Mathematics for biology

The course provides an overview of the concepts required 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 non-linear dynamical systems, the qualitative theory of differential equations (attractors, phase portraits, zero-level isoclines) is presented, as an alternative to the often complicated calculation of solutions. The TD covers a wide range 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

- using mathematics to understand the living world

Biomathematics level L1