Differential Calculus and Differential Equations

  • ECTS

    6 credits

  • Component

    Faculty of Science

Description

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

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

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Objectives

This EU will address the following:

Differential calculation

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

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

 Differential equations

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

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

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Necessary pre-requisites

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 math

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Additional information

Hourly volumes:

            CM : 27

            TD : 27

            TP: -

            Land: -

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