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Fourier Transform Question

Hi, it's just to ask for some help with transforming some initial conditions for a PDE question. Just a bit unsure how to do it although I think it must be really simple...
The fourier transform of,


u(x,0) = 1, if 1 <=x<=2, 0 otherwise

Thanks for any help.
The fourier transform of the indicator function of an interval [a,b][a,b] is given by z↦∫abeizxdxz \mapsto \int\limits_a^b e^{izx} dx, which you can check is exactly eizb−eizaiz\frac{e^{izb} - e^{iza}}{iz} (with the obvious extension at z = 0).
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Blue7195
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Original post by BlueSam3
The fourier transform of the indicator function of an interval [a,b][a,b] is given by z↦∫abeizxdxz \mapsto \int\limits_a^b e^{izx} dx, which you can check is exactly eizb−eizaiz\frac{e^{izb} - e^{iza}}{iz} (with the obvious extension at z = 0).


thank you very much

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