Mathematics-III Exam Prep
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Mathematics-III Exam Prep
Sample questions with model answers
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Find the Fourier transform of $f(x) = xe^{-a|x|}$.
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The Fourier transform is $F(\omega) = \frac{2a}{(a^2 + \omega^2)^2}$.
The full exam-length answer is in the app.
Find the inverse Fourier transform of $F(\omega) = \frac{1}{a+i\omega}$, $a > 0$.
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The inverse Fourier transform is $f(x) = e^{-a|x|}$.
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Find the sine transform of $f(x) = 3e^{-2x} + 2e^{-4x}$.
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The sine transform is $F_s(\omega) = \frac{3}{4 + \omega^2} + \frac{2}{16 + \omega^2}$.
The full exam-length answer is in the app.
Find the cosine transform of $f(x) = 2e^{-x} - 5e^{-3x}$.
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The cosine transform is $F_c(\omega) = \frac{2}{1 + \omega^2} - \frac{5}{9 + \omega^2}$.
The full exam-length answer is in the app.
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