MATH-325 / 5 crédits

Enseignant: Vela Arevalo Luz Vianey

Langue: Anglais


Summary

Introduction to local and global behavior of nonlinear dynamical systems arising from maps and ordinary differential equations. Theoretical and computational aspects studied.

Content

Keywords

Systèmes dynamiques à temps discrets et à temps continu, discrete and continuous dynamical systems, elementary bifurcations: saddle-node, transcritical, hysteresis, pitchfork; Lyapunov stability, Poincaré maps, mechanical systems. 

Learning Prerequisites

Required courses

Analyse I, Analyse II, Algebre linéaire

Recommended courses

Equations différentielles ordinaires

Learning Outcomes

  • Analyze dynamical systems in continue and discrete time
  • Describe local and global behavior of differential equations and maps
  • Work out / Determine stability properties as a function of one or more parameters

Transversal skills

  • Communicate effectively, being understood, including across different languages and cultures.
  • Communicate effectively with professionals from other disciplines.
  • Use a work methodology appropriate to the task.

Teaching methods

Lectures 2 hours a week and exercise sessions 2 hours a week. 

Expected student activities

Attendance to lectures, attendance to exercise sessions, solution of homework problems that may involve theoretical or numerical solutions, give a final exam. 

Assessment methods

Final exam.

Dans le cas de l'art. 3 al. 5 du Règlement de section, l'enseignant décide de la forme de l'examen qu'il communique aux étudiants concernés

Supervision

Office hours No
Assistants Yes
Forum Yes

Dans les plans d'études

  • Semestre: Printemps
  • Forme de l'examen: Ecrit (session d'été)
  • Matière examinée: Dynamics and bifurcation
  • Cours: 2 Heure(s) hebdo x 14 semaines
  • Exercices: 2 Heure(s) hebdo x 14 semaines

Semaine de référence

 LuMaMeJeVe
8-9     
9-10     
10-11     
11-12     
12-13     
13-14     
14-15     
15-16     
16-17     
17-18     
18-19     
19-20     
20-21     
21-22