Mathematics for Environmental Sciences

The aim of this course is to acquire, through practical experience, the mathematical basis for analyzing environmental problems in a way that is different from a purely physical approach. In some cases, mathematical modeling is the only way to gain a quantitative and qualitative understanding of the mechanics of a hydrogeological or ecological phenomenon, and to predict its evolution over time. The physical approach, like mathematical modelling, has its limits, advantages and disadvantages. Several areas of mathematics will be covered: algebra, but above all analysis, with a particular focus on the analytical resolution of differential equations. Indeed, the mathematical modeling of geological, geophysical, hydrogeological and even ecological phenomena is generally expressed in the form of differential equations.This course will use case studies to introduce students to mathematics and scientific programming in Matlab. Emphasis will be placed on examples from the fields of hydrogeology, geophysics, chemistry and imaging.
Minimum skills to be acquired:Be able to solve a simple environmental problem analytically, and then implement it using computer tools.

Fundamentals of algebra, analysis and geometry

I. Mathematics applied to earth sciences (30h)Review of basic concepts in matrix, differential and integral calculusVector analysis: gradient, divergence, rotational, tensors.Differential equations: linear (order 1 and higher), non-linear, special (Gauss, Legendre, Bessel), partial derivatives, introduction to finite elements.Transforms: Laplace, Fourier.II. Scientific programming applied to earth sciences (10h)Introduction to scientific programming in Matlab: vectors and matrices, operators, simple instructions.Implementation of algorithms needed to solve concrete earth science problemsrelated to mathematics, in particular matrix manipulation, linear algebra and vector calculus.