 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-2-of-the-natural-sciences-course-of-the-university-of-cambridge/2008/paper-1/4/a/solution

f (k) = \int_{- \infty}^{\infty} f (x) e^{- ik x} d x, f (x) = \frac{1}{2 π} \int_{- \infty}^{\infty} f (k) e^{ik x} d k .

For the piecewise smooth functions here, the inverse gives the function at continuity points and the mean of one-sided limits at a jump. Values assigned at individual points do not affect the transform.

 New to topics? Read the docs here!