The differential-calculus tag has no wiki summary.

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### Laplace transform for integral of product of two functions [on hold]

Consider the following integral of product of two function
$$
\int_0 ^t f(s)g(s-t)ds
$$
i want to know the laplace transform of above term w.r.t t.
if $g(s-t)$ is replaced by $g(t-s)$, there is a ...

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24 views

### Existence and Uniqueness of solution of volterra integral equation of the first kind

$$
\int_0^t k(s,t)f(s)ds=g(t)
$$
To know the existence and uniquness of solution of volterra integral equation(VIE) of the first kind, we differentiate it and convert to the VIE of the second kind.
...

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31 views

### existence of solution of volterra integral equation for the first kind

$$
\int_0^t k(s,t)f(s)ds=g(t)
$$
To know the existence and uniquness of solution of volterra integral equation(VIE) of the first kind, we differentiate it and convert to the VIE of the second kind.
...

**0**

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27 views

### How to solve integral equation? [duplicate]

I have an integral equation such that
$$
\int_t^T f(s)g(s,t)ds= h(t)
$$
where g and h is given. we want to know function f explicitly. As i know, this type of question is about the integral equation. ...

**3**

votes

**1**answer

147 views

### A functional equality

I don't know if this is known, but I was fiddling around with this equality :
$$f:(-1,1)\to (-1,1)\quad \text{satisfies}\quad(f(z)+1)^s=\sum_{j=0}^{\infty}\dbinom{s}{j}f(z^k)
\quad \forall z\in ...

**1**

vote

**1**answer

187 views

### Question about extending a solution to Monge-Ampere solution

I am interested in solutions to the Monge-Ampere equation for a smooth function
$h(x,y)$ of two variables(though I suppose I could try to make do with $C^2$ solutions). The equation is:
...

**3**

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136 views

### Boundary of an open, bounded and convex set in $\mathbb{R} ^n$

Let $U$ be an open, bounded and convex set in $\mathbb{R} ^n$. Since $\partial U$ is a rectifiable set it follows that up to a set of $H^{n-1}$-measure zero $\partial U$ is contained in a countable ...

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154 views

### Looking for author of calculus quote

When I was a lowly calculus student many many years ago, my calculus teacher quoted some famous mathemtician: "Calculus is the last course in arithmetic and the first course in mathematics that one ...

**3**

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**1**answer

65 views

### Counting extrema on a simplex

Let $p(x_{1},x_{2},\ldots,x_{n})=\sum_{i,j=1}^{n}{a_{ij}x_{i}x_{j}}$ be a homogenous multivariate polynomial of degree $2$.
I would like to know how many extrema $p$ has on the standard simplex
...

**1**

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**1**answer

196 views

### Request for help with two integrals

It would be great if someone can help me do these integrals - using numerical integration on Mathematica it seems that these converge - in what follows $a \in \mathbb{R}$ and $q \in \mathbb{N}$ and $n ...

**0**

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127 views

### Fractional Derivatives Of Sums

I have a question regarding the definition of a fractional derivative. I've searched, but I can't find a definition of fractional derivatives that explain the concept in terms of an operator on some ...

**2**

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**1**answer

857 views

### The Jones-Sato-Wada-Wiens polynomial for prime numbers and differential calculus?

After works of Davis, Matijasevic, Putman and Robinson between 1960 and 1970, we know that every recursively enumerable set of numbers can be represented by a polynomial.
In particular, it's the case ...

**8**

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**1**answer

749 views

### Differential Calculus and the De Rham Homotopy Operator

Suppose $M$ is a smooth manifold, $\Omega^k(M)$ the vector space (or $C^\infty(M)$-module in case this is better suited) of $k$-differentialforms on $M$ and
$$I: \Omega^k(M\times \mathbb{R}) \to ...

**4**

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155 views

### Co-filtered and pro-finite manifolds, filtered algebras, and differential calculus on them

Hello! I've come across a lot of questions (and nice answers) on MO, concerning infinite-dimensional manifolds and differential calculus over them, but nothing suiting the simpler and special case I ...

**23**

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**2**answers

808 views

### Is there a convenient differential calculus for cojets?

I understand the basics of exterior differential geometry and how to do calculus with exterior differential forms. I know how to use this to justify the notation dy/dx as a literal ratio of the ...

**2**

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349 views

### Finding the Universal Ideal of a (Covariant) Differential Calculus

Let $(\Omega,d)$ be a differential calculus over an algebra $A$. It is easy to show that $\Omega$ is always equal to a quotient of $\Omega_u(A)$, the universal calculus over $A$, by some ideal $N$ of ...