List questions from vector-analysis | MathQA

Understanding why $\nabla f$ points to greatest rate of change in a function, & why the derivative of $f(\mathbf r + \mathbf{\delta r})$ is $\nabla f$

Published on 10 May 2026 - 17:02

Question on intuitive understanding of directional derivative

Published on 28 Mar 2026 - 17:56

Show equivalence of dot product and differential form surface integrals

Published on 10 May 2026 - 16:12

Proving a vector identity for $\text{div}(\mathbf{F} \times \mathbf{G})$

Published on 05 Apr 2026 - 13:47

Let $f:\mathbb{R}^3\to \mathbb{R}^2$ be of class $C^1$; write $f$ in the form $f(x, y_1, y_2)$. Assume that $f(3, -1, 2)=0$ and

Published on 04 Apr 2026 - 11:22

Prove $det(F'(x)) = 0$

Published on 10 May 2026 - 15:29

Vectors, finding acute angle between VB and plane OVA on a square base pyramid

Published on 12 Apr 2026 - 23:46

Given $f: \mathbb{R}^5\to \mathbb{R}^2$, of class $C^1$. Let $a= (1,2,-1,3,0)$; suppose that $f(a) = 0$ and $Df(a)=$

Published on 05 Apr 2026 - 1:24

Solenoid and non-conservative vector field

Published on 17 Apr 2026 - 4:45

Formula involving cross products $\nabla \times (F \times G)$?

Published on 14 Apr 2026 - 2:41

Let $f:\mathbb{R}^2\to \mathbb{R}$ be of class $C^1$, with $f(2,-1)=-1$. Set $G(x,y,u)=f(x,y)+u^2, H(x,y,u)= ux+3y^3+u^3$.

Published on 07 Apr 2026 - 14:49

Improved Gradient Algorithm

Published on 10 May 2026 - 17:55

Let $F:\mathbb{R}^2\to \mathbb{R}$ be of class $C^2$, with $F(0, 0) = 0$ and $DF(0, 0) =\begin{bmatrix}2 & 3\end{bmatrix}$.

Published on 16 Apr 2026 - 14:49

Christoffel Symbols for elliptic coordinate system

Published on 10 May 2026 - 13:49

How to evaluate $\int_{|X|<1}e^{1\over|X|^2-1} dX$, here $X\in \mathbb R^n$.

Published on 15 Apr 2026 - 3:04