Steve Brunton Courses

Numerical Integration of ODEs with Forward Euler and Backward Euler in Python and Matlab

Explore Forward and Backward Euler integration methods for ODEs using Python and Matlab. Compare stability, error, and implementation on a spring-mass-damper system with analytic solutions.

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

Deriving Forward Euler and Backward-Implicit Euler Integration Schemes for Differential Equations

Explore Forward and Backward Euler integration methods for ODEs, including derivations, error sources, and stability analysis. Gain insights into numerical integration techniques for solving differential equations.

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

Numerical Simulation of Ordinary Differential Equations - Integrating ODEs

Explore numerical integration of ODEs to analyze nonlinear systems and generate trajectories. Learn techniques for solving complex dynamics where analytic methods fall short.

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

Differential Equations with Forcing: Method of Variation of Parameters

Learn to solve forced linear differential equations using the powerful method of variation of parameters, replacing unknown coefficients with time-dependent functions based on external forcing.

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

Differential Equations with Forcing: Method of Undetermined Coefficients

Learn to solve linear differential equations with external forcing using the method of undetermined coefficients. Understand homogeneous solutions, particular solutions, and how to combine them for a complete solution.

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

High-Order Ordinary Differential Equations with More Derivatives - From Physics

Explore derivation of higher-order differential equations from F=ma, focusing on spring-mass systems. Learn to chain simple systems for complex equations in physics.

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

Calculus Review - The Derivative, the Power Law, and the Chain Rule

Comprehensive review of derivatives, power law, and chain rule in calculus. Essential concepts for understanding differential equations and dynamical systems.

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

Physics-Informed Dynamic Mode Decomposition

Explore how physical laws enhance dynamic mode decomposition, improving model accuracy and generalization in complex systems analysis. Learn techniques for integrating conservation, symmetry, and other principles.

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

Deriving the Heat Equation in 2D and 3D and in N Dimensions with Control Volumes and Vector Calculus

Explore the derivation of the heat equation in multiple dimensions using Gauss's theorem, control volumes, and vector calculus techniques for a comprehensive understanding of heat transfer.

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

Partial Differential Equations Overview

Explore the mathematical language of physical phenomena with an overview of partial differential equations, covering canonical PDEs, linear superposition, and nonlinear PDEs like Burgers Equation.

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

Potential Flow Part 2 - Details and Examples

Explore advanced potential flow concepts, solving Laplace's equation for idealized fluid flows. Learn contour integrals, analyze examples, and understand how PDE solutions establish vector fields.

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

Gauss's Divergence Theorem

Explore Gauss's Divergence Theorem, a fundamental tool in mathematical physics for deriving conservation laws and translating them into partial differential equations.

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

Reinforcement Learning Series - Overview of Methods

Comprehensive overview of reinforcement learning methods, covering model-based and model-free approaches, from dynamic programming to deep RL and policy gradient optimization.

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

Sparse Identification of Nonlinear Dynamics - Sparse Machine Learning Models 5 Years Later

Explore advancements in SINDy algorithm for discovering dynamical systems models from data, including challenges and applications in nonlinear systems and PDEs.

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

Turbulence - Reynolds Averaged Navier Stokes Equations - Momentum Equation

Explore the derivation of Reynolds averaged Navier-Stokes equations for turbulence modeling, focusing on the momentum equation and its applications in engineering fluid dynamics.

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