Does the Finite Calculus exist? And is it used?

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LearyJr

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Does the Finite Calculus exist? (Please, don't confuse it for Discrete Mathematics.) Is it the synonym of the Discrete Calculus or the synonym of the Finite Differences Calculus? Is it applicable for Pure & Applied Physics nowadays? Could you recommend some resources for such subject?
Because I'm trying to study not only Classic Calculus, but the Calculus of Finite Variables and Functions, I'm writing you this question.
 
The "finite Calculus" is also known as "finite differences" or "the calculus of finite differences". Like "infinitesimal Calculus" (regular Calculus) it starts by defining the "difference quotient", \(\displaystyle \frac{f(x+h)- f(x)}{h}\). Where (infinitesimal) Calculus takes the limit as h goes to 0, "finite Calculus" either leaves "h" as a parameter or, equivalently, takes h= 1. For example where the derivative in (infinitesimal) Calculus of \(\displaystyle x^2\) is \(\displaystyle 2x\), in finite Calculus it is either \(\displaystyle \frac{(x+ h)^2- x^2}{h}= \frac{2xh+ h^2}{h}= 2x+ h\) or, taking h= 1, 2x+ 1.
 
Whats resources could you recommend books or resources on Finite Differences for wide studying that subject?
 
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Any textbook on "Numerical Methods" should provide an adequate introduction.
 
tkhunny said:
Any textbook on "Numerical Methods" should provide an adequate introduction.
Click to expand...
Formally, the Numerical Methods discipline is the Finite Calculus. Isn't it?
Is it Pure Mathematics or only Applied Maths?
 
tkhunny said:
Why is that important?
Click to expand...

Because of possible developing of this discipline and huge amount of its applications, it seems significant. Doesn't it?
Please, don't forget to read my first question higher one you've already mentioned. Thank you for your attention.
 
No, "numerical analysis" and "finite differences" are completely different fields of mathematics (although approximating a differential equation by a finite differences equation will lead to one method of numerically solving the differential equation). George Boole (of "Boolean Algebra") wrote a classic book on "finite differences" that has been reprinted by Dover Books.
 
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