Ordinary Differential Equation

MATH-6400

Analytical and computational methods for ordinary differential equations: existence and uniqueness of solutions, similarity methods, linear equations, regular singular points, hypergeometric equations, asymptotic expansions near irregular singular points, WKB theory, turning points, stability theory, stable and unstable manifolds, periodic solutions and Poincare maps, Floquet theory, stabilization and destabilization by periodic forcing, calculus of variations, Lagrangian and Hamiltonian systems, Poincare invariants, symplectic integrators, basic bifurcation theory, examples of chaotic dynamics, applications to physics, chemistry, and biology.

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