inverselaplace 1/((s+1)^{1/2)}

解答

的拉普拉斯逆变换

\frac{1}{( s + 1 ) ^{\frac{1}{2}}}

\frac{e ^{- t}}{π t ^{\frac{1}{2}}}

求解步骤

L^{- 1} {\frac{1}{( s + 1 ) ^{\frac{1}{2}}}}

应用逆变换法则: if

L^{- 1} {F (s)} = f (t)

则

L^{- 1} {F (s - a)} = e^{a t} f (t)

对于

\frac{1}{( s + 1 ) ^{\frac{1}{2}}} : a = - 1, F (s) = \frac{1}{s ^{\frac{1}{2}}}

= e^{- t} L^{- 1} {\frac{1}{s ^{\frac{1}{2}}}}

L^{- 1} {\frac{1}{s ^{\frac{1}{2}}}} : \frac{1}{π t ^{\frac{1}{2}}}

= \frac{e ^{- t}}{π t ^{\frac{1}{2}}}

s l o p e (- 6, 4), (- 1, 4)

\frac{d}{d x} (\frac{x ^{n - 1}}{n})

n = 0 \sum \infty \frac{n ^{3}}{5 ^{n}}

\frac{\partial}{\partial x} (2 x^{3} y + sin (x^{2}))

t an g e n t f (x) = \frac{4 x}{x ^{2} - 5}, (3, 3)