appreciate your help. Why is the result of the Laplacian different from that of a double derivative?

Thank you JJacquelin, Why is this 0 instead of \frac{2}{r^{3}}?

I hope I typed that in right

Sorry, I guess I need to be more clear with my example. I am assuming: \frac{1}{r^{2}}\frac{d}{dr}r^{2}\frac{d}{dr}(\frac{e^{ar}}{r}) = \frac{1}{r^{2}}\frac{d}{dr} r^{2}(\frac{-e^{ar}}{r^{2}}+\frac{ae^{ar}}{r}) = \frac{1}{r^{2}}\frac{d}{dr} (-e^{ar}+are^{ar}) = \frac{1}{r^{2}}...

Also, I'm new to this forum. I have some level of uncertainty how to tag this.

Ok, there are a couple of other threads about this, but they don't seem to answer my question. If I take the double derivative of 1/r, I'll get 2/r^3, but if I take the laplacian, I get something different. Why? Namely: \frac{d}{dr}\frac{d}{dr}(\frac{1}{r}) = \frac{d}{dr}...