Steve Brunton Courses

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

Gentle Introduction to Modeling with Matrices and Vectors - A Probabilistic Weather Model

Explore probabilistic weather modeling using matrices and vectors, with practical examples in Python and MATLAB. Learn to represent and update weather states mathematically.

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

Differential Equations and Dynamical Systems - Overview

Explore dynamical systems and their applications in various fields. Learn classic and modern techniques for modeling real-world phenomena, from fluid dynamics to epidemiology.

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

Complex Analysis - Overview & Motivation, Complex Arithmetic, Euler's Formula & Polar Coordinates

Introduction to complex numbers, their arithmetic operations, Euler's formula, and polar coordinates. Covers solutions to differential equations and lays foundation for further complex analysis topics.

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

Topics in Dynamical Systems - Fixed Points, Linearization, Invariant Manifolds, Bifurcations & Chaos

Explore dynamical systems: fixed points, linearization, manifolds, bifurcations, and chaos. Gain insights into nonlinear dynamics and their applications in describing our changing world.

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

Solving PDEs with the Laplace Transform - The Wave Equation

Explore solving the wave equation using Laplace transforms, covering problem setup, PDE to ODE conversion, and solution methods including the Heaviside function and method of characteristics.

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

Moore's Law, Exponential Growth, and Extrapolation!

Explore Moore's Law, exponential growth in computing, and its impact on AI, scientific computing, and future technologies. Understand the implications for technological advancement.

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

Linearizing Nonlinear Differential Equations Near a Fixed Point

Explore techniques to analyze nonlinear differential equations by linearizing dynamics near fixed points, enabling powerful linear ODE solutions for nonlinear systems.

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

Solving Systems of Differential Equations with Eigenvalues and Eigenvectors

Learn to solve systems of linear ODEs using eigenvalues and eigenvectors. Covers problem setup, solution methods, and intuitive interpretation, with code examples in Python and MATLAB.

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

Motivating Eigenvalues and Eigenvectors with Differential Equations

Explore eigenvalues and eigenvectors through differential equations, deriving key concepts and visualizing their applications in matrix systems for a deeper understanding of linear algebra.

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