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Introduction to Linear Systems of Differential Equations

L. Ya. Adrianova St. Petersburg State University, Russia
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Hardcover ISBN: 978-0-8218-0328-8
Product Code: MMONO/146
List Price: $104.00 MAA Member Price:$93.60
AMS Member Price: $83.20 Electronic ISBN: 978-1-4704-4563-8 Product Code: MMONO/146.E List Price:$98.00
MAA Member Price: $88.20 AMS Member Price:$78.40
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List Price: $156.00 MAA Member Price:$140.40
AMS Member Price: $124.80 Click above image for expanded view Introduction to Linear Systems of Differential Equations L. Ya. Adrianova St. Petersburg State University, Russia Available Formats:  Hardcover ISBN: 978-0-8218-0328-8 Product Code: MMONO/146  List Price:$104.00 MAA Member Price: $93.60 AMS Member Price:$83.20
 Electronic ISBN: 978-1-4704-4563-8 Product Code: MMONO/146.E
 List Price: $98.00 MAA Member Price:$88.20 AMS Member Price: $78.40 Bundle Print and Electronic Formats and Save! This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.  List Price:$156.00 MAA Member Price: $140.40 AMS Member Price:$124.80
• Book Details

Translations of Mathematical Monographs
Volume: 1461995; 204 pp
MSC: Primary 34;

The theory of linear systems of differential equations is one of the cornerstones of the whole theory of differential equations. At its root is the concept of the Lyapunov characteristic exponent.

In this book, Adrianova presents introductory material and further detailed discussions of Lyapunov exponents. She also discusses the structure of the space of solutions of linear systems. Classes of linear systems examined are from the narrowest to widest: 1) autonomous, 2) periodic, 3) reducible to autonomous, 4) nearly reducible to autonomous, 5) regular.

• stability of linear systems and the influence of perturbations of the coefficients on the stability
• the criteria of uniform stability and of uniform asymptotic stability in terms of properties of the solutions
• several estimates of the growth rate of solutions of a linear system in terms of its coefficients

How perturbations of the coefficients change all the elements of the spectrum of the system is definitely the most complicated and involved problem in the whole theory of linear systems. Introduction to Linear Systems of Differential Equations presents the proof of the necessary and sufficient conditions for stability of the exponents for the simplest case of a two-dimensional diagonal system.

Graduate students and research mathematicians interested in the theory of differential equations.

• Chapters
• Chapter I. Linear autonomous and periodic systems
• Chapter II. Lyapunov characteristic exponents in the theory of linear systems
• Chapter III. Reducible, almost reducible, and regular systems
• Chapter IV. Stability and small perturbations of the coefficients of linear systems
• Chapter V. On the variation of characteristic exponents under small perturbations of coefficients
• Chapter VI. A linear homogeneous equation of the second order
• Reviews

• Gives a very good introduction to the theory of linear systems of differential equations … One of the best features of the book is the very large number of examples … suitable for research and graduate students working in the theory of differential equations and in mathematical applications … gives a good foundation for the study of more involved and specialized parts of the theory of linear differential equations.

Zentralblatt MATH
• Request Review Copy
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Volume: 1461995; 204 pp
MSC: Primary 34;

The theory of linear systems of differential equations is one of the cornerstones of the whole theory of differential equations. At its root is the concept of the Lyapunov characteristic exponent.

In this book, Adrianova presents introductory material and further detailed discussions of Lyapunov exponents. She also discusses the structure of the space of solutions of linear systems. Classes of linear systems examined are from the narrowest to widest: 1) autonomous, 2) periodic, 3) reducible to autonomous, 4) nearly reducible to autonomous, 5) regular.

• stability of linear systems and the influence of perturbations of the coefficients on the stability
• the criteria of uniform stability and of uniform asymptotic stability in terms of properties of the solutions
• several estimates of the growth rate of solutions of a linear system in terms of its coefficients

How perturbations of the coefficients change all the elements of the spectrum of the system is definitely the most complicated and involved problem in the whole theory of linear systems. Introduction to Linear Systems of Differential Equations presents the proof of the necessary and sufficient conditions for stability of the exponents for the simplest case of a two-dimensional diagonal system.

Graduate students and research mathematicians interested in the theory of differential equations.

• Chapters
• Chapter I. Linear autonomous and periodic systems
• Chapter II. Lyapunov characteristic exponents in the theory of linear systems
• Chapter III. Reducible, almost reducible, and regular systems
• Chapter IV. Stability and small perturbations of the coefficients of linear systems
• Chapter V. On the variation of characteristic exponents under small perturbations of coefficients
• Chapter VI. A linear homogeneous equation of the second order
• Gives a very good introduction to the theory of linear systems of differential equations … One of the best features of the book is the very large number of examples … suitable for research and graduate students working in the theory of differential equations and in mathematical applications … gives a good foundation for the study of more involved and specialized parts of the theory of linear differential equations.

Zentralblatt MATH
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