Notation of Leibniz

Of Analysis, the notation of Leibniz , named in the honor of Gottfried Wilhelm von Leibniz, consists of the use of the notations “D right” (d) or “Delta” (Δ) followed by a quantity to represent a Infinitésimal quantity in question. For example, if X are a quantity, D X and Δ can there represent an infinitesimal quantity of X . By extension, it is a notation usually used to write the Dérivée S.

In Physical, this notation is almost unanimously interpreted like an elementary modification (of position, speed…) or an elementary sample (of surface, volume…).

Details

According to Leibniz, the derived from there compared to X , which is written in modern terms like the limit:

$\ lim_ {\ Delta X \ to 0} \ frac {\ Delta there} {\ Delta X}$

of an infinitesimal increment of there by an infinitesimal increment of X is the quotient. Thus, if one poses a function F derivable, it is legitimate to write, while posing:

$y = F (X) \$

that the derivative of F is:

$\ frac {\ mathrm Dy} {\ mathrm dx} =f' \ left (X \ right).$

In a similar way, the Intégrale of the function $f \$ on the interval $\ left has, B \ right \$ , defined by:

$\ lim_ {\ Delta_i {X} \ rightarrow 0} {\ sum_ {N} {F (x_n). {\ Delta_n X}}}$

with

{\ Delta_n X} = x_ {n+1} - x_n \ Ge 0, \ \ sum_ {N} {\ Delta_n X} = Ba, \ x_0 = has \

or by the theorem of Riemann:

$(Ba) \ cdot \ lim_ {NR \ rightarrow \ infin} \ frac {1} {NR} \ sum_ {N = 1} ^ {NR} {F \ left (+ N \ cdot \ frac {Ba} {NR} \ right has)}$

Leibniz saw it as the sum of an infinite quantity of infinitesimal quantities. By using the letter S to note this sum, that gave the modern notation of the integral:

$\ int F \ left (X \ right) \; \ mathrm dx$ .

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