Galois Theory of Linear Differential Equations

  • Marius van der Put
  • Michael F. Singer

Part of the Grundlehren der mathematischen Wissenschaften book series (GL, volume 328)

Table of contents

  1. Front Matter
    Pages I-XVII
  2. Algebraic Theory

    1. Front Matter
      Pages 1-1
    2. Marius van der Put, Michael F. Singer
      Pages 3-36
    3. Marius van der Put, Michael F. Singer
      Pages 37-58
    4. Marius van der Put, Michael F. Singer
      Pages 59-98
    5. Marius van der Put, Michael F. Singer
      Pages 99-140
  3. Analytic Theory

    1. Front Matter
      Pages 141-141
    2. Marius van der Put, Michael F. Singer
      Pages 143-155
    3. Marius van der Put, Michael F. Singer
      Pages 157-185
    4. Marius van der Put, Michael F. Singer
      Pages 187-228
    5. Marius van der Put, Michael F. Singer
      Pages 229-243
    6. Marius van der Put, Michael F. Singer
      Pages 245-259
    7. Marius van der Put, Michael F. Singer
      Pages 261-270
    8. Marius van der Put, Michael F. Singer
      Pages 271-293
    9. Marius van der Put, Michael F. Singer
      Pages 295-315
    10. Marius van der Put, Michael F. Singer
      Pages 317-335
  4. Back Matter
    Pages 337-440

About this book

Introduction

Linear differential equations form the central topic of this volume, Galois theory being the unifying theme.
A large number of aspects are presented: algebraic theory especially differential Galois theory, formal theory, classification, algorithms to decide solvability in finite terms, monodromy and Hilbert's 21st problem, asymptotics and summability, the inverse problem and linear differential equations in positive characteristic. The appendices aim to help the reader with concepts used, from algebraic geometry, linear algebraic groups, sheaves, and tannakian categories that are used.
This volume will become a standard reference for all mathematicians in this area of mathematics, including graduate students.

Keywords

Arithmetic Asymptotics Computer Algebra Direct Problems Galois Theory Global Classification Inverse Problems algebra Linear Differential Equations Local Classification partial differential equation

Authors and affiliations

  • Marius van der Put
    • 1
  • Michael F. Singer
    • 2
  1. 1.Department of MathematicsUniversity of GroningenGroningenThe Netherlands
  2. 2.Department of MathematicsNorth Carolina State UniversityRaleighUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-55750-7
  • Copyright Information Springer-Verlag Berlin Heidelberg 2003
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-642-62916-7
  • Online ISBN 978-3-642-55750-7
  • Series Print ISSN 0072-7830
  • About this book