Ordinary Differential Equations: Qualitative Theory (graduate Studies In Mathematics)
by Luis Barreira /
2012 / English / PDF
8.4 MB Download
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.
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.
