A finite difference is a mathematical expression of the form f (x + b) − f (x + a). If a finite difference is divided by b − a, one gets a difference quotient. The approximation of derivatives by finite differences plays a central role in finite difference methods for the numerical solution of differential equations, especially boundary value problems.
The difference operator, commonly denoted
Δ
{\displaystyle \Delta }
is the operator that maps a function f to the function
Δ
[
f
]
{\displaystyle \Delta [f]}
defined by
Δ
[
f
]
(
x
)
=
f
(
x
+
1
)
−
f
(
x
)
.
{\displaystyle \Delta [f](x)=f(x+1)-f(x).}
A difference equation is a functional equation that involves the finite difference operator in the same way as a differential equation involves derivatives. There are many similarities between difference equations and differential equations, specially in the solving methods. Certain recurrence relations can be written as difference equations by replacing iteration notation with finite differences.
In numerical analysis, finite differences are widely used for approximating derivatives, and the term "finite difference" is often used as an abbreviation of "finite difference approximation of derivatives". Finite difference approximations are finite difference quotients in the terminology employed above.
Finite differences were introduced by Brook Taylor in 1715 and have also been studied as abstract self-standing mathematical objects in works by George Boole (1860), L. M. Milne-Thomson (1933), and Károly Jordan (1939). Finite differences trace their origins back to one of Jost Bürgi's algorithms (c. 1592) and work by others including Isaac Newton. The formal calculus of finite differences can be viewed as an alternative to the calculus of infinitesimals.
Ask ko lang po ano pinag kaiba ng dalawang yan ui lang po o pati processor? meron kasi akong nakita na same model isa nka google tv at yung isa standard na android tv.
Mga sir ano po bang pinagkaiba ng ComSci sa IT? Saan mas nag fo-focus ang ComSci pati na rin ang IT? Please help naman sa mga IT/ComSci students or graduates diyan. <3
good eve...
ewan ko kung dito ba dapat to popost... :)
ano ba pagkakaiba ng light novel at manga?
kung may light novel at manga version yung story... alin ang mas maganda basahin?
salamat sa insights...
plano ko kasi magexplore sa ln at manga... more on anime kasi ako... try ko lang... :)