
Preface  Introduction  Preview Material  Table of Contents  Supplementary Material 
 Differential Galois theory has seen intense research activity during the last decades in several directions: elaboration of more general theories, computational aspects, model theoretic approaches, applications to classical and quantum mechanics as well as to other mathematical areas such as number theory. This book intends to introduce the reader to this subject by presenting PicardVessiot theory, i.e. Galois theory of linear differential equations, in a selfcontained way. The needed prerequisites from algebraic geometry and algebraic groups are contained in the first two parts of the book. The third part includes PicardVessiot extensions, the fundamental theorem of PicardVessiot theory, solvability by quadratures, Fuchsian equations, monodromy group and Kovacic's algorithm. Over one hundred exercises will help to assimilate the concepts and to introduce the reader to some topics beyond the scope of this book. This book is suitable for a graduate course in differential Galois theory. The last chapter contains several suggestions for further reading encouraging the reader to enter more deeply into different topics of differential Galois theory or related fields. Request an examination or desk copy. Readership Graduate students and research mathematicians interested in algebraic methods in differential equations, differential Galois theory, and dynamical systems. Reviews "This wellcrafted book certainly serves its intended purpose well: it is a very good selfcontained introduction to PicardVessiot theory. ... It is a very nice book indeed."  MAA Reviews 


AMS Home 
Comments: webmaster@ams.org © Copyright 2014, American Mathematical Society Privacy Statement 