Linear Differential Equations Courses and Certifications

Steve Brunton

Matrix Systems of Differential Equations

Convert high-order linear ODEs into coupled first-order matrix systems and connect their characteristic roots to matrix eigenvalues.

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

Steve Brunton

Matrix Systems of First Order Equations Using Eigenvectors and Eigenvalues

Explore how eigenvalues and eigenvectors diagonalize matrix systems of first-order ODEs and reveal the geometric behavior of their solutions.

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

Steve Brunton

Second Order Harmonic Oscillator, Characteristic Equation, Ode45 in MATLAB

Solve second-order harmonic oscillator and spring-mass-damper equations using Taylor series, characteristic equations, and MATLAB's ode45.

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

Steve Brunton

Review of Calculus and First Order Linear ODEs

Review calculus concepts and solve first-order linear ordinary differential equations through exponential and physical-systems examples.

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

Steve Brunton

Systems of Differential Equations - Diagonalization and Jordan Canonical Form

See how repeated eigenvalues lead to generalized eigenvectors and Jordan canonical form for solving linear differential systems.

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

Steve Brunton

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

See how non-normal linear systems can grow transiently despite stable eigenvalues, providing a mechanism for bypass transition to turbulence in fluid flows.

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

Steve Brunton

Systems of ODEs - Sources and Sinks

Analyze 2×2 linear ODE systems through eigenvalues, eigenvectors, and phase portraits, distinguishing unstable sources from stable sinks.

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

Steve Brunton

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

Solve the harmonic oscillator from a spring-mass model in four ways, including guessed solutions, Taylor series, and a matrix formulation.

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

Michael Penn

Will You Survive This Differential Equation?

A focused walkthrough of a differential equation using integrating factors and a problem-solving trick.

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

Tom Rocks Maths

Oxford Calculus - Integrating Factors Explained

Derive and apply integrating factors to solve first-order linear differential equations, with and without initial conditions.

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

Steve Brunton

2x2 Systems of ODEs - With Eigenvalues and Eigenvectors, Phase Portraits

Analyze 2x2 systems of ordinary differential equations using eigenvalues, eigenvectors, and phase portraits.

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

Steve Brunton

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

Solves higher-order linear ODEs using characteristic equations and reformulates first-order systems in matrix form.

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

Professor Leonard

Special Integration in a Linear Differential Equation Problem

A long, intricate example of solving a first-order linear differential equation with substitutions, product rules, and an integrating factor.

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

Steve Brunton

Systems of ODEs - Saddle Points and Instability

Explore saddle-point dynamics in 2D linear systems and their role in efficient walking, aircraft maneuvering, and interplanetary transport.

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

Steve Brunton

More Examples of Second Order Differential Equations

Works through second-order linear ODE examples, linking characteristic roots to matrix eigenvalues and verifying solutions with MATLAB plots.

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