Lectures related to Linear system

Linear Systems: Direct Methods

Covers the formulation of linear systems, direct and iterative methods for solving them, and the cost of LU factorization.

Stability of Collisionless Systems

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

Convolution and Laplace Transform

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

Signals & Systems I: Distributions and Linear Systems

Explores distributions, linear systems, impulse response, convolution operators, and causal systems in signals and systems.

Signals & Systems I: Distributions and Linear Systems

Covers distributions, linear systems, impulse response, convolution, and examples of linear systems.

Fluctuation-dissipation relations for reversible diffusions

Covers linear response, steady states, Girsanov transforms, and covariance limits in reversible diffusions.

1st Harmonic: Stability and Adaptation

Covers stability, adaptation, Nyquist criterion, and predicting limit cycle existence.

Discrete Signals and Linear Systems

Explores discrete signals, linear systems, categorization examples, and convolution properties in signal processing.

Harmonic Response: Theory

Covers the theory of harmonic response, including decomposition into simple elements and stable system behavior.

Multivariable Control: System Theory and Linear Systems

Introduces the basics of multivariable control, focusing on system theory and linear systems.

Dynamical Systems: Laplace Transform

Covers the Laplace transform, transfer functions, and properties of common functions in dynamical systems.

Linear Systems: Factorization and Cholesky

Explores linear systems, Cholesky factorization, LU factorization, and matrix precision.

Linear Systems Resolution

Covers the resolution of linear systems using the Gauss method to determine unique, infinite, or no solutions.

Matrix Construction and Function Manipulation

Covers tips on matrix construction and function manipulation using MATLAB.

The z-transform: Basics and Applications

Introduces the z-transform, covering its basics, applications to systems, and practical examples.

Vectorization in Python: Efficient Computation with Numpy

Covers vectorization in Python using Numpy for efficient scientific computing, emphasizing the benefits of avoiding for loops and demonstrating practical applications.

Multivariable Control: System Theory and Linear Systems

Introduces multivariable control, covering system theory, linear systems, and time discretization.

Jacobi Method: Part I

Introduces the Jacobi method for solving linear systems and determining convergence.

Matrix Exponential: Properties and Convergence

Explores the properties and convergence of the matrix exponential for linear systems.

Signals & Systems II: Discrete Linear Systems

Explores categorization of signals, linear systems, LID, convolution, and impulse response.