Numerical methods come into play in applied mathematics as soon as the numerical value for some quantity of interest is needed, for which no analytic expression is available. This quantity may be e.g. anintegral or the solution of a differential equation.
The scope of application of this course thus embraces such diverse fields as Physics, Biology, Economy or Finance. The role played by numerical
analysis has substantially grown these past few years, together with extensive computing power.
Numerical methods may be divided into two broad classes: deterministic methods on the one hand, based on discrete approximations of integrals or state evolution equations, and stochastic methods on the other hand, which consist in random sampling under an appropriate probability distribution in order to approximate an integral or atrajectory. This may be done by independent sampling (Monte-Carlo methods) or by simulating a well chosen Markov Chain (MCMC methods).
The purpose of this course is to introduce the students to essential methods in Numerical Analysis and to give them the key tools for understanding the mathematical principles behind.