Differential Calculus and Differential Equations

In the first part: deepen the basic notions of differential calculus seen in L2.

In the second part: introduce the qualitative study of differential equations.

This UE will cover the following points:

Differential calculation

    - definition of differential, finite increase inequality, Ck class functions, Taylor formula.

    - Notion of diffeomorphism, local inversion theorem, global inversion, implicit function theorem.

 Differential equations

    - Maximum solution, global, Cauchy Lipschitz theorem, finite-time explosion, global Cauchy Lipschitz theorem, exit theorem for any compact.

    - Linear differential equations: linear Cauchy Lipschitz theorem, constant operator linear systems, general linear systems

    - Autonomous equations and vector fields: flow and integral curve of a vector field, stable and unstable equilibrium. Autonomous differential systems of size 2.

Analysis courses in L1 and L2, in particular :

- HAX302X Analysis III Integration and elementary differential equations

- HAX404X Topology of ^Rn and functions of several variables

Recommended prerequisites: L2 maths

Hourly volumes :

            CM: 27

            TD : 27

            TP: -

            Land: -