Steve Brunton Courses

Numerical Differentiation with Finite Difference Derivatives

Learn techniques for approximating derivatives numerically using finite difference schemes. Explore error analysis with Taylor series and see practical implementations in MATLAB and Python.

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

Linear Systems of Differential Equations with Forcing - Convolution and the Dirac Delta Function

Explores linear differential equations with forcing, covering impulse response, Dirac delta function, and convolution integral. Essential for control theory and linear systems analysis.

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

Systems of Differential Equations - Diagonalization and Jordan Canonical Form

Explore diagonalization and Jordan Canonical Form for systems of differential equations, covering eigenvectors, complex conjugates, repeated eigenvalues, and general matrix applications.

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

Non-Normal Linear Systems and Transient Energy Growth - Bypass Transition to Turbulence

Explore non-normal linear systems and their role in turbulence, including examples, code demonstrations, and applications in fluid dynamics and bypass transition.

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

Drawing Phase Portraits for Nonlinear Systems

Learn to analyze nonlinear systems by drawing phase portraits, identifying fixed points, linearizing, and inferring global dynamics. Gain practical skills in stability analysis using eigenvalues and eigenvectors.

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

Systems of ODEs: Imaginary Eigenvalues and Center Fixed Points

Explore imaginary eigenvalues and center fixed points in 2D ODE systems. Learn to compute eigenvectors, write solutions, and understand geometric intuition behind rotational dynamics.

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

Systems of ODEs - Saddle Points and Instability

Explore unstable saddle points in 2D linear ODEs, their applications in energy-efficient transport, and analysis using eigenvalues, eigenvectors, and phase portraits.

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

Systems of ODEs - Sources and Sinks

Explore 2D linear ODEs with real eigenvalues, analyzing unstable sources and stable sinks through eigenvalues, eigenvectors, and phase portraits. Gain insights into solution methods and visualizations.

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

Eigenvalues and Eigenvectors

Explore eigenvalues and eigenvectors, key concepts in linear algebra. Learn to compute them for any matrix, understand their significance in transformations, and apply them to solve complex linear systems.

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

More Examples of Second Order Differential Equations

Explore advanced examples of second-order ODEs, including characteristic polynomials, initial conditions, and matrix systems. Learn to solve, plot, and interpret results using MATLAB.

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

Engineering Math Pre-Req - Quick and Dirty Introduction to Python

High-level introduction to essential Python commands for engineering math, covering arithmetic, loops, arrays, plotting, and solving equations and differential equations.

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

Engineering Math Pre-Req - Quick and Dirty Introduction to Matlab

High-level introduction to essential Matlab commands for engineering math, covering arithmetic, loops, matrices, plotting, and solving equations and differential equations.

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

Second-Order ODE: Spring-Mass-Damper

Comprehensive tutorial on solving second-order ODEs for damped harmonic oscillators, covering derivation, solution methods, and practical implementation in Matlab and Python.

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

Second-Order Ordinary Differential Equations - Solving the Harmonic Oscillator Four Ways

Explore four methods to solve second-order ODEs for harmonic oscillators: guessing, Taylor series, alternative guessing, and matrix systems. Gain practical problem-solving skills in differential equations.

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

The Simplest Ordinary Differential Equation and Its Exponential Solution

Explore exponential solutions to simple ODEs through real-world examples like population growth, compound interest, and radioactive decay. Gain intuitive understanding of Euler's number and its applications.

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