# Questions tagged [multivariable-calculus]

The tag has no usage guidance.

32 questions
Filter by
Sorted by
Tagged with
33 views

### How does one visualize this on a graph? (confused) [closed]

I was given a function where f(x,y) = 3 where -1<=x<1, -1<=y<1. How does one exactly interpret/visualize this? What does the value 3 mean?
128 views

### Strong convexity inequality w.r.t. infinity norm $\lVert\cdot\rVert_{\infty}$

Consider a twice differentiable 1-strongly convex function $f:\mathbb{R}^n \to \mathbb{R}$. Is it true that there exists $\alpha>0$ independent of $n$ such that, for all $x \in \mathbb{R}^n$: \...
115 views

932 views

### How to generalize the various vector calculus theorems to distributions?

Here is a list of vector calculus identities; in the proof of these identities, we all assume that these functions are $𝐶^𝑘$ in an open set, and we usually use these identities to calculate ...
75 views

71 views

### Conditions for a function to vanish almost nowhere on its support?

Let $f:\mathbb{R}^d\rightarrow\mathbb{R}$ be a continuous function and $\mathrm{supp}(f) := \mathrm{cl}\{x\in\mathbb{R}^d\mid f(x)\neq 0\}$ its support. Under which conditions is it true that $f≠0$ (...
I have two Gaussian random variables $$X \sim \mathcal N(0, I), \ \ \ W \sim \mathcal N(0, \sigma\cdot I)$$ and I known a parametric change-of-variable $Y(\theta) = T(X; \theta)$. I would like to ...