Steve Brunton Courses

Higher-Order ODEs, Characteristic Equation, Matrix Systems of First Order ODEs

Explore higher-order linear ODEs, characteristic equations, and matrix systems of first-order equations in engineering mathematics, with accompanying notes and MATLAB code.

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

Taylor Series and Solutions to First and Second Order Linear ODEs

Explore Taylor series and solutions to linear ODEs, enhancing your understanding of engineering mathematics with practical applications and MATLAB code examples.

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

SVD Part 2

Explore advanced concepts of Singular Value Decomposition (SVD) in data analysis and dimensionality reduction, building on fundamental principles to enhance understanding of matrix factorization techniques.

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

Complex Analysis - Bromwich Integrals and the Inverse Laplace Transform

Explore Bromwich integrals and inverse Laplace transforms in complex analysis, culminating this series with practical computation techniques.

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

Counting Probabilities with Combinatorics and the Factorial

Master combinatorics and factorial concepts in probability. Learn to count event occurrences, analyze sampling methods, and apply formulas for various probability scenarios, including coin flips and poker hands.

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

Set Theory in Probability - Sample Spaces and Events

Explore fundamental set theory concepts and their application in probability, including sample spaces, events, and key operations like unions and intersections through clear examples.

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

The Birthday Problem in Probability - Computing Probability Through Complements

Explore the fascinating Birthday Problem in probability theory, learning how to calculate shared birthday chances through complementary probability and factorial computations.

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

SINDy-RL: Interpretable and Efficient Model-Based Reinforcement Learning

Explores SINDy-RL, a framework combining sparse identification of nonlinear dynamics with reinforcement learning for efficient, interpretable control policies in complex environments.

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

AI/ML and Physics - Choosing What to Model in Physics-Informed Machine Learning

Explore the intersection of AI/ML and physics, focusing on problem formulation and incorporating physics into machine learning models. Learn through case studies and practical applications.

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

Physics-Informed Machine Learning: Curating Training Data - Part 2

Explore physics-informed data curation for machine learning, covering data augmentation, coordinate systems, simulation vs. experiments, and strategies for handling expensive, biased, and rare data in AI/ML applications.

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

New Advances in Artificial Intelligence and Machine Learning - Lecture 3

Explore cutting-edge AI and ML advancements, including generative models, reinforcement learning, and computer vision. Gain insights into the capabilities and applications of modern machine learning technologies.

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

Neural ODEs - From ResNet to Continuous-Time Machine Learning

Explore Neural ODEs: a powerful machine learning approach for learning ODEs from data. Discover its advantages over ResNet and extensions like HNNs and LNNs.

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

Gentle Introduction to Probability: Counting Coin Flips and Dice

Explore fundamental probability concepts through coin flips and dice rolls, uncovering the nature of randomness and its practical applications in everyday scenarios.

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

Probability and Statistics: An Introductory Overview

Explore probability and statistics fundamentals, from basic concepts to advanced topics, covering applications, history, and key principles in data science and machine learning.

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

Proof of the Central Limit Theorem

Discover the mathematical proof of the Central Limit Theorem using moment generating functions, exploring why this fundamental probability result holds true through rigorous analysis.

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