Is this the right way to use Jordan's Lemma to show that integration over the semi-circle does not contribute to the closed-contour integration for t...

Show that every vector $\vec{u}$$\in$$U$ can be uniquely decomposed into $\vec{u}$$=$$\vec{u}_{1}$$+$$\vec{u}_{2}$ where $\vec{u}_{1}\in{W}\subset{U}$ and...

I am trying to show that if $f_n$ converges to $f$ in $L^p(X,\mu)$ then $f_n\to f$ in measure, where $1\le p \le \infty$. Here is my attempt for $p\ge 1$:...

how can I use the residue theorem to calculate $$\int_{-\infty}^\infty dx\, \frac{e^{-i x}}{(\sinh x)^2}$$ Im confused about how to tackle the double pole...

Problem: $y'+yx=0, \quad y(0)=-1$ We separate it: $\frac{dy}{dx}=-yx \Rightarrow \int\frac{-1}{y}dy=\int x dx = \frac{1}{2}x^2 + C_1$ With $\int\frac...

I need to calculate $$\left| \frac{3}{\sqrt{20}} + i\!\cdot\!\frac{1}{\sqrt{20}}\!\cdot\!e^{i\!\cdot\!\frac{\pi}{3}} \right|$$ Is there a way to do it wit...

What is the practical proof for $-1(-1)=+1$. Actually multiplication is repetitive addition. I am struggling how can I provide an activity to prove practi...

Game theory is defined (here) as follows: "Game theory, branch of applied mathematics that provides tools for analyzing situations in which parties, calle...

I'm sure this is a really simple question but I hear "X choose Y" in speech. What does this mean?

I am having trouble understanding visually what a gradient is. My understanding is it is a generalisation of tangential slopes to higher dimensions and gi...