Today we continue our discussion of linear differential equations in 2D. We will discuss classification of fixed points, and introduce the concept of oscillatory fixed points both stable and unstable. Using the trace and determinant of the characteristic matrix we will be able to categorize the fixed points of a system and begin to get a sense of the geometry of its behavior. Using eigenvectors and plotting nullclines further helps to get a sense of what the system will do and how it will behave. These techniques applied to linear differential equations will prove very useful in studying nonlinear systems in upcoming classes, because we will see that the behavior of nonlinear systems in the vicinity of their critical points can often be approximated by a linearized version of the system.