Learn Invest About

Where Understanding Creates Value. Open education — built by a family, for everyone.

Learn

Quantum Engineering
All Curricula

Company

About SIIEA
Investment Hub
Contact

Legal

Terms of Service
Privacy Policy
Disclaimer

© 2026 SIIEA Innovations, LLC. All rights reserved.

Educational content licensed under CC BY-NC-SA 4.0. Content is AI-assisted — see disclaimer.

Quantum Engineering Year 0: Mathematical Foundations Month 3Day 74

This content was created with AI assistance and may contain errors or inaccuracies. Always verify against authoritative academic sources.

Full disclaimer

Year 0·Month 3·Week 3

Day 74: Phase Portraits and Stability

Day 74 of 2,016~7 min read

Learning Objectives

•Sketch phase portraits for 2×2 linear systems
•Classify equilibrium points (nodes, saddles, spirals, centers)
•Determine stability from eigenvalues
•Understand the relationship between eigenvalues and phase portrait geometry
•Apply stability analysis to physical systems

Today's Schedule (7 hours)

Previous dayNext day

On this page

Schedule Overview Learning Objectives Required Reading Primary Text Boyce DiPrima 11th Edition Phase Portraits 1 The Phase Plane 2 Equilibrium Points 3 Classification by Eigenvalues Stability Definitions 4 Types of Stability 5 Stability Criterion Classification Examples Example 1 Stable Node Example 2 Saddle Point Example 3 Center Example 4 Spiral Phase Portrait Gallery Nodes Real Eigenvalues Same Sign Saddle Real Eigenvalues Opposite Signs Spirals Complex Eigenvalues with 0 Center Pure Imaginary Eigenvalues Quick Classification Algorithm Practice Problems Level 1-3 Classification Level 4-6 From Trace and Determinant Level 7-9 Sketch Phase Portraits Level 10 Applications Answers Quantum Mechanics Connection Bloch Sphere Dynamics Daily Checklist Preview Tomorrow

Day 73Day 74 of 2,016Day 75