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dynamical-systems

The eigenvalue method -- distinct real eigenvalues

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Classifying centers Classifying saddles Degenerate and repeated-eigenvalue cases The matrix exponential Classifying nodes Fundamental matrices Repeated eigenvalues and generalized eigenvectors The eigenvalue method -- complex eigenvalues The eigenvalue method -- distinct real eigenvalues Complex roots and Euler's formula Direction fields for systems Eigenvalue problems from boundary conditions Every operator on a complex space has an eigenvalue Hyperbolicity: real, distinct eigenvalues Multivariable first- and second-order optimality conditions The DFT, defined and as a matrix transformation The characteristic polynomial The power method for eigenvalues The regular Sturm-Liouville problem Trajectories vs. solution curves Eigenvalues and the characteristic equation The eigenvector question Vector-valued solutions and the vector Wronskian Converting an $n$th-order equation to a first-order… Linear independence of two functions Regularization geometry: what ridge does to the normal… Writing a system in matrix form

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