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Phase Space
Oct 11, 2023
ODE Foundations
24 min readOrdinary Differential Equations (7): Stability Theory
Will a bridge survive the wind? Will an ecosystem recover from a shock? Stability theory answers these questions using Lyapunov functions, linearization, and bifurcation analysis.
Sep 24, 2023
ODE Foundations
22 min readOrdinary Differential Equations (6): Linear Systems and the Matrix Exponential
When multiple variables interact, you need systems of ODEs. Learn the matrix exponential, eigenvalue-based solutions, phase portrait classification, and applications to coupled oscillators and RLC circuits.