martes, 13 de agosto de 2013

Matemática

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Un optimista ve una oportunidad en toda calamidad, un pesimista ve una calamidad en toda oportunidad.
        -- Winston Churchill. (1874-1965) Político inglés.



El pesimista sabe rebelarse contra el mal. Sólo el optimista sabe extrañarse del mal.
        -- Gilbert Chesterton. (1874-1936) Escritor británico.



Diferencial


y=x2, obtener: Ay, dy (x2: x elevado al cuadrado, Ay: delta y, dy: diferencial de y)
Ay = f(x+Ax) - f(x) =
= (x+Ax)2 - x2 =
= x2 + 2xAx + Ax2 - x2 =
= 2xAx + Ax2


dy = f'(x) dx =
= 2x Ax (*)


* Recordar:
x' = 1 (*2)
dx = x' Ax = Ax (*3)


*2 Recordar:
(1): lím Ax->0 Ax/Ax = x' (derivada de 1 variable con respecto a sí misma, toda variable está en función de sí misma x = f(x) / x = x)
(2): lím Ax->0 Ax/Ax = lím Ax->0 1 = 1
Por (1) y (2): x' = 1


*3 Recordar:
lím Ax->0 Ax/Ax = x'
Ax / Ax = x' + alfa / Ax -> 0 => alfa -> 0
Ax = x' Ax + alfa Ax
dx = x' Ax = Ax (diferencial de la variable independiente con respecto a sí misma, obviamente por ser independiente)



Integral

lím i → ∞ ∑ f(xi) ∆xi = ∆x lím i → ∞ ∑ f(xi) = ∫def.[a..b] f(x) ∆x, ∆x0 = ∆x1 = ... = ∆xi  = ∆x, i → ∞ <=> ∆x → 0



∫def.[a..b] f(x) ∆x = primitiva de f(b) - primitiva de f(a) = primitiva de f(b).g(z) - primitiva de f(a)


si primitiva de f(a) = 0:
∫def.[a..x] f(x) ∆x = primitiva de f(x) = primitiva de f(x). g(z) = ∫def.[a..x] f(x) ∆x.g(z) = ∫def.[a..x] f(x) dx


si no:
∫def.[a..x] f(x) ∆x = ∫def.[a..x] f(x) g(z1)-g(z0), g(z1)-g(z0)=∆x




si F(x) = x => dx = ∆x
si y=F(x) ^ x=G(z) => dx = f(x) . g(z) . ∆z
si no => dx = f(x) ∆x


primitiva de f(x) = primitiva de f(x).g(z)


Matemática, teoría de juegos, software libre


Positivism and Software Engineering

When Aristoteles stated his geocentric theory, the sustained theories were hard to explain without complex formulas describing weird trajectories about the other corps over the system.
About the same idea, Greek mechanics was largely accepted for describing accurately enough trajectories of objects near the grounth and above the heights. But it still miss something...

In my humilde opinion, the success key which lead Galileo and Newton theories superseed their ancestors was that these are based on postulates of equality among all the interveinig elements of analysis. In other words, each element being under analysis posseses undistinguishable properties over the others, and any of them hasn't special atributes and/or governementship over the others: The apple goes towards the Earth, and the Earth does the same towards the apple all simultaneously; A hunt walks it's way over the Earth's surface, and the Earth moves arround its centre as a reaction to the strength excerced by the hunt steps.

"Logic carries you from A to B, imagination everywhere", and "There's 1 thing more valuable than knowledge: imagination", are quotes from Einstein, this makes me question if the status we attribute to intelligence should be reevaluated.

I'm still wondering, what would Arquimedes have mean to say when he said "Give me a standpoint and I'll move the world".

Your post raised my interest up!