Differential Calculus and Differential Equations

In the first part: deepen the basic concepts of differential calculus covered in L2.

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

This EU will address the following points:

Differential calculus

    - definition of the differential, finite increment inequality, Ck functions, Taylor's formula.

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

 Differential equations

    - Maximum solution, global solution, Cauchy-Lipschitz theorem, explosion in finite time, global Cauchy-Lipschitz theorem, exit theorem for all compact sets.

    - Linear differential equations: Cauchy's linear Lipschitz theorem, linear systems with constant operators, 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.

The L1 and L2 analysis courses, 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: -