Laplace-Transformation (陰性)

Description:

The Laplace transformation is used to convert initial-value (Cauchy) problems for inhomogeneous linear differential equations with constant coefficients into algebraic equations. It is therefore often applied to dynamic systems.

The Laplace transform of $f(t)$is the function $F(s)=\int\limits_{0}^{\infty }{f(t){{e}^{-st}}dt}$.

The original function $f(t)$ is also called the inverse transform (time domain) and the image function $F(s)$ the transform (frequency domain).

Description:

The Laplace transformation is used to convert initial-value (Cauchy) problems for inhomogeneous linear differential equations with constant coefficients into algebraic equations. It is therefore often applied to dynamic systems.

The Laplace transform of $f(t)$is the function $F(s)=\int\limits_{0}^{\infty }{f(t){{e}^{-st}}dt}$.

The original function $f(t)$ is also called the inverse transform (time domain) and the image function $F(s)$ the transform (frequency domain).

Description: La transformación de Laplace se usa para convertir problemas de valor inicial (Cauchy) para ecuaciones diferenciales lineales no homogéneas con coeficientes constantes en ecuaciones algebraicas. Por lo tanto, se aplica a menudo en sistemas dinámicos. La transformación de Laplace de $f(t)$ es la función $F(s)=\int\limits_{0}^{\infty }{f(t){{e}^{-st}}dt}$ . La función original $f(t)$ también se llama transformación inversa (dominio de tiempo) y la función imagen $F(s)$ , transformación (dominio de frecuencia).

Description: 拉普拉斯变换用于将常系数非齐次线性微分方程组（柯西）初值问题转化为代数方程组。因此经常应用于动力系统。 $f(t)$ 的拉普拉斯变换即为函数 $F(s)=\int\limits_{0}^{\infty }{f(t){{e}^{-st}}dt}$。 原函数 $f(t)$ 也称为逆变换（时间域），象函数 $F(s)$ 则称为拉普拉斯变换（频率域）。