White R. Asymptotic Analysis of Differential Equations 2010 torrent

Textbook in PDF format

The material for this book has resulted from teaching a graduate course
in ordinary differential equations at Princeton for several years. Methods
of asymptotic analysis covered include dominant balance, the use of divergent
asymptotic series, phase-integral methods, asymptotic evaluation of
integrals, and boundary layer analysis. The construction of integral solutions
and the use of analytic continuation are used in conjunction with
the asymptotic analysis, to show the interrelatedness of these methods.
Some of the functions of classical analysis are used as examples, to provide
an introduction to their analytic and asymptotic properties, and to give
derivations of some of the important identities satisfied by them, since it is
my experience that students are insufficiently familiar with Whittaker and
Watson. There is no attempt to give a complete presentation of all these
functions. The emphasis is on the various techniques of analysis: obtaining
asymptotic limits, connecting different asymptotic solutions, and obtaining
integral representations. Less attention is paid to strict mathematical
rigor. A sufficient number of different examples are chosen to demonstrate
the various techniques and approaches. Prerequisite material consists of
elementary calculus and a basic knowledge of the theory of functions of a
complex variable