timescalewiki.org

timescalewiki

This wiki is a resource for people who do research in time scale calculus. Time scale calculus is a unification and extension of differential and difference calculus in which one does calculus upon a set $ mathbb{T}$ of real numbers called a time scale. When $ mathbb{T}= mathbb{R}$. The resulting theory becomes differential calculus. But when $ mathbb{T}= mathbb{Z}$. The resulting theory becomes difference calculus. Are also subsumed in the theory. How to get access to edit this wiki. In order to temper ...

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This wiki is a resource for people who do research in time scale calculus. Time scale calculus is a unification and extension of differential and difference calculus in which one does calculus upon a set $ mathbb{T}$ of real numbers called a time scale. When $ mathbb{T}= mathbb{R}$. The resulting theory becomes differential calculus. But when $ mathbb{T}= mathbb{Z}$. The resulting theory becomes difference calculus. Are also subsumed in the theory. How to get access to edit this wiki. In order to temper ...

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5 delta$ calculus

6 nabla$ calculus

7 diamond { alpha}$ calculus

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timescalewiki | timescalewiki.org Reviews

https://timescalewiki.org

This wiki is a resource for people who do research in time scale calculus. Time scale calculus is a unification and extension of differential and difference calculus in which one does calculus upon a set $ mathbb{T}$ of real numbers called a time scale. When $ mathbb{T}= mathbb{R}$. The resulting theory becomes differential calculus. But when $ mathbb{T}= mathbb{Z}$. The resulting theory becomes difference calculus. Are also subsumed in the theory. How to get access to edit this wiki. In order to temper ...

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timescalewiki.org

1

Multiples of integers - timescalewiki

http://timescalewiki.org/./index.php/Multiples_of_integers

The set $h mathbb{Z}= { ldots,-2h,-h,0,h,2h, ldots }$ of multiples of the integers is a time scale. F { Delta}(t)= dfrac{f(t h)-f(t)}{h}$. F { nabla}(t)= dfrac{f(t)-f(t-h)}{h}$. Displaystyle int s t f( tau) Delta tau=$. Displaystyle int s t f( tau) nabla tau=$. H k(t,s) = dfrac{1}{k! Displaystyle prod { ell=0} {k-1}(t- ell h-s)$. Mathbf{E}(t)= left[(1 h) { frac{1}{h} right] { frac{-t(t-h)}{2} $. Mathrm{ sin} 1(t,s)$. Widehat{ sin} p(t,s)$. Widehat{ sin} p(t,s)=$. Mathrm{ cos} p(t,s)$. Mathrm{ cos} 1(t,s)$.

2

Integers - timescalewiki

http://timescalewiki.org/./index.php/Integers

The set $ mathbb{Z}= { ldots,-2,-1,0,1,2, ldots }$ of integers is a time scale. F { Delta}(t)=f(t 1)-f(t)$. Displaystyle int s t f( tau) Delta tau= displaystyle int s t f( tau) Delta tau = left { begin{array}{ll} displaystyle sum {k=s} {t-1} f(k) &; t gt s 0 &; t=s - displaystyle sum {k=t} {s-1} f(k) &; t lt s end{array} right.$. H k(t,s)= dfrac{(t-s) { underline{k} }{k! Hat{h} k(t,s)= dfrac{(t-s) { overline{k} }{k! Mathbf{E}(t)=2 { frac{-t(t-1)}{2} $. Mathrm{ sin} 1(t,s)$. Widehat{ sin} p(t,s)$. Cos 1(t...

3

Harmonic numbers - timescalewiki

http://timescalewiki.org/./index.php/Harmonic_numbers

The set $ mathbb{H}= left { displaystyle sum {k=1} n dfrac{1}{k} colon n in mathbb{Z} right } = left {1, frac{3}{2}, frac{11}{6}, frac{25}{12}, frac{137}{60}, frac{49}{20}, frac{ 363}{140}, frac{761}{280}, ldots right }$ of harmonic numbers is a time scale. If $t in mathbb{H}$, then for some positive integer $n$, $t=H n= displaystyle sum {k=0} n dfrac{1}{k}$. Sigma(t)= sigma left( displaystyle sum {k=1} {n} dfrac{1}{k} right)= t dfrac{1}{n 1}$. Displaystyle int s t f( tau) Delta tau=$. L { mathbb{H} (t)=$.

4

Square integers - timescalewiki

http://timescalewiki.org/./index.php/Square_integers

The set $ mathbb{Z} 2 = {0,1,4,9,16, ldots }$ of square integers is a time scale. Sigma(t)=t 2 sqrt{t} 1$. F { Delta}(t)= dfrac{f(t 2 sqrt{t} 1)-f(t)}{2 sqrt{t}-1}$. Displaystyle int s t f( tau) Delta tau=$. Displaystyle int s t f( tau) nabla tau=$. Mathrm{ sin} 1(t,s)$. Widehat{ sin} p(t,s)$. Widehat{ sin} p(t,s)=$. Mathrm{ cos} p(t,s)$. Mathrm{ cos} 1(t,s)$. Widehat{ cos} p(t,s)$. Widehat{ cos} p(t,s)=$. Widehat{ sinh} p(t,s)$. Widehat{ sinh} p(t,s)=$. Widehat{ cosh} p(t,s)$. Widehat{ cosh} p(t,s)=$.

5

Isolated points - timescalewiki

http://timescalewiki.org/./index.php/Isolated_points

Let $ mathbb{T}$ be a time scale. We say that $ mathbb{T}$ is a time scale of isolated points if there exists $ epsilon 0$ such that for all $t in mathbb{T}$, $ mu(t) geq epsilon$. Let $ mathbb{T}= { ldots,t {-1},t 0,t 1, ldots }$ be a time scale. Of isolated points with $t k t n$ iff $k n$. Define the bijection. Pi colon mathbb{T} rightarrow mathbb{Z}$, $ pi(t k)=k$. Mathbb{T}= mathbb{T} { mathrm{iso} $. Generic element $t in mathbb{T}$:. For some $n in mathbb{Z}$, $t=t n$. Sigma(t n)=t {n 1}$. Mathscr{...

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This wiki is a resource for people who do research in time scale calculus. Time scale calculus is a unification and extension of differential and difference calculus in which one does calculus upon a set $ mathbb{T}$ of real numbers called a time scale. When $ mathbb{T}= mathbb{R}$. The resulting theory becomes differential calculus. But when $ mathbb{T}= mathbb{Z}$. The resulting theory becomes difference calculus. Are also subsumed in the theory. How to get access to edit this wiki. In order to temper ...

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