Steve Brunton Courses

Hankel Alternative View of Koopman Analysis

Explore how HAVOK analysis represents chaotic nonlinear dynamics as linear systems with intermittent forcing using Koopman theory and eigen-time-delay coordinates.

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

A Compressed Overview of Sparsity

See how sparsity lets engineers reconstruct high-dimensional signals from surprisingly few, strategically chosen measurements using compressed sensing.

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

Laplace Transform and ODEs with Forcing and Transfer Functions

Use Laplace transforms and transfer functions to solve forced spring-mass-damper ODEs, then analyze sinusoidal responses and Bode plots in MATLAB.

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

Laplace Transform and ODEs

Solve ordinary differential equations with Laplace transforms, initial conditions, partial fractions, and inverse transforms.

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

Fourier Transform to Solve PDEs - 1D Heat Equation on Infinite Domain

Learn how the Fourier transform turns the 1D heat equation on an infinite rod into frequency-domain damping and spatial Gaussian smoothing.

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

FFT and Image Compression

See how the fast Fourier transform reveals image structure and enables compression by discarding small Fourier coefficients in MATLAB.

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

Fast Fourier Transforms and Audio

Learn how the fast Fourier transform accelerates discrete Fourier analysis and use MATLAB to filter audio and visualize frequency content with spectrograms.

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

Properties of Fourier Transforms and Examples

Develops Fourier transform properties and examples, connecting frequency-domain methods with PDEs and fast computer-based transforms.

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

Fourier Series

Explore Fourier series as orthogonal sine-and-cosine representations of functions, including L2 norms, symmetry, discontinuities, Gibbs phenomenon, and MATLAB approximations.

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

Infinite Dimensional Function Spaces and Fourier Series

Learn how functions form infinite-dimensional inner product spaces and provide orthogonal bases for Fourier series.

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

Fourier Transforms

Derives the continuous Fourier transform from Fourier series, interpreting it as a continuum of frequency coefficients for representing nonperiodic functions.

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

Canonical Linear PDEs- Wave Equation, Heat Equation, and Laplace's Equation

An introduction to canonical linear PDEs, using the wave, heat, and Laplace equations to compare oscillation, diffusion, and steady-state behavior.

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

Heat Equation- Derivation and Equilibrium Solution in 1D - Laplace's Equation

Derives the one-dimensional heat equation from conservation laws and Fourier’s law, then solves its equilibrium form under common and insulated boundary conditions.

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

ODE for Particle Trajectories in a Time-Varying Vector Field

Model and visualize how particle patches move, stretch, and separate in a time-varying double-gyre flow using MATLAB.

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

Roots of Unity, Branch Cuts, Analytic Functions, and the Cauchy-Riemann Conditions

Explores roots of unity, multivalued complex functions and branch cuts, and the Cauchy-Riemann conditions for analytic functions.

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