In the Appendix 5 to Ballmann, Gromov and Schroeder's Manifolds of nonpositive curvature, Schroeder mentions that for a rank one symmetric space of n...

Is there a name or symbol convention for what I might call the "anti" Kronecker delta (that is, $1 - \delta_{ij}$)?

Below, $\Delta$ means taking the derivative, $\frac{d}{dx}$. For $n\in\mathbb{Z}$, $n\geq 0$, we have $$\Delta^n\sin{x}=\sin{(x+n\tau/4)} \\ \Delta^n\cos{...

I'm really confused about matrix calculus and especially partial derivatives. When do we need to sum up partial derivatives to get a total derivative...

I was wondering what the natural domain of $$(1+x)^{\frac{1}{x}}$$ was. I know it's defined on interval $x\in(-1,0)\cup (0,\infty)$. However, I'...

In a $2 × 4$ rectangle grid shown below, each cell is a rectangle. How many rectangles can be observed in the grid? My attempt: I found a formula somewher...

I am a high schooler with no prior exposure to calculus. I want a calculus book to learn math for classical mechanics on my own, and perhaps learning math...

I saw in a proof somewhere that a square matrix $AA^T$ is similar to $A^T A$, so I thought about it and I don't know why (or whether) it's true....

First of all i have created a sequence of remainder of an expression just like below $33^{1}$ 33% 7 =5(remainder) $33^{2}$ 5*33% 7 =5*5%7=25%7=4(remainder...

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...