wm\̑Ŝɂ̃Ot}C ֘Ay[Wɂ̃Ot}𗘗pĂD
pF vXϊC vXϊ{\C

$ℒ\text{\hspace{0.17em}}\left\{\frac{df\left(t\right)}{dt}\right\}=sF\left(s\right)-f\left(0\right)$

$ℒ\text{\hspace{0.17em}}\left\{-tf\left(t\right)\right\}=\frac{dF\left(s\right)}{ds}$

$n\geqq 1$ ̂Ƃ

$ℒ\text{\hspace{0.17em}}\left\{{f}^{\left(n\right)}\left(t\right)\right\}={s}^{n}F\left(s\right)-\left\{{s}^{n-1}f\left(0\right)+{s}^{n-2}{f}^{\left(1\right)}\left(0\right)+\cdots +s{f}^{\left(n-2\right)}\left(0\right)+{f}^{\left(n-1\right)}\left(0\right)\right\}$

$ℒ\text{\hspace{0.17em}}\left\{{\left(-t\right)}^{n}f\left(t\right)\right\}={F}^{\left(n\right)}\left(s\right)$

ؖ

 $ℒ\text{\hspace{0.17em}}\left\{\frac{df\left(t\right)}{dt}\right\}$ @ $={\int }_{0}^{\infty }{e}^{-st}\frac{df\left(t\right)}{dt}dt$ @ @ $={\left[f\left(t\right){e}^{-st}\right]}_{0}^{\infty }-{\int }_{0}^{\infty }\frac{d}{dt}\left\{{e}^{-st}\right\}f\left(t\right)dt$ @ @ $={\left[f\left(t\right){e}^{-st}\right]}_{0}^{\infty }-{\int }_{0}^{\infty }\left(-s{e}^{-st}\right)f\left(t\right)dt$ @ @ $=-f\left(0\right)+s{\int }_{0}^{\infty }{e}^{-st}f\left(t\right)dt$ @ @ $=-f\left(0\right)+sF\left(s\right)$ @ $=sF\left(s\right)-f\left(0\right)$ @

ؖ

 $\frac{dF\left(s\right)}{ds}$ @ $=\frac{d}{ds}\left\{{\int }_{0}^{\infty }{e}^{-st}f\left(t\right)dt\right\}$ @ @ $={\int }_{0}^{\infty }\frac{d}{ds}\left({e}^{-st}\right)f\left(t\right)dt$ @ @ $={\int }_{0}^{\infty }\left(-t{e}^{-st}\right)f\left(t\right)dt$ @ @ $=-{\int }_{0}^{\infty }{e}^{-st}\left\{tf\left(t\right)\right\}dt$ @ @ $=-ℒ\text{\hspace{0.17em}}\left\{tf\left(t\right)\right\}$ @

$ℒ\text{\hspace{0.17em}}\left\{-tf\left(t\right)\right\}=\frac{dF\left(s\right)}{ds}$

z[>>JeS[>>>>vXϊ>>

wX^bt쐬

@ŁF2009N35CŏIXVF 2010N225