Mathematics 3 [ LFSAB1103 ]

Partial differential equations (3 ECTS)

• Fundamental properties of first and second order PDE and their classification. Links with physics. Illustration of concepts and definitions using examples. " Initiation to different analytical methods for the resolution of fundamental and simple problems (convection, waves, diffusion, elliptic), to the physical interpretation and to the critical assessment of the results.

Discrete mathematics (2 ECTS)

" Counting methods and linear recurrences. Introduction to graph theory. Study of some fundamental algebraic structures. " Introduction to certain parts of discrete mathematics, selected according to their educational value and their usefulness in applications. Presentation of the subject in a precise mathematical framework, with numerous illustrative examples.

Following this course, the students will be able to :

" Master the fundamental properties of the different types of partial differential equations (PDE): first and second order PDE of linear and quasi-linear type.

Determine the adequate initial conditions and/or boundary conditions for each type.

Solve simple PDE using analytical methods.

Model fundamental physical phenomena governed by PDE; understand the underlying hypotheses and the limitations of the modelisation. "

Master combinatorial reasoning in classical counting subjects; discuss and solve linear recurrences of a simple form.

Apply fundamental notions of graph theory; to use some algorithms relative to these notions.

Argue and compute in the domain of discrete structures.