Nonlinear Dynamical Systems: Key Concepts

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Covers the basics of linear algebra, including solving equations and understanding systems of linear equations graphically.

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

Explores uniform continuity in functions, covering definitions, examples, and properties.

Covers the limitations of Lagrange formalism and the transition to Hamiltonian formalism for dynamic variables.

Introduces the course ME-426 on Micro/Nanomechanical Devices, covering objectives, key concepts, practical matters, and take-home messages.

Explores logistic maps, bifurcations, equilibrium points, and periodic orbits in nonlinear dynamics and chaos.

Explores linear response for chaotic systems, discussing SRB states, Lyapunov exponents, and convergence of the response formula.

Introduces equilibrium points and bifurcations in differential equations, discussing their stability and relevance in various contexts.

Explores learning and adaptive control for robots through SEDS and LPV-DS, emphasizing stability, non-linear dynamics, and optimization.