<em id="zlul0"></em><dl id="zlul0"><menu id="zlul0"></menu></dl>

<em id="zlul0"></em>

<dl id="zlul0"></dl>
<div id="zlul0"><tr id="zlul0"><object id="zlul0"></object></tr></div>
<em id="zlul0"></em>

<div id="zlul0"><ol id="zlul0"></ol></div>

# Questions tagged [differential-calculus]

The tag has no usage guidance.

95 questions
Filter by
Sorted by
Tagged with
0answers
43 views

In engineering mechanics, a classic approach for the calculation of displacements (virtual work method) requires the evaluation of the definite integral of the product of two continuous functions in $[... 1answer 2k views ### Was Jacobi the first to notice the ambiguity in the partial derivatives notation? And did anyone object to his fix? In his 1841 article De determinantibus, Jacobi remarked that the notation$\frac{\partial z}{\partial x}$for partial derivatives is ambiguous. He observed that when$z$is a function of$x,y$as well ... 3answers 279 views ### Mathematical Techniques to Reduce the Width of a Gaussian Peak In the chemical analysis by instruments, the signals of several molecules are overlapped which makes it difficult to determine the true area of each peak, such as those shown in red. I simulated this ... 22answers 5k views ### Which high-degree derivatives play an essential role? Q. Which high-degree derivatives play an essential role in applications, or in theorems? Of course the 1st derivative of distance w.r.t. time (velocity), the 2nd derivative (acceleration), and the ... 1answer 67 views ### Representation of finite differences of order k We define recursively finite differences$ g_k (x) $of order$ k $of function$ f $as follows:$g_0(x)=f(x)$,$g_n(x)=g_{n-1}(x+h_n)-g_{n-1}(x) (n\in\mathbb{N})$. It is known that all arguments of ... 0answers 73 views ### Differentiability (Hessian) of$\int \log F$when$\int \log f$is differentiable? For a specific probability density function$f$with support on${\mathbb R}$, which is not differentiable everywhere, I have proven that the Hessian matrix of $$g(\theta) = \int \log f(x;\theta)d H(... 0answers 143 views ### A vector calculus formula Let me answer my own question, hoping to be forgiven for that. I asked unsuccessfully that question on Mathematics. Let A, B be vector fields in \mathbb R^3. We have$$ \text{curl}\bigl((A\cdot \... 1answer 151 views ### About$\displaystyle\int_{\mathbb{R}_y^3}\int_{\mathbb{S}^2}e^{-\frac{1}{2}|x-[(x-y)\cdot\omega]\omega|^2}d\omega dy$An integral has been pushed me over the edge for several weeks. It reads as: $$\displaystyle\int_{\mathbb{R}_y^3}\int_{\mathbb{S}^2}e^{-\frac{1}{2}|x-[(x-y)\cdot\omega]\omega|^2}d\omega dy$$ I tried ... 1answer 72 views ### Existence of a certain type of function Trying to find functions with the given property: Given$M>0, K$compact in$\mathbf{R^n}$,$f:U\rightarrow\mathbf{R}$a$C^2$function, where$U$open in$\mathbf{R^n}$and$K\subset U$such that$...
2answers
153 views

### Dominant root of a family of polynomials

Let $f(x)=x^5-x^4-x^3-x^2-x-c$, where $c>2$ is a real number. It is easy to prove that there exists a positive real root $\alpha>2$ of $f(x)$ and all the other roots are non real. Also, by ...
0answers
55 views

### Looking for example of integral transformations that preserve number of zeros

Let $f:\mathbb{R} \to \mathbb{R}$ have $n<\infty$ zeros. I am looking for non-trivial examples of integral transformation \begin{align} g(x)= \int f(t) h(t,x) dt \end{align} such that $f$ and $g$...
3answers
118 views

### Literature request: Function that depends on a linear optimization problem [closed]

my question is about functions of the following form: $$f(t) = \max_{\mathbf{x}}~ \mathbf{c^T x} ~ {\rm s.t. \mathbf{Ax} +t \cdot \mathbf{a} \leq \mathbf{b}},$$ where $\mathbf{x},\mathbf{b},$ ...
1answer
266 views

### A Conjecture about the integral related to Chebyshev polynomial

I am interested in the following integral related to the Chebyshev polynomials $$I_{n,m}:= \int_0^\pi \left(\frac {\sin nx}{\sin x}\right)^{m} dx,$$ where $n,m\in \mathbb{Z}^+.$ It is easy to see ...
1answer
123 views

### A geometric property about certain polynomials in two variables

Assume that $p(x,y)$ is a polynomial in $\mathbb{R}[x, y]$ in the form $$p=p_{2n}+ p_{2n-1}+\ldots +p_1+p_0$$ where $p_i$ is a homogenous polynomial of degree $i$. Moreover we assume that the last ...
0answers
346 views

### An integral in Gradshteyn and Ryzhik

Section 3.248 of the 4th edition of the table of integrals by Gradshteyn and Ryzhik contains three entries. They are of elementary examples of the beta function. In the 5th edition there are two new ...

15 30 50 per page
山西福彩快乐十分钟
<em id="zlul0"></em><dl id="zlul0"><menu id="zlul0"></menu></dl>

<em id="zlul0"></em>

<dl id="zlul0"></dl>
<div id="zlul0"><tr id="zlul0"><object id="zlul0"></object></tr></div>
<em id="zlul0"></em>

<div id="zlul0"><ol id="zlul0"></ol></div>
<em id="zlul0"></em><dl id="zlul0"><menu id="zlul0"></menu></dl>

<em id="zlul0"></em>

<dl id="zlul0"></dl>
<div id="zlul0"><tr id="zlul0"><object id="zlul0"></object></tr></div>
<em id="zlul0"></em>

<div id="zlul0"><ol id="zlul0"></ol></div>
体彩金七乐走势图 最新时时走势图 江苏时时代理公司 3d走势图50期 江西时时事件结果 彩票快3 陕西11选5开奖查询 吉林时时技巧 秒速时时彩彩70 gs甘肃11选5开奖结果