Complex Integrals
For complex integrals in the form:
with t >> 1, we make the substitution t = iu and the change of variable s = c + ix to get the Laplace bilateral transform:
We then split g(c+ix) in its real and complex part, after which we recover u = t / i. This is useful for inverse Laplace transforms, the Perron formula and complex integration.
Read more about this topic: Laplace's Method
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“Uneducated people are unfortunate in that they do grasp complex issues, educated people, on the other hand, often do not understand simplicity, which is a far greater misfortune.”
—Franz Grillparzer (1791–1872)