Lectures related to Dynamical System Theory for Engineers: Large Scale Stability

Introduces dynamical systems, equilibrium points, stability, vector fields, phase plots, and Lyapunov stability.

Transcritical Bifurcations: Understanding Dynamical Systems

Explores transcritical bifurcations and the dynamics near critical points.

Covers the concept of fold bifurcation in dynamical systems, focusing on the saddle-mode behavior.

Existence of Solutions for Poisson-Dirichlet Problem

Covers the existence of solutions for the Poisson-Dirichlet problem, focusing on showing that certain conditions hold for locally bounded and Hölder continuous functions.

Fubini's Theorem: Multiple Integrals

Explores Fubini's Theorem for multiple integrals, emphasizing the n=2 case.

A Conjecture of Erdös: Proof by Moreira, Richter and Robertson

Presents a short proof of a conjecture by Erdös, exploring related questions and detailed proof of the proposition.

Dynamic Systems: Course Review

Covers dynamic systems, trajectories, growth models, stability of fixed points, and linearization of models.

Dynamical System Theory: Bifurcations

Covers the topic of bifurcations in dynamical system theory, focusing on the pitchfork bifurcation.