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- https://math.libretexts.org/Bookshelves/Differential_Equations/Elementary_Differential_Equations_with_Boundary_Value_Problems_(Trench)/08%3A_Laplace_Transforms/8.06%3A_ConvolutionThis section deals with the convolution theorem, an important theoretical property of the Laplace transform.
- https://math.libretexts.org/Courses/Monroe_Community_College/MTH_225_Differential_Equations/08%3A_Laplace_Transforms/8.06%3A_ConvolutionThis section deals with the convolution theorem, an important theoretical property of the Laplace transform.
- https://math.libretexts.org/Courses/Mission_College/Math_4B%3A_Differential_Equations_(Reed)/07%3A_Laplace_Transforms/7.06%3A_ConvolutionThis section deals with the convolution theorem, an important theoretical property of the Laplace transform.
- https://math.libretexts.org/Courses/Cosumnes_River_College/Math_420%3A_Differential_Equations_(Breitenbach)/09%3A_Laplace_Transforms/9.06%3A_Convolution\[\begin{aligned}{\cal L}|\sin t|&={1\over 1-e^{-s\pi}}\int_0^\pi e^{-st}|\sin t|\,dt \\[5pt] &={1\over 1-e^{-s\pi}}\int_0^\pi e^{-st}\sin t\,dt\\[5pt] &={1\over 1-e^{-s\pi}}\left(\int_0^\pi e^{-st}\s...\[\begin{aligned}{\cal L}|\sin t|&={1\over 1-e^{-s\pi}}\int_0^\pi e^{-st}|\sin t|\,dt \\[5pt] &={1\over 1-e^{-s\pi}}\int_0^\pi e^{-st}\sin t\,dt\\[5pt] &={1\over 1-e^{-s\pi}}\left(\int_0^\pi e^{-st}\sin t\,dt+\int_\pi^\infty e^{-st}(0)\,dt\right)\\[5pt] &={1\over 1-e^{-s\pi}}{\cal L}\left(\sin t-\sin t {\cal U}(t-\pi)\right)\\[5pt] &={1\over 1-e^{-s\pi}}{\cal L}\left(\sin t+\sin (t-\pi){\cal U}(t-\pi)\right)\\[5pt] &={1\over 1-e^{-s\pi}}\left({1\over s^2+1}+{e^{-\pi s}\over s^2+1}\right)\\[5pt]…
- https://math.libretexts.org/Courses/Red_Rocks_Community_College/MAT_2561_Differential_Equations_with_Engineering_Applications/08%3A_Laplace_Transforms/8.06%3A_ConvolutionThis section deals with the convolution theorem, an important theoretical property of the Laplace transform.
- https://math.libretexts.org/Courses/Mission_College/Math_4B%3A_Differential_Equations_(Kravets)/07%3A_Laplace_Transforms/7.06%3A_ConvolutionThis section deals with the convolution theorem, an important theoretical property of the Laplace transform.
- https://math.libretexts.org/Courses/Chabot_College/Math_4%3A_Differential_Equations_(Dinh)/06%3A_Laplace_Transforms/6.06%3A_ConvolutionThis section deals with the convolution theorem, an important theoretical property of the Laplace transform.
