Applied mathematics and modeling

Analyze and model natural processes numerically, using the Matlab scientific computing and programming tool, to explain, forecast and exploit geo-resources, prevent risks and protect the environment. The concepts acquired will be applied to various types of data, such as hydrogeological, geophysical, geochemical and satellite data.
Minimum skills to be acquired:Mastery of the theoretical bases, mathematical tools and software used in geo-environment.

Mathematics for Earth Sciences.

1. Numerical methods (18h) Samia Boukir (100%)

Solving systems of linear equations: Gauss, SVD
Solving systems of nonlinear equations: Finite differences, Newton.
Approximation, interpolation and geometric modeling: nonlinear least-squares fitting. Lagrange. Piecewise polynomial interpolation (splines)
Numerical integration: Trapezoids, Simpson.
Numerical solution of ordinary differential equations: Euler, Runge-Kutta.
Numerical solution of partial differential equations using the finite element method.

2. Application to geosciences (12h) Samia Boukir (50%) and Laurent Fallot (50%)

Water chemistry
Remote sensing
Geophysics
Electromagnetism