The Hudson School of Mathematics
Ordinary Differential Equations (ODEs)
This class is an advanced introduction to the field of the analysis of Ordinary Differential Equations. The class consists in 9x3 hours sessions. This course is part of an experimental COIL (Collaborative Online International Learning) initiative in collaboration with Le Havre Normandie University.
The program is as follows.
Chapters
- General Introduction
- Theoretical Results.
- Steady states, qualitative analysis and stability of solutions.
Students will also be asked to work on a specific non trivial problem (project), this will be part of the grade. The work will be done at home and in class.
Schedule (expected)
- Lectures 1-3: examples and exercices: 2nd Newton's Law, Radioactivity, electricity, Hodgkin Huxley Equations, FitzHugh-Nagumo Equations, Lotka-Volterra, Oregonator, Lorenz system.Projects
- Lectures 4-6: the Cauchy problem, exercises. Maximal solutions, global solutions. Regularity of solutions.Projects.
Integral Equation and the Cauchy Problem. Approximate solutions
Ascoli Theorem. Projects.
Theorem of Existence (Cauchy, Arzela, Peano). Theorem of Existence and Uniqueness (Cauchy-Lipschitz). The Gronwall Lemma. Convergence of Euler method towards exact solutions.
- Lectures 7-9: Qualitative Analysis of 2d linear systems: saddle, sources, sinks, centers, spirals, Repeated eigenvalues. Non Linear Systems. Proof of stability for sinks. Examples.
- January 14 (to be confirmed): Dissertation.
To register for the class, contact us at contact@hudsonschoolmath.com or fill out this form
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