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Ordinary Differential Equations and Dynamical Systems by Gerald Teschl

MathSchoolinternational.com contain houndreds of Free Math e-Books. Which cover almost all topics of mathematics. To see an extisive list of Complex Analysis eBooks . We hope mathematician or person who’s interested in mathematics like these books.

Ordinary Differential Equations and Dynamical Systems written by Gerald Teschl . This is an other great free downloadable mathematics book cover the following topics of complex number.

  • Part 1. Classical theory
  • 1. Introduction
    Newton’s equations, Classification of differential equations, First order autonomous equations, Finding explicit solutions, Qualitative analysis of first-order equations, Qualitative analysis of first-order periodic equations

  • 2. Initial value problems
    Fixed point theorems, The basic existence and uniqueness result, Some extensions, Dependence on the initial condition, Regular perturbation theory, Extensibility of solutions, Euler’s method and the Peano theorem

  • 3. Linear equations
    The matrix exponential, Linear autonomous first-order systems, Linear autonomous equations of order n, General linear first-order systems, Linear equations of order n, Periodic linear systems, Perturbed linear first order systems, Appendix: Jordan canonical form

  • 4. Differential equations in the complex domain
    The basic existence and uniqueness result, The Frobenius method for second-order equations, Linear systems with singularities, The Frobenius method

  • 5. Boundary value problems
    Introduction, Compact symmetric operators, Sturm–Liouville equations, Regular Sturm–Liouville problems, Oscillation theory, Periodic Sturm–Liouville equations

  • Part 2. Dynamical systems
  • 6. Dynamical systems
    Dynamical systems, The flow of an autonomous equation, Orbits and invariant sets, The Poincar´e map, Stability of fixed points, Stability via Liapunov’s method, Newton’s equation in one dimension

  • 7. Planar dynamical systems
    Examples from ecology, Examples from electrical engineering, The Poincar´e–Bendixson theorem

  • 8. Higher dimensional dynamical systems
    Attracting sets, The Lorenz equation, Hamiltonian mechanics, Completely integrable Hamiltonian systems, The Kepler problem, The KAM theorem

  • 9. Local behavior near fixed points
    Stability of linear systems, Stable and unstable manifolds, The Hartman–Grobman theorem, Appendix: Integral equations

  • Part 3. Chaos

  • 10. Discrete dynamical systems
    The logistic equation, Fixed and periodic points, Linear difference equations, Local behavior near fixed points

  • 11. Discrete dynamical systems in one dimension
    Period doubling, Sarkovskii’s theorem, On the definition of chaos, Cantor sets and the tent map, Symbolic dynamics, Strange attractors/repellors and fractal sets, Homoclinic orbits as source for chaos

  • 12. Periodic solutions
    Stability of periodic solutions, The Poincar´e map, Stable and unstable manifolds, Melnikov’s method for autonomous perturbations, Melnikov’s method for nonautonomous perturbations

  • 13. Chaos in higher dimensional systems
    The Smale horseshoe, The Smale–Birkhoff homoclinic theorem, Melnikov’s method for homoclinic orbits

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