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62) where CR is a semicircle of infinite radius in either the right or left half of the z-plane and C is the closed contour that includes CR and Bromwich’s contour. 1. Our first task is to choose an appropriate contour so that the integral along CR vanishes. By Jordan’s lemma, this requires a semicircle in the right half-plane if t − 3 < 0 and a semicircle in the left half-plane if t − 3 > 0. 62 to zero and the inversion simply equals the closed contour. Consider the case t < 3 first. Because Bromwich’s contour lies to the right of any singularities, there are no singularities within the closed contour and f (t) = 0.

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