Contents of the lecture

Numerical integration: simple deterministic methods in 1D; Monte Carlo integration.

- 1D classical integration methods: trapezoidal rule, Simpson...

- 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
 

References:

- Chapter 1.2 "Numerical quadrature" from "Computational Physics" by Koonin; chapter 8.1-2

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