Mathematics for biology

The course provides a synthetic approach to the notions necessary for mathematical modeling in biology. The focus is on linear and non-linear dynamical systems, in dimension one and two. The course begins with essential notions of linear algebra: matrices, systems of linear equations, geometric interpretation of the solutions of these systems as vectors and subspaces (line, plane, etc.). The theory of vectors and eigenvalues of matrices is introduced in relation to linear dynamical systems. For nonlinear dynamical systems, the qualitative theory of differential equations (attractors, phase portrait, zero-level isoclines) is presented, as an alternative to the often complicated calculation of solutions. The course covers a large number of biological models used in ecology, epidemiology, oncology, and systems biology.

- matrix calculation, linear algebra

- qualitative theory of differential equations 

- solutions of differential equations in simple cases

- use of mathematics to understand the living

Biomathematics level L1