Steve Brunton Courses

Singular Value Decomposition

2 reviews

Comprehensive exploration of Singular Value Decomposition, covering mathematical foundations, applications in data processing, and implementation in MATLAB and Python for various real-world scenarios.

• YouTube
• 7 hours
• On-Demand
• Free Video

Control Bootcamp - Kalman Filter Example in Matlab

1 review

Explore Kalman Filter implementation on inverted pendulum using Matlab, covering theory and practical application in dynamical systems and control engineering.

• YouTube
• 22 minutes
• On-Demand
• Free Video

Fluid Dynamics

1 review

Explore machine learning applications in fluid dynamics, from turbulence modeling to control strategies, with a focus on data-driven approaches and advanced computational techniques.

• YouTube
• 6 hours
• On-Demand
• Free Video

Data-Driven Science and Engineering

1 review

Explora técnicas avanzadas de aprendizaje automático, sistemas dinámicos y control con ejemplos prácticos en Matlab y Python, basados en el libro "Data-Driven Science and Engineering" de Brunton y Kutz.

• YouTube
• 20 hours
• On-Demand
• Free Video

Taylor Series and Power Series Made Easy - Review of Calculus

1 review

Comprehensive review of Taylor and Power Series with visual aids and coding examples in Python and Matlab. Covers definitions, expansions for sine and cosine, and practical implementations.

• YouTube
• 29 minutes
• On-Demand
• Free Video

Complex Analysis - The Complex Logarithm, Log(z)

Explore the complex logarithm, its infinite values, branch cuts, and principle n-th roots. Gain insights into this inverse of the complex exponential and its unique properties.

• YouTube
• 28 minutes
• On-Demand
• 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
• On-Demand
• 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
• On-Demand
• 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
• On-Demand
• 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
• On-Demand
• 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
• On-Demand
• 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
• On-Demand
• 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
• On-Demand
• 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
• On-Demand
• 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
• On-Demand
• Free Video