Ordinary Differential Equations: Qualitative Theory (Graduate Studies in Mathematics) by Luis Barreira (PDF)

Description

This textbook provides a comprehensive introduction to the qualitative theory of ordinary differential equations. It includes a discussion of the existence and uniqueness of solutions, phase portraits, linear equations, stability theory, hyperbolicity and equations in the plane. The emphasis is primarily on results and methods that allow one to analyze qualitative properties of the solutions without solving the equations explicitly. The text includes numerous examples that illustrate in detail the new concepts and results as well as exercises at the end of each chapter. The book is also intended to serve as a bridge to important topics that are often left out of a course on ordinary differential equations. In particular, it provides brief introductions to bifurcation theory, center manifolds, normal forms and Hamiltonian systems.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐One of the best book on ODE.

⭐An excellent book. It contains the most important theorems of the qualitative theory, not much more but not less. The proofs are well written and clear. I used it for self-study but I think it could also work as a guide for a second course in ODEs.

⭐Muy bueno, para comenzar tiene todo el análisis cualitativo de las ecuaciones diferenciales, riguroso en tu tecnicismo.

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