University of Iowa 3 credits MATH
Linear systems of differential equations (fundamental solutions, matrix exponentials, Floquet theory); nonlinear differential equations (theorem for existence and uniqueness, flows, attractors); local nonlinear theory (invariant manifolds, Hartman-Grobman theorem, Poincare maps); global nonlinear theory (Poincare-Bendixson criterion, Lyapunov functions, gradient systems, Hamiltonian systems); bifurcations (saddle-node, pitchfork, transcritical, Hopf); introduction to chaos theory (Lorenz equations); computational methods to solve numerically differential equations and to draw phase planes and trajectories. Prerequisites: MATH:3600 and (MATH:3770 or MATH:4220).
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