L [ f ( t ) ] = ∫ 0 ∞ e ? s t f ( t ) d t = F ( s ) L[f(t)]=\int_{0}^{\infty}e^{-st}f(t)dt = F(s) L[f(t)]=∫0∞?e?stf(t)dt=F(s)
1 2 π j ∫ a ? j ∞ a + j ∞ f ( s ) e s t d s = L ? 1 [ F ( s ) ] = f ( t ) \frac{1}{2\pi j}\int_{a-j\infty}^{a+j\infty}f(s)e^{st}ds=L^{-1}[F(s)]=f(t) 2πj1?∫a?j∞a+j∞?f(s)estds=L?1[F(s)]=f(t)
线性定理
f 1 ( t ) + f 2 ( t ) f_1(t)+f_2(t) f1?(t)+f2?(t)的拉普拉斯变换为 L [ f ( t ) ] = L [ f 1 ( t ) ] + L [ f 2 ( t ) ] L[f(t)]=L[f_1(t)]+L[f_2(t)] L[f(t)]=L[f