LAPLACE TRANSFORM

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Laplace Transform transforms a function from

• $f\left(t\right)\ to\ F\left(s\right)$

• $F\left(s\right)\ to\ f\left(t\right)$

• $f\left(t\right)\ to\ f'\left(t\right)$

• $f"\left(t\right)\ to\ f'\left(t\right)$

Tags

CCSS.HSF.IF.A.2

What is the Laplace Transform for  $f\left(t\right)=t^3$  ?

•  $\frac{1}{s^3}$  

•  $\frac{2}{s^3}$  

•  $\frac{6}{s^4}$  

•  $\frac{3}{s^3}$  

Which one is the correct definition of Laplace Transform?

• $F\left(s\right)=\int_0^{\infty}e^{-st}f\left(t\right)dt$

• $F\left(s\right)=\int_0^tf\left(t\right)g\left(t-u\right)$

Define this property:  $L\left(f\left(t\right)e^{at}\right)=F\left(s-a\right)$  

• Linearity Property

• First Shifting Property

• Convolution Theorem

• Second Shifting Property