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
Famous quotes containing the word complex:
“Young children constantly invent new explanations to account for complex processes. And since their inventions change from week to week, furnishing the “correct” explanation is not quite so important as conveying a willingness to discuss the subject. Become an “askable parent.””
—Ruth Formanek (20th century)