Recent content by Darren73

This is taken from "The Einstein Theory of Relativity" by Lillian R. Lieber. It is supposed to be a high school introduction to relativity using simple algebra and calculus. From page 45 in the "First Paul Dry Books Edition, 2008". In it we are supposing that there are two frames of reference...

Hi, I saw a derivation in a book and I don't see the logical connection. Suppose 1.\ \ a=b \text{ and } 2.\ \ x=y Then 3.\ \ a-b= \lambda (x-y) makes sense to me since 0=\text{Anything}⋅0 However they said "similarly" 4.\ \ a+b= \mu (x+y) , and this I don't understand. To me a+b= 2a...

Hi all, in following the many available derivations of the Boltzmann distribution I was trying to do it by maximizing W, which is N choose n1,n2,...nt., instead of lnW, because it should give the same answer (since W is monotonically increasing with lnW, am I wrong?). So given the two...

I got the answer while trying to find a good example, so thank you ! The reason is that the "proper" form of A. is ##P=g\int_{z}^{z_{o}}\rho(u)du ## (where u is a dummy variable for z). Instead, I had it such that the right side of A was the "integral in disguise" by assuming ρ was constant and...

This trouble popped up while I was deriving the simple "barometric formula". But it seems to be more of calculus (or self-referral) problem that I am having. There are two simple "known" equations. A. P = ρg(zo-z) P = atmospheric pressure, ρ = the density of the air, g = gravitational...

I know that the example I use has been done online many times, but my question isn't about how to get the answer, that is obvious, my question goes a little deeper. For example when deriving the equation for an ellipse we have the constraint that the ellipse equation describe the set of (x,y)...

That clears up a lot thanks! So just to make sure I understand. The solution domain is split into two regions, and because the boundary condition lies in one region, the independent variable is confined to that region. Is all this because the solution domain must be continuous?, because if it...

I took a picture of a simple problem from my Diff Eq book. It is split up into two pictures for better resolution. In summary, ty'+2y=4t^2 (1) Has the solutions, y=t^2+C/t^2 (2) So, equation (1) has infinite solutions of the form of (2). But imposing the initial...