Week 13
Seeing it all: Geometry of systems of differential equations
13.1: The geometry of systems of differential equations
The geometry of systems of differential equations involves visualizing how the solutions we’ve been solving for behave in the plane.
In these notes, you’ll learn how to analyze and solve for the types of trajectories of solutions in time, focusing on critical points, stability, and how to map them by hand.
Nonlinear autonomous systems are systems of differential equations where the variables interact in a non-linear way and do not explicitly depend on time.
In these notes, you’ll explore how we rationalize solving these systems with critical point analysis, the Jacobian, a special type of matrix, and how to map them by hand.
13.2: Nonlinear autonomous systems of differential equations
13.3: Physical applications
Physical applications of differential equations showcase how first order systems can be used to solve and visualize the motion of springs and pendulums.
Recitation Slides
Attend recitation! But in case you were staying up late the night before or you’re looking to last-minute study cram, here are Week 13 recitation slides and solutions!
Ryann Joseph 