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lines changed Original file line number Diff line number Diff line change @@ -168,11 +168,10 @@ berechnet:
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::
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- sage: s = var("s")
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- sage: t = var("t")
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+ sage: s,t = SR.var("s,t")
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sage: f = t^2*exp(t) - sin(t)
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- sage: f.laplace(t,s)
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- -1 /(s^2 + 1) + 2 /(s - 1)^3
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+ sage: f.laplace(t,s).expand()
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+ 2 /(s^3 - 3*s^ 2 + 3*s - 1) - 1 /(s^2 + 1)
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Hier ist ein komplizierteres Beispiel. Die Verschiebung des
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Gleichgewichts einer verkoppelten Feder, die an der linken Wand
Original file line number Diff line number Diff line change @@ -178,11 +178,10 @@ You can compute Laplace transforms also; the Laplace transform of
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::
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- sage: s = var("s")
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- sage: t = var("t")
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+ sage: s,t = SR.var("s,t")
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sage: f = t^2*exp(t) - sin(t)
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- sage: f.laplace(t,s)
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- -1 /(s^2 + 1) + 2 /(s - 1)^3
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+ sage: f.laplace(t,s).expand()
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+ 2 /(s^3 - 3*s^ 2 + 3*s - 1) - 1 /(s^2 + 1)
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Here is a more involved example. The displacement from equilibrium
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(respectively) for a coupled spring attached to a wall on the left
Original file line number Diff line number Diff line change @@ -160,11 +160,10 @@ de :math:`t^2e^t -\sin(t)` se calcula como sigue:
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::
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- sage: s = var("s")
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- sage: t = var("t")
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+ sage: s,t = SR.var("s,t")
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sage: f = t^2*exp(t) - sin(t)
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- sage: f.laplace(t,s)
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- -1 /(s^2 + 1) + 2 /(s - 1)^3
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+ sage: f.laplace(t,s).expand()
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+ 2 /(s^3 - 3*s^ 2 + 3*s - 1) - 1 /(s^2 + 1)
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Veamos un ejemplo más complicado. El desplazamiento desde el punto de equilibrio
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de dos resortes acoplados, sujetos a una pared a la izquierda
Original file line number Diff line number Diff line change @@ -145,11 +145,10 @@ transformée de Laplace de :math:`t^2e^t -\sin(t)` s'obtient comme suit :
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::
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- sage: s = var("s")
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- sage: t = var("t")
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+ sage: s,t = SR.var("s,t")
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sage: f = t^2*exp(t) - sin(t)
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- sage: f.laplace(t,s)
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- -1 /(s^2 + 1) + 2 /(s - 1)^3
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+ sage: f.laplace(t,s).expand()
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+ 2 /(s^3 - 3*s^ 2 + 3*s - 1) - 1 /(s^2 + 1)
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Voici un exemple plus élaboré. L'élongation à partir du point
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d'équilibre de ressorts couplés attachés à gauche à un mur
Original file line number Diff line number Diff line change @@ -146,11 +146,10 @@ Si può anche calcolare la trasformata di Laplace; la trasformata di Laplace di
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::
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- sage: s = var("s")
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- sage: t = var("t")
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+ sage: s,t = SR.var("s,t")
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sage: f = t^2*exp(t) - sin(t)
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- sage: f.laplace(t,s)
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- -1 /(s^2 + 1) + 2 /(s - 1)^3
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+ sage: f.laplace(t,s).expand()
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+ 2 /(s^3 - 3*s^ 2 + 3*s - 1) - 1 /(s^2 + 1)
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Il successivo è un esempio più articolato. Lo scostamento dall'equilibrio
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(rispettivamente) per due molle accoppiate fissate ad un muro a sinistra
Original file line number Diff line number Diff line change @@ -172,11 +172,10 @@ Sageを使って常微分方程式を研究することもできる. :math:`x'
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::
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- sage: s = var("s")
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- sage: t = var("t")
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+ sage: s,t = SR.var("s,t")
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sage: f = t^2*exp(t) - sin(t)
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- sage: f.laplace(t,s)
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- -1 /(s^2 + 1) + 2 /(s - 1)^3
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+ sage: f.laplace(t,s).expand()
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+ 2 /(s^3 - 3*s^ 2 + 3*s - 1) - 1 /(s^2 + 1)
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もう少し手間のかかる問題を考えてみよう.
Original file line number Diff line number Diff line change @@ -165,11 +165,10 @@ Laplace de :math:`t^2e^t -\sin(t)` é calculada da seguinte forma:
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::
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- sage: s = var("s")
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- sage: t = var("t")
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+ sage: s,t = SR.var("s,t")
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sage: f = t^2*exp(t) - sin(t)
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- sage: f.laplace(t,s)
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- -1 /(s^2 + 1) + 2 /(s - 1)^3
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+ sage: f.laplace(t,s).expand()
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+ 2 /(s^3 - 3*s^ 2 + 3*s - 1) - 1 /(s^2 + 1)
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A seguir, um exemplo mais complicado. O deslocamento, com respeito à
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posição de equilíbrio, de duas massas presas a uma parede através de
Original file line number Diff line number Diff line change @@ -162,11 +162,10 @@ Sage может использоваться для решения диффер
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::
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- sage: s = var("s")
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- sage: t = var("t")
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+ sage: s,t = SR.var("s,t")
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sage: f = t^2*exp(t) - sin(t)
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- sage: f.laplace(t,s)
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- -1 /(s^2 + 1) + 2 /(s - 1)^3
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+ sage: f.laplace(t,s).expand()
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+ 2 /(s^3 - 3*s^ 2 + 3*s - 1) - 1 /(s^2 + 1)
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Приведем более сложный пример. Отклонение от положения равновесия для пары
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пружин, прикрепленных к стене слева,
Original file line number Diff line number Diff line change @@ -165,11 +165,10 @@ Sage 可以对许多函数进行微分和积分。
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::
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- sage: s = var("s")
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- sage: t = var("t")
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+ sage: s,t = SR.var("s,t")
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sage: f = t^2*exp(t) - sin(t)
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- sage: f.laplace(t,s)
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- -1 /(s^2 + 1) + 2 /(s - 1)^3
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+ sage: f.laplace(t,s).expand()
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+ 2 /(s^3 - 3*s^ 2 + 3*s - 1) - 1 /(s^2 + 1)
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这里是一个更复杂的示例。左侧连接到墙上的耦合弹簧的平衡位移
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