1.5.12 Integral Transforms
| LaplaceTransform[expr, t, s] | find the Laplace transform of expr |
InverseLaplaceTransform[expr, s, t]
| | find the inverse Laplace transform of expr |
Laplace transforms. | This computes a Laplace transform. | |
In[1]:=
LaplaceTransform[t^3 Exp[a t], t, s]
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Out[1]=
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| Here is the inverse transform. | |
In[2]:=
InverseLaplaceTransform[%, s, t]
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Out[2]=
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| FourierTransform[expr, t, w] | find the symbolic Fourier transform of expr |
InverseFourierTransform[expr, w, t]
| | find the inverse Fourier transform of expr |
Fourier transforms. | This computes a Fourier transform. | |
In[3]:=
FourierTransform[t^4 Exp[-t^2], t, w]
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Out[3]=
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| Here is the inverse transform. | |
In[4]:=
InverseFourierTransform[%, w, t]
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Out[4]=
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Note that in the scientific and technical literature many different conventions are used for defining Fourier transforms. Section 3.8.4 describes the setup in Mathematica.
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