Wolfgang Wasow Knihy

Focusing on the nature and structure of turning points in linear analytic differential equations, this book revisits the author's insights from his earlier work while incorporating significant new ideas and developments. It reflects the advancements in the field over nearly two decades, emphasizing the deepened understanding of the formal theory near singularities and the potential applications of modern algebra and topology. The author suggests that while these methods may enhance certain aspects of the theory, the analytic dimensions of turning point theory may remain less impacted.

"A book of great value ... it should have a profound influence upon future research." —  Mathematical Reviews In this outstanding text, author Wolfgang Wasow concentrates on the mathematical ideas underlying various asymptotic methods for ordinary differential equations that lead to full, infinite expansions. Starting with some basic properties of linear differential equations in the complex domain, the treatment advances to considerations of regular and irregular singular points, asymptotic power series, generalizations by means of Jordan's canonical form, and some special asymptotic methods. Subsequent chapters explore asymptotic expansions with respect to a parameter, turning point problems, nonlinear equations, singular perturbations, and integration of differential equations by factorial series. Numerous problems appear throughout the text, which is ideal for course work or self-study.