Aspects of Integrability of Differential Systems and Fields A Mathematical Primer for Physicists

This book serves as an introduction to the concept of integrability as it applies to systems of differential equations as well as to vector-valued fields. The author focuses on specific aspects of integrability that are often encountered in a variety of problems in applied mathematics, physics and e...

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Bibliographic Details
Main Author: Papachristou, Costas J.
Format: eBook
Language:English
Published: Cham Springer International Publishing 2019, 2019
Edition:1st ed. 2019
Series:SpringerBriefs in Physics
Subjects:
Online Access:
Collection: Springer eBooks 2005- - Collection details see MPG.ReNa
Description
Summary:This book serves as an introduction to the concept of integrability as it applies to systems of differential equations as well as to vector-valued fields. The author focuses on specific aspects of integrability that are often encountered in a variety of problems in applied mathematics, physics and engineering. The following general cases of integrability are examined: (a) path-independence of line integrals of vector fields on the plane and in space; (b) integration of a system of ordinary differential equations by using first integrals; and (c) integrable systems of partial differential equations. Special topics include the integration of analytic functions and some elements from the geometric theory of differential systems. Certain more advanced subjects, such as Lax pairs and Bäcklund transformations, are also discussed. The book is written at an intermediate level for educational purposes. The presentation is as simple as the topics allow, often sacrificing mathematical rigor in favor of pedagogical efficiency
Physical Description:VIII, 94 p. 20 illus online resource
ISBN:9783030350024