Linear Systems in 2D: Stability

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.