Contents of the lecture

Deterministic integration:

with equispaced points (rectangular, trapezoidal, Simpson...) and Gaussian-Legendre integration

Monte Carlo integration

- Monte Carlo integration in 1D: "hit or miss" (or "acceptance-rejection"); "sample mean".

- algorithms to improve the efficiency: importance sampling

- Handling errors: variance reduction with (i) average of the averages (ii) block average  

Multidimensional numerical integration: comparison between deterministic and Monte Carlo methods.

Error analysis

- error in classical methods with equispaced abscissas in one and higher dimensions

- comparison with errors in Monte Carlo methods

References:

- Chapter 11 "Numerical Integration" from "Computer simulation Methods" by Gould-Tobochnik (II ed)