# Questions tagged [multivariable-calculus]

The tag has no usage guidance.

17 questions
Filter by
Sorted by
Tagged with
48 views

### How to define a function that has these specific properties?

Suppose $x = (x_1,x_2,\dots,x_K) \in \mathbb{Z}^K_{\geq 0}$. For $x,y \in \mathbb{Z}^K_{\geq 0}$, we write $x \succ y$ or $y \prec x$ if $x \neq y$ and \begin{align*} x_{i(x,y)} > y_{i(x,y)...
45 views

### Class of functions which are defined by their second derivative [closed]

I asked this question on math stackexchange but I didn't get much input. I am looking for classes of differentiable functions that are characterized by their second derivative. For example: convex ...
26 views

### Hessian generating functions

I am looking for a characterization of functions $\Phi: \mathbb{R}^n \to \mathbb{R}^{n \times n}$ such that $\Phi(\mathbf{x}) = \nabla^2 f(\mathbf{x})$ for a function $f$ which is twice continuously ...
28 views

### What relationship exists between samples of a function and samples of its vector gradient field?

A real function $f(x)$ is defined on $N$-dimensional real space where $N \ge 3$. $f(x)$ is differentiable and its gradient with respect to x is $g(x)$. So $g(x)$ is a vector field. Assume we do not ...