Hardcover ISBN:  9780821853184 
Product Code:  GSM/122 
List Price:  $60.00 
MAA Member Price:  $54.00 
AMS Member Price:  $48.00 
Electronic ISBN:  9781470411831 
Product Code:  GSM/122.E 
List Price:  $56.00 
MAA Member Price:  $50.40 
AMS Member Price:  $44.80 

Book DetailsGraduate Studies in MathematicsVolume: 122; 2011; 225 ppMSC: Primary 12; 13; 14; 17; 20; 34; 68;
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.ReadershipGraduate students and research mathematicians interested in algebraic methods in differential equations, differential Galois theory, and dynamical systems.

Table of Contents

Part 1. Algebraic geometry

Chapter 1. Affine and projective varieties

Chapter 2. Algebraic varieties

Part 2. Algebraic groups

Chapter 3. Basic notions

Chapter 4. Lie algebras and algebraic groups

Part 3. Differential Galois theory

Chapter 5. PicardVessiot extensions

Chapter 6. The Galois correspondence

Chapter 7. Differential equations over $\mathbb {C}(z)$

Chapter 8. Suggestions for further reading


Additional Material

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


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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.
Graduate students and research mathematicians interested in algebraic methods in differential equations, differential Galois theory, and dynamical systems.

Part 1. Algebraic geometry

Chapter 1. Affine and projective varieties

Chapter 2. Algebraic varieties

Part 2. Algebraic groups

Chapter 3. Basic notions

Chapter 4. Lie algebras and algebraic groups

Part 3. Differential Galois theory

Chapter 5. PicardVessiot extensions

Chapter 6. The Galois correspondence

Chapter 7. Differential equations over $\mathbb {C}(z)$

Chapter 8. Suggestions for further reading

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