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 25 Mar 2026 - 2:03

Question on intuitive understanding of directional derivative

Published on 13 Feb 2018 - 20:27

Show equivalence of dot product and differential form surface integrals

Published on 15 Feb 2018 - 15:55

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

Published on 16 Feb 2018 - 6:30

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 17 Feb 2018 - 2:41

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

Published on 17 Feb 2018 - 7:16

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

Published on 17 Feb 2018 - 7:20

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 17 Feb 2018 - 20:15

Solenoid and non-conservative vector field

Published on 17 Feb 2018 - 20:28

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

Published on 18 Feb 2018 - 2:57

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 18 Feb 2018 - 17:25

Improved Gradient Algorithm

Published on 16 Mar 2026 - 22:21

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 19 Feb 2018 - 21:20

Christoffel Symbols for elliptic coordinate system

Published on 24 Mar 2026 - 19:01

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

Published on 20 Feb 2018 - 8:42