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Softcover ISBN:  9780821870044 
Product Code:  ULECT/7 
List Price:  $69.00 
MAA Member Price:  $62.10 
AMS Member Price:  $55.20 
eBook ISBN:  9781470421564 
Product Code:  ULECT/7.E 
List Price:  $65.00 
MAA Member Price:  $58.50 
AMS Member Price:  $52.00 
Softcover ISBN:  9780821870044 
eBook ISBN:  9781470421564 
Product Code:  ULECT/7.B 
List Price:  $134.00 $101.50 
MAA Member Price:  $120.60 $91.35 
AMS Member Price:  $107.20 $81.20 

Book DetailsUniversity Lecture SeriesVolume: 7; 1994; 105 ppMSC: Primary 12
Differential Galois theory studies solutions of differential equations over a differential base field. In much the same way that ordinary Galois theory is the theory of field extensions generated by solutions of (one variable) polynomial equations, differential Galois theory looks at the nature of the differential field extension generated by the solutions of differential equations. An additional feature is that the corresponding differential Galois groups (of automorphisms of the extension fixing the base and commuting with the derivation) are algebraic groups. This book deals with the differential Galois theory of linear homogeneous differential equations, whose differential Galois groups are algebraic matrix groups. In addition to providing a convenient path to Galois theory, this approach also leads to the constructive solution of the inverse problem of differential Galois theory for various classes of algebraic groups. Providing a selfcontained development and many explicit examples, this book provides a unique approach to differential Galois theory and is suitable as a textbook at the advanced graduate level.
ReadershipGraduate students and researchers.

Table of Contents

Chapters

Chapter 1. Differential ideals

Chapter 2. The Wronskian

Chapter 3. PicardVessiot extensions

Chapter 4. Automorphisms of PicardVessiot extensions

Chapter 5. The structure of PicardVessiot extensions

Chapter 6. The Galois correspondence and its consequences

Chapter 7. The inverse Galois problem


Additional Material

Reviews

The present book offers an elegant alternative approach to the Galois theory of linear homogeneous differential equations, based on the principle that the Galois correspondence should be obtained as a consequence of the algebraic grouptheoretic construction of PicardVessiot extensions.
Mathematical Reviews 
The selfcontained introduction Magid's 100page book provides should help the newcomer to proceed further into this beautiful and active field.
Bulletin of the AMS


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Differential Galois theory studies solutions of differential equations over a differential base field. In much the same way that ordinary Galois theory is the theory of field extensions generated by solutions of (one variable) polynomial equations, differential Galois theory looks at the nature of the differential field extension generated by the solutions of differential equations. An additional feature is that the corresponding differential Galois groups (of automorphisms of the extension fixing the base and commuting with the derivation) are algebraic groups. This book deals with the differential Galois theory of linear homogeneous differential equations, whose differential Galois groups are algebraic matrix groups. In addition to providing a convenient path to Galois theory, this approach also leads to the constructive solution of the inverse problem of differential Galois theory for various classes of algebraic groups. Providing a selfcontained development and many explicit examples, this book provides a unique approach to differential Galois theory and is suitable as a textbook at the advanced graduate level.
Graduate students and researchers.

Chapters

Chapter 1. Differential ideals

Chapter 2. The Wronskian

Chapter 3. PicardVessiot extensions

Chapter 4. Automorphisms of PicardVessiot extensions

Chapter 5. The structure of PicardVessiot extensions

Chapter 6. The Galois correspondence and its consequences

Chapter 7. The inverse Galois problem

The present book offers an elegant alternative approach to the Galois theory of linear homogeneous differential equations, based on the principle that the Galois correspondence should be obtained as a consequence of the algebraic grouptheoretic construction of PicardVessiot extensions.
Mathematical Reviews 
The selfcontained introduction Magid's 100page book provides should help the newcomer to proceed further into this beautiful and active field.
Bulletin of the AMS