Steve Brunton Courses

Properties of Chi-Squared and Student's t Distributions

Discover key properties of Chi-Squared and Student's t distributions, including their construction, degrees of freedom, and relationships to sample variance and normal distributions.

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

The Chi Squared Distribution: The Square of the Normal Distribution

Explore the Chi-squared distribution, its relationship to Gaussian variables, and its applications in statistical comparisons of distributions.

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

Population Statistics and Random Sampling

Discover how to estimate population statistics through random sampling, including mean and variance calculations, uncertainty quantification, and practical coding demonstrations.

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

Random Sampling in Statistics - Expected Value and Variance of the Sample Mean

Discover how sample means provide unbiased population estimates and learn to calculate their expected values and variance for applications in polling, drug trials, and A/B testing.

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

Sample Variance in Random Population Sampling

Discover how to compute the expected value of sample variance in random population sampling to understand larger population properties through statistical analysis.

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

Random Sampling Without Replacement - Finite Population Correction

Explore finite population sampling techniques and learn the correction factor needed when sampling without replacement from limited-sized populations.

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

Confidence Intervals - Statistical Estimates with Uncertainty Bounds

Discover how to quantify statistical estimates with uncertainty bounds through confidence intervals, covering definitions, computations, and practical applications.

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

Independence in Probability - Concepts and Applications

Explore the concept of independent events in probability through card games and real-world reliability examples, learning to determine when events truly affect each other.

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

The Connection Between the Exponential Distribution and the Poisson Process

Explore the relationship between exponential distribution and Poisson process, including practical examples like email arrivals and mathematical foundations of event timing probabilities.

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

The Moment Generating Function

Discover how moment generating functions connect probability densities to Taylor series expansions, with examples using Poisson, normal, and exponential distributions.

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

Covariance and Correlation in Probability

Explore covariance and correlation between random variables, essential concepts for probability, statistics, data science, and machine learning in higher-dimensional systems.

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

Solving the Wave Equation with Separation of Variables and Guitar String Physics

Explore wave equation solutions using separation of variables, with applications to guitar string physics. Gain insights into optics, acoustics, and fundamental physics concepts.

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

Deriving the Wave Equation

Comprehensive derivation of the Wave Equation, exploring its applications in physics and engineering, with examples from guitar strings to illustrate key concepts.

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

PDE 101 - Separation of Variables or How I Learned to Stop Worrying and Solve Laplace's Equation

Explore the powerful Separation of Variables technique for solving PDEs, focusing on Laplace's equation in 2D for steady-state heat distribution, with applications in physics and engineering.

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

The Curl of a Vector Field - Measuring Rotation

Explore the curl operator in vector calculus, understanding its role in measuring rotation in vector fields and its applications in fluid dynamics, including vorticity and tornado analysis.

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