Download E-books Ordinary Differential Equations and Dynamical Systems (Graduate Studies in Mathematics) PDF

By Gerald Teschl

This booklet offers a self-contained creation to dull differential equations and dynamical structures appropriate for starting graduate scholars. the 1st half starts off with a few basic examples of explicitly solvable equations and a primary look at qualitative equipment. Then the basic effects about the preliminary worth challenge are proved: life, strong point, extensibility, dependence on preliminary stipulations. moreover, linear equations are thought of, together with the Floquet theorem, and a few perturbation effects. As a bit self sustaining themes, the Frobenius strategy for linear equations within the complicated area is validated and Sturm-Liouville boundary worth difficulties, together with oscillation thought, are investigated. the second one half introduces the idea that of a dynamical procedure. The Poincaré-Bendixson theorem is proved, and a number of other examples of planar structures from classical mechanics, ecology, and electric engineering are investigated. furthermore, attractors, Hamiltonian platforms, the KAM theorem, and periodic ideas are mentioned. ultimately, balance is studied, together with the solid manifold and the Hartman-Grobman theorem for either non-stop and discrete platforms. The 3rd half introduces chaos, starting with the fundamentals for iterated period maps and finishing with the Smale-Birkhoff theorem and the Melnikov technique for homoclinic orbits. The textual content comprises nearly 300 routines. also, using mathematical software program platforms is included all through, displaying how they could assist in the research of differential equations.

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