The Trapezoidal rule in the complex plane

The trapezoidal rule for numerical integration is remarkably accurate when

the integrand under consideration is smooth and periodic. In this

situation it is superior to more sophisticated methods like Simpson's rule

and even the Gauss-Legendre rule. In the first part of the talk we

discuss this phenomenon and give a few elementary examples. In the second

part of the talk we discuss the application of this idea to the numerical

evaluation of contour integrals in the complex plane.

Demonstrations involving numerical differentiation, the computation

of special functions, and the inversion of the Laplace transform will be

presented.