Explore the stability of Forward Euler and Backward/Implicit Euler integration schemes for differential equations in this 33-minute video lecture. Delve into the eigenvalues of discrete-time update equations and their relation to algorithm stability. Learn about stability analysis techniques applicable to more advanced integrators. Begin with an overview of stability analysis goals, then progress through continuous dynamics stability, discrete-time dynamics stability, and complex plane eigenvalues. Examine Euler integration stability for both scalar dynamics and matrix systems. Access additional resources through the provided playlist, course website, and social media links.