Скачать или смотреть ℒ[1] = 1/s GRAPHICAL Meaning (Laplace Transform of 1 EXPLAINED Graphically — Why F(s)=1/s)

Ever wondered why the Laplace transform of the constant function f(t)=1 is F(s)=1/s for positive values of s? In this 60-second video, I show the graphical meaning of this relationship using Wolfram Mathematica. We look at: 1) The graph of the original function f(t) = 1. 2) The graph of the Laplace transform integrand f(t)*e^(-s*t) for different s-values. And 3) The graph of the resulting Laplace transform F(s)=1/s. As s increases, the exponential decay term squeezes the area under the curve - and that's why F(s) decreases! This visual demo connects the geometry of the integral to the formula F(s) = 1/s - perfect for students of differential equations, signals, or complex analysis.

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ℒ[1] = 1/s GRAPHICAL Meaning (Laplace Transform of Constant Function 1 is 1/s for positive s, WHY??)

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