After trying to get my head around this for an embarrassingly long time, I think I need some help... We defined local (lyapunov) stability and asymptotic ...

I can't calm down when I can't realized of principles of working something. Quaternion is that place where I spend а few days! Unfortunately, no...

If given a function $f$ that I am supposed to demonstrate is derivable, is it enough for me to try to compute its derivative $f'$ and if the result is...

In order to prove that $n$ is $O(n\log n)$, as per my understanding if we have to say $f(n)$ is $O(g(n))$ then $\lim\limits_{n \to \infty} \frac{f(n)}{g(n...

The problem I am working on is, "Show that a finite poset can be reconstructed from its covering relation. [Hint:Show that the poset is the reflexive tran...

A dinghy is pulled toward a dock by a rope from the bow through a ring on the dock 6 ft. above the bow. The rope is hauled in a rate of 2 ft/s. At what ra...

---The statement: Let $m$ and $n$ be two integers. Prove that $mn+m$ is odd if and only if $m$ is odd and $n$ is even. ---Solution: First, we show that if...

I have a polar equation defined as: $r = ae^{θ \tan m}$ where, $a$ and $m$ are constants, $θ$ is the angle between the horizontal axis from the origin $(x...

After coming across this question: How to verify this limit, I have the following question: When taking the limit of an integral, is it valid to move the ...

Let $~F = \langle x,y,z \rangle~$ be a vector field on $ R^3$ . Let $S$ be the graph of $ g(x,y)=1- y^2 + x^2 $ over the unit disc $D$ in $ R^2$ and let $...