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Student Solution Manual for Mathematical Methods for Physics and Engineering, Third Edition by M. P. Hobson, K. F. Riley

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13

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Integral transforms

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13.1  Find the Fourier transform of the function f(t) = exp(−|t|).

(a)  By applying Fourier’s inversion theorem prove that

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(b)  By making the substitution ω = tan θ, demonstrate the validity of Parseval’s theorem for this function.

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As the function | t | is not representable by the same integrable function throughout the integration ...

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