Lectures related to Response Theory and Phase Transitions

Covers system variables, types of systems, and process control in static and dynamic systems.

Explores control of dynamic systems, impulse response, Laplace transform, and Fourier transform for solving differential equations.

Linear Response in High-Dimensional Systems

Explores linear response in high-dimensional systems, covering theory, practice, and implications of non-hyperbolicity and inhomogeneous subsystems.

Stochastic Models for Communications: Continuous-Time Stochastic Processes

Covers continuous-time stochastic processes and linear systems.

Dynamical Systems for Engineers

Covers the theoretical basis of linear and nonlinear dynamical systems for engineers.

Equilibrium Points and Bifurcations

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

Phase Transitions in Energy Systems

Explores phase transitions in energy systems, including non-analytic behavior and the Ising model.

Frequency Response and Filters

Explores frequency response properties, system composition, and frequency-selective filters in LTI systems, emphasizing the importance of magnitude.

GFF Convergence and Six Vertex Models: Phase Transitions

Covers GFF convergence and the six vertex model's phase transitions.

Dynamics of Simple Pendulum and Lorenz Equations

Explores the dynamics of a simple pendulum and the intriguing Lorenz equations, highlighting sensitivity to initial conditions and the transition to chaos.

Signals and Systems: Introduction

Introduces the fundamental concepts of Signals and Systems course, emphasizing practical applications of system behavior analysis.

Stochastic Calculus: Lecture 1

Covers the essentials of probability, algebras, and conditional probability, including the Borel o-algebra and Poisson processes.

Linear Response and Complex Diffusivity

Explores martingale-based linear response, complex diffusivity, and Nyquist relation in stochastic systems with time-dependent perturbation.

State-space Modeling

Introduces the state-space approach to modeling dynamical systems and its utility for high-speed solution of differential equations and computer algorithms.

Stability of Collisionless Systems

Explores the stability of collisionless systems, covering entropy, weak perturbations, Jeans instability, and Landau damping.

Linear Systems in Sinusoidal Regime

Explores linear systems in sinusoidal regime, discussing frequency response, transfer functions, stability, quadripoles, and Bode diagrams.

Stability Analysis: Linear Systems

Explores stability analysis in linear systems, emphasizing eigenvalues, eigenvectors, and stable manifolds.

Multivariable Control: Gaussian Processes and Linear Systems

Explores Gaussian processes, linear systems, transformations, and noise properties in multivariable control applications.

Nonlinear Dynamics: Homoclinic Orbits and Bifurcations

Delves into homoclinic orbits, bifurcations, and limit cycles in nonlinear dynamics.

Parameter Estimation of SDEs with Linear Response Theory

Explores parameter estimation of SDEs using Linear Response Theory and covers challenges, examples, algorithms, and convergence.