# Questions tagged [vector-analysis]

Questions related to understanding line integrals, vector fields, surface integrals, the theorems of Gauss, Green and Stokes. Some related tags are (multivariable-calculus) and (differential-geometry).

4,182 questions
Filter by
Sorted by
Tagged with
20 views

### Chain rule for multivariable differentiation

For one-dimensional case, after affine transformation \begin{equation} x=\hat{x}+\sigma c . \end{equation} Using the chain rule for differentiation, we can write \begin{equation} \frac{d}{dc}=\frac{...
35 views

### Suitable books for further study on mathematical analysis

I have self-studied mathematical analysis using books written by people from my country. These books cover traditional topics including green formula and stokes formula ($\mathbb{R}^3$ form). However,...
16 views

### Flux through the curved surface of the cylinder in the first octant.

I am given a vector field $\vec{F}=z\hat{i}+x\hat{j}+y\hat{k}$. The flux of the vector field passing through the curved surface of the cylinder $x^2+y^2=a^2$ in the first octant and below $Z=h$ plane ...
41 views

73 views

18 views

34 views

### How to compute $(\mathbf{A} \cdot \mathbf{\nabla})\mathbf{B}$?

I'm currently reading Intro to Electrodynamics by Griffiths, and in the maths section, there is the following problem: "If $\mathbf{A}$ and $\mathbf{B}$ are two vector functions, what does the ...
48 views

64 views

### Compatibility condition for Poisson's equation - Divergence theorem

Let $\Omega \subset \mathbb R^n$ be open and bounded. Given the Poissons equation with Neumann-boundary, e.g. $$-\Delta u = f \quad \text{and}\quad \frac{\partial u}{\partial n}=g,$$ we must require ...
10 views

According to this question Understanding the idea of a pseudo-gradient vector field, I have another question. In a book I found the following "explanation": [...] as a substitute for the notion of ...
12 views

### Understanding a vector analysis formula for finite volume method

I have an equation which is used for the finite volume method in partial differential equations. I can read it but I had to few vector analysis to really get it. The equation is: \begin{equation} \...
14 views

12 views

### Why is Kullback–Leibler divergence a divergence. How is it related to divergence of a vector field? [closed]

Why is Kullback–Leibler divergence a divergence. How is it related to divergence of a vector field
17 views

I have non-uniform quadrilateral mesh. For each volume from my mesh I have a point which represents the volume. I need gradient approximation using representation points. Any ideas?
27 views

### Difference between $\nabla(\nabla . F)$ and $\nabla^2F$, where $F$ is a vector function

I recently started vector calculus and saw that following identity $\nabla\times(\nabla\times F)=\nabla(\nabla.F)-\nabla^2F$ But aren't $\nabla(\nabla.F)$ and $\nabla^2F$ the same or I am missing ...
37 views

### Least square method, why gradient gives the minimum and not the maximum?

I'm bit confused about finding critical points of functions. Studying the least square method we got some data $\{(y_{1},x_{1}),...,(y_{n},x_{n}))\}$ and can define error associating with $y=ax+b$ by ...
For a given: $A \in \mathbb{R}^{m \times n}$ I am trying to calculate the gradient of: $$f(x) := \frac{1}{2}\left\|{A^T x}\right\|_2^2 - b^Tx.$$ Therefore I wrote $f$ like this: f(x) = \frac{1}{...