Einführung in die nichtlineare Dynamik und Chaostheorie
| Umfang, Credits | 2 SWS, 3 ECTS |
| Kontakt | Camilo Silva |
| Vorlesung | Freitag, 09:00 - 10:30 Uhr, MW 1701 |
| Art | Vorlesung |
|---|---|
| Semester | Sommersemester 2022 |
| Unterrichtssprache | English |
Teilnahmekriterien
Beschreibung
Diese Lehrveranstaltung wird in englischer Sprache durchgeführt, eine detaillierte Kursbeschreibung findet sich dem entsprechend als "Course - detail view" auf der englischen Version dieser Seite.
Inhaltliche Voraussetzungen
Calculus
Lehr- und Lernmethoden
Almost all sessions open with a practical example of nonlinear dynamic systems, which can be found in several fields of study such as biology, chemistry, neuroscience, structural mechanics, electromagnetism, acoustics and combustion, among others. These examples will be illustrated generally with power-point slides and Youtube videos in order to captivate the attention of the students.
Once the system of differential equations is derived in common participation with the students, the corresponding dynamic properties are under a `rationalistic debate’ approach discussed. The purpose of this is to not only consider an answer as the truth but to be able to construct an answer and understand why it can be considered as correct. Subsequently, methods of analysis are introduced where the solutions are qualitatively assessed. Finally, the physical implications of the solutions are discussed.
In addition to power-point presentations, the blackboard will be used for mathematical derivations. Also, extracts and examples of he book “Strogatz, S. H. (2014). Nonlinear dynamics and chaos: with applications to physics, biology, chemistry, and engineering. Hachette UK.” will be introduced during the lectures.
The course is based on 14 lectures full of examples on classical nonlinear dynamic systems. Instead of a monologue, a dialogue with the students will be aimed at each session.
Following the methodology previously exposed, it is expected that the students use analysis (instead of memory) to build intuition and, consequently, be able to `look through’ nonlinear differential equations.
Once the system of differential equations is derived in common participation with the students, the corresponding dynamic properties are under a `rationalistic debate’ approach discussed. The purpose of this is to not only consider an answer as the truth but to be able to construct an answer and understand why it can be considered as correct. Subsequently, methods of analysis are introduced where the solutions are qualitatively assessed. Finally, the physical implications of the solutions are discussed.
In addition to power-point presentations, the blackboard will be used for mathematical derivations. Also, extracts and examples of he book “Strogatz, S. H. (2014). Nonlinear dynamics and chaos: with applications to physics, biology, chemistry, and engineering. Hachette UK.” will be introduced during the lectures.
The course is based on 14 lectures full of examples on classical nonlinear dynamic systems. Instead of a monologue, a dialogue with the students will be aimed at each session.
Following the methodology previously exposed, it is expected that the students use analysis (instead of memory) to build intuition and, consequently, be able to `look through’ nonlinear differential equations.