Recent content by Hall

Sir, you can very well see that post #3 answered my main question very well, without asking any personal details. the helpers will always help, bullies will always do ragging (the more learned they are the more disguised their ragging would be). And none of these applies to you.

You have not even touched the IMF and its headquarter in USA issue which I mentioned.

Amazon began with selling books only, it should be shut down now as it has trespassed with what it began with.

You've got the power, but if you still want to know then yes I'm not from any of European countries. The ratio 10:1 which was presented in OP was from a well-researched effort, and therefore, I would say it holds for me.

I didn't use the word 'physics' a single time in this post before this one, though this sub-forum is for STEM only, yet I have seen economics have been allowed upto a certain degree. I used the institutions like IMF and World Bank for explanatory purpose because they are global level...

What about the tag effect? A man of letters, upon being asked if IMF, World Bank or other similar institutions would prefer an OxBridge (and Ivy League) degree holders to, say, Goethe University or Heidelberg University, responded that in today's era the personal skills matters the most and the...

I have searched for almost all courses and all universities and found that the fees of universities in UK is more than 10 times than those of Germany (if I were to convert both of those national currencies in my country's currency). Had education been some market product, I would have instantly...

If I have been given a system of inhomogeneous linear ODEs, $$ \vec{x'} = \begin{bmatrix} 4 & -1 \\ 5 & -2 \\ \end{bmatrix} \vec{x} + \begin{bmatrix} 18e^{2t} \\ 30e^{2t}\\ \end{bmatrix} $$ I have found its particular solution to be: $$ 1/4 \begin{bmatrix} -31e^{2t} - 25e^{6t} \\ 85e^{2t} -...

I have tried, but without any extension this definition: $$ \begin{align*} \text{For every epsilon > 0 there exists a delta > 0, such that} \\ ||\dot{P}|| \lt \delta \implies | S(f,\dot P) - L| \lt \epsilon \\ \end{align*} $$ alone isn't proving to be helpful. We can extend it and come with...

One of the advantage of Riemann's definition that I have come up with is: it help in proving the following powerful theorem: If ##f_n \to f## uniformly, and ##f_n## is integrable for all ##n## on ##[a,b]##, then ##f## is also integrable on ##[a,b]##.

We can use the sequential definition, easily derivable from epsilon-delta definition, to find the integral. I'll surely do it on my own.

Given a function ##f##, interval ##[a,b]##, and its tagged partition ##\dot P##. The Riemann Sum is defined over ##\dot P## is as follows: $$ S (f, \dot P) = \sum f(t_i) (x_k - x_{k-1})$$ A function is integrable on ##[a,b]##, if for every ##\varepsilon \gt 0##, there exists a...

Yes.

. If ##y## lies between ##f'(a)## and ##f'(b)##, then it is surely to between the end-points of one of the graphs. It was not very obvious for me to see, I was considering ##f_a(a)## and ##f_a(b)## individually and not in connection with that "or" ##f_b(a)## and ##f_b(a)##.