Steve Brunton Courses

Dynamical Systems

Explore advanced techniques in dynamical systems analysis, including SINDy, Koopman theory, and deep learning applications for modeling complex nonlinear systems.

• YouTube
• 6 hours
• Self-Paced
• Free Video

Data-Driven Dynamical Systems with Machine Learning

Explore modern machine learning methods for modeling complex dynamical systems from data. Learn data-driven control techniques and apply them to various fields of science and engineering.

• YouTube
• 15 hours
• Self-Paced
• Free Video

Reinforcement Learning

Explora el Aprendizaje por Refuerzo, desde métodos básicos hasta redes neuronales y aplicaciones en dinámica de fluidos y control, en esta serie de 3.5 horas por Steve Brunton.

• YouTube
• 3 hours 30 minutes
• Self-Paced
• Free Video

Sparsity and Compression

Explore sparsity and compression techniques, from compressed sensing to robust regression, with practical applications in image processing, signal analysis, and machine learning.

• YouTube
• 4 hours 30 minutes
• Self-Paced
• Free Video

Intro to Data Science

Comprehensive introduction to data science and machine learning, covering key concepts, techniques, and applications. Includes hands-on examples in MATLAB and Python for practical implementation.

• YouTube
• 22 hours
• Self-Paced
• Free Video

Complex Analysis - Overview & Motivation, Complex Arithmetic, Euler's Formula & Polar Coordinates

Introduction to complex numbers, their arithmetic operations, Euler's formula, and polar coordinates. Covers solutions to differential equations and lays foundation for further complex analysis topics.

• YouTube
• 29 minutes
• Self-Paced
• Free Video

Topics in Dynamical Systems - Fixed Points, Linearization, Invariant Manifolds, Bifurcations & Chaos

Explore dynamical systems: fixed points, linearization, manifolds, bifurcations, and chaos. Gain insights into nonlinear dynamics and their applications in describing our changing world.

• YouTube
• 32 minutes
• Self-Paced
• Free Video

Solving PDEs with the Laplace Transform - The Wave Equation

Explore solving the wave equation using Laplace transforms, covering problem setup, PDE to ODE conversion, and solution methods including the Heaviside function and method of characteristics.

• YouTube
• 25 minutes
• Self-Paced
• Free Video

Moore's Law, Exponential Growth, and Extrapolation!

Explore Moore's Law, exponential growth in computing, and its impact on AI, scientific computing, and future technologies. Understand the implications for technological advancement.

• YouTube
• 30 minutes
• Self-Paced
• Free Video

Linearizing Nonlinear Differential Equations Near a Fixed Point

Explore techniques to analyze nonlinear differential equations by linearizing dynamics near fixed points, enabling powerful linear ODE solutions for nonlinear systems.

• YouTube
• 23 minutes
• Self-Paced
• Free Video

Solving Systems of Differential Equations with Eigenvalues and Eigenvectors

Learn to solve systems of linear ODEs using eigenvalues and eigenvectors. Covers problem setup, solution methods, and intuitive interpretation, with code examples in Python and MATLAB.

• YouTube
• 22 minutes
• Self-Paced
• Free Video

Motivating Eigenvalues and Eigenvectors with Differential Equations

Explore eigenvalues and eigenvectors through differential equations, deriving key concepts and visualizing their applications in matrix systems for a deeper understanding of linear algebra.

• YouTube
• 24 minutes
• Self-Paced
• Free Video

Matrix Systems of Differential Equations

Learn to transform high-order linear differential equations into matrix systems, enabling powerful solutions using eigenvalues and eigenvectors. Explore practical examples and key concepts in linear algebra applications.

• YouTube
• 25 minutes
• Self-Paced
• Free Video

Solving General High-Order, Linear Ordinary Differential Equations

Learn to solve high-order linear differential equations using characteristic polynomials and linear superposition. Covers guessing solutions, finding general solutions, and applying initial conditions.

• YouTube
• 25 minutes
• Self-Paced
• Free Video

Deriving the Heat Equation - A Parabolic Partial Differential Equation for Heat Energy Conservation

Comprehensive derivation of the heat equation, exploring its mathematical foundations and physical principles in thermal energy conservation and transfer.

• YouTube
• 24 minutes
• Self-Paced
• Free Video