Program
There are three courses in the school including Functional analysis, Ordinary differential equations and Pratical resolution of differential equations.
The lecture notes will be daily updated. The information of courses including lecturers are as the following.
LIST OF COURSES
1. FUNCTIONAL ANALYSIS
by Joaquim Correia, University of Évora, Portugal
In this course, we present the main results of functional analysis essential to the study and resolution of differential equations. This course is composed of:
i.- Hilbert spaces
ii.- Theorems of Stampacchia and Lax-Milgram
iii.- Variational formulation and Sobolev spaces
2. ORDINARY DIFFERENTIAL EQUATIONS: THEORY and NUMERICS
by Youcef Mammeri, University of Picardie
This lecture deals with the classical tools to study ordinary differential equations. It contains the following topics:
i.- Notion of solutions, fundamental solution, Duhamel’s formula
ii.- Existence and uniqueness, local and global solution
iii.- Qualitative properties, stability
iv.- Finite difference schemes, one-step methods
v.- Stiff problem
vi.- Multi-step methods.
3. PRACTICAL RESOLUTION OF DIFFERENTIAL SYSTEMS
by Marilia Pires, University of Évora, Portugal
This practice presents the main features of a free software to solve mathematical equations derived from concrete problems:
i.- Presentation of Scilab (or python)
ii.- Basics (number, characters, function)
iii.- Graphics
iv.- Linear and nonlinear systems
v.- Differential equations
SCHEDULE
