Recent content by starzero

In my differential equations book (Edward and Penny) there are many examples of Laplace transforms being applied to linear differential equations with constant coefficients and no examples of them being applied to linear differential equations with variable coefficients. My question is, can this...

This is the real issue. We can describe what gravity is and what it does. The reason it is there is the real mind blower.

Thank you both for your fast insightful and illustrative replies.

Hi All and sorry if this is too easy a question but here goes... Sines, Cosines and the rest of the trig functions are the ratio of two lengths and thus are dimensionless quantities. That is if I plug in a value for t in sin(ωt) there are no units. For example the solution of x'' +...

Thank your all for your answers and insight – a few follow up questions/comments. I fully agree with you here. It is the physical interpretations that make the subject come alive. Following up with your physical explanation I have a follow up question … In three dimensions the...

Many texts in deriving the fundamental solution of the Laplace equation in three dimensions start by noting that the since the Laplacian has radial symmetry that Δu=δ(x)δ(y)δ(z) That all that needs to be considered is d^2u/dr^2 + 2/r du/dr = δ(r) For r > 0 the solution given is u= c1/r +...

Statistical Mechanics -- Maximum Temperature We know that at zero degrees kelvin the only energy is zero point energy. As we heat a substance, the atoms move faster and faster. The question is, is there a maximum temperature since the fastest a atom can move is the speed of light?

Thank you both for the information.

I recently read a paper on fractional derivatives. That is how to take derivatives of fractional order rather than the usual integral order. The paper made perfect sense to me, however I wondered: 1) Are there geometric interpretations of fractional derivatives? Kind of like how first...

When we drive a car on a hot day we have all experienced what appears to be water on the road. I believe that this is related to the facts that 1) the air near the hot pavement is less dense than the air a few feet above and 2) light will travel from point A to B along the fastest path (in this...

Thanks for the explanation. It's getting me closer to the understaning that I want to get with this problem. I am sorry to say that I made a mistake in part of the statement. In 2 d the solution involves u = (1/2 PI) log r ... ie the potential involves log r and the field drops off like...

I have asked this question before in another section of the forum but I still don’t have an answer so I thought I would try here. Ok…here goes.. In three dimensions, Poissons equation can be used to model an electrostatic problem in which there is a single point charge at the origin. The...

All of the books mentioned are really good. Here are a few more. Markushevich's "Theory of Functions of a Complex Variable" This is my all time favorite complex variable book. Get the three volume set not the abridged version (also good but get the whoe thing). The translation by the way...

It's great that you are really thinking about this as eigenvectors and eigenvalues are really important in many aspects of applied mathematics. So let me try with the explanation again. You have a square matrix A and you notice that for most vectors Y when we multiply by the matrix A that...

Not exactly. The thing that must be thought about first is the eigenvector. All non-eigenvectors will rotate. The eigenvalue is only associated with an eigenvector and represents a measure of how much the eigenvector gets strecthed or compressed when multiplied by matrix A.