Phase Portraits Courses and Certifications

Ross Dynamics Lab

Bifurcation Theory - Saddle-Node, Hopf, Transcritical, Pitchfork

2 reviews

Explore saddle-node, transcritical, pitchfork, and Hopf bifurcations in dynamical systems. Learn how these phenomena affect phase portraits and system behavior as parameters change.

• YouTube
• 1 hour 17 minutes
• On-Demand
• Free Online Course

Differential Equations I

Go on a grand tour of differential equations and get the hands-on experience needed to master the essentials.

• Brilliant
• 40-50 hours
• On-Demand
• Paid Course

Ross Dynamics Lab

Friction and Phase Portraits - Coulomb Friction - Cone of Friction - Falling Broom - Spinning Top

Explore Coulomb friction, phase portraits, and 3D rigid body dynamics. Analyze friction effects on equilibrium, falling objects, and spinning tops using experiments and mathematical models.

• YouTube
• 1 hour 12 minutes
• On-Demand
• Free Online Course

Ross Dynamics Lab

Phase Portraits from Potential Energy - Bifurcations - Constraint Forces from Lagrange Multipliers

Explore phase portraits, bifurcations, and constraint forces in dynamical systems. Learn graphical methods, analyze system behavior changes, and understand Lagrangian mechanics with practical applications.

• YouTube
• 1 hour 13 minutes
• On-Demand
• Free Online Course

Ross Dynamics Lab

Lagrange’s Equations with Conservative and Non-Conservative Forces - Phase Space Introduction

Explore Lagrange's equations for conservative and non-conservative forces, rigid body systems, and phase space analysis. Learn to solve and classify motions using advanced analytical dynamics techniques.

• YouTube
• 1 hour 17 minutes
• On-Demand
• Free Online Course

Steve Brunton

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 Online Course

Steve Brunton

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 Online Course

Steve Brunton

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 Online Course

Steve Brunton

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

Explore 2x2 systems of ODEs, eigenvalues, eigenvectors, and phase portraits in engineering mathematics. Learn to analyze and visualize complex dynamical systems.

• YouTube
• 49 minutes
• On-Demand
• Free Online Course

Steve Brunton

Linearization of Nonlinear ODEs, 2x2 Systems, Phase Portraits

Explore linearization techniques for nonlinear ODEs, analyze 2x2 systems, and visualize phase portraits in this advanced engineering mathematics lecture.

• YouTube
• 49 minutes
• On-Demand
• Free Online Course

Steve Brunton

Examples of Nonlinear Systems - Particle in a Potential Well

Explore nonlinear systems through the particle in a potential well example, covering Euler-Lagrange equations, vector fields, phase portraits, and damping in engineering mathematics.

• YouTube
• 50 minutes
• On-Demand
• Free Online Course

Differential Equations: 2x2 Systems

5 reviews

In order to understand most phenomena in the world, we need to understand not just single equations, but systems of differential equations. In this course, we start with 2x2 systems.

• edX
• 10 weeks, 2-5 hours a week
• Finished
• Free Online Course (Audit)

IIT Madras;  NPTEL

Nonlinear System Analysis

2 reviews

Explore nonlinear system analysis tools, from mathematical foundations to stability analysis, bifurcations, and physical non-linearities. Gain insights for robotics, space, and defense applications.

• Swayam
• 12 weeks
• Finished
• Free Online Course

IIT Roorkee;  NPTEL

Dynamical System and Control

The objective of this course is to enhance the understanding of the theory, properties and applications of various dynamical and control systems.

• Swayam
• 12 weeks
• Finished
• Free Online Course