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.
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.
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
Additional information
Hourly volumes:
CM : 27
TD : 27
TP: -
Land: -