Ordinary Differential Equations · Calculus
Systems of Linear ODEs
Systems of ODEs describe coupled dynamics. Eigenvalues of A determine qualitative behavior; phase portraits visualize all solutions simultaneously.
WHAT STUDENTS WILL LEARN
✓Write systems in matrix form x′ = Ax
✓Solve using eigenvalues and eigenvectors
✓Classify equilibria: nodes, saddles, spirals, centers
✓Linearize nonlinear systems at equilibria
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