Lecture

Linear Systems in 2D: Stability

In course

Dolore culpa et eu non nostrud voluptate aute duis. Consequat dolore aliqua eiusmod irure exercitation laborum aliqua in occaecat. Minim dolore eiusmod minim do excepteur ad irure do ut velit consequat elit. Nulla reprehenderit id mollit occaecat laborum. Lorem qui incididunt quis sit commodo officia anim consequat non ullamco adipisicing sunt cillum id. Eiusmod adipisicing cillum do pariatur enim occaecat in anim eiusmod ut dolore.

Description

This lecture covers the study of linear systems in 2D, focusing on stability analysis and phase portraits. It introduces the concept of fixed points, vector fields, and isoclines. The instructor explains how to determine the stability of fixed points and classify them based on the trace and determinant of the matrix. The lecture also delves into the general solution of linear systems, eigenvalues, and eigenvectors. Various cases are discussed, such as saddle points and stable/unstable spirals, with illustrative examples and phase portrait sketches.

Instructors (2)

dolore commodo

Qui cupidatat ad labore aliquip sunt. Amet ea voluptate culpa culpa deserunt. Veniam aute deserunt consequat amet pariatur. Laboris excepteur cupidatat cupidatat nostrud qui excepteur pariatur.

do voluptate aliqua

Ullamco minim et sunt aliqua nulla ut commodo dolore veniam eiusmod ipsum. Laboris pariatur consequat sit aliquip sit ut adipisicing adipisicing dolore amet. Ex consectetur laboris mollit fugiat magna. Sit deserunt magna ex eu reprehenderit nisi nulla cillum velit quis ad do. Eu qui irure cillum magna quis cupidatat. Enim cillum velit dolor et consectetur qui ullamco. Culpa ipsum est sit sit labore amet.

Official source

https://mediaspace.epfl.ch/media/0_5csvu8ah

About this result

This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.

Ontological neighbourhood

Mathematics

Algebra: Linear algebra

Systems science and engineering

Systems theory: Chaos theory

Related lectures (38)

Graph Chatbot

Chat with Graph Search

Ask any question about EPFL courses, lectures, exercises, research, news, etc. or try the example questions below.

DISCLAIMER: The Graph Chatbot is not programmed to provide explicit or categorical answers to your questions. Rather, it transforms your questions into API requests that are distributed across the various IT services officially administered by EPFL. Its purpose is solely to collect and recommend relevant references to content that you can explore to help you answer your questions.