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SpringerBriefs in Physics

Aspects of Integrability of Differential Systems and Fields

A Mathematical Primer for Physicists

Authors: Papachristou, Costas J.

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  • Offers a simple introduction to the concept of integrability as this applies to both differential systems and vector-valued fields
  • Contributes to the preparation of the intermediate-level physics student for advanced subjects 
  • Suitable for self-study, as well as useful as a tutorial companion in intermediate or advanced-level courses in physics, applied mathematics and engineering
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  • ISBN 978-3-030-35002-4
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Softcover $59.99
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About this book

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 B├Ącklund 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.

About the authors

Dr. Costas J. Papachristou is a senior faculty member at the Hellenic Naval Academy (The Naval Academy of Greece). He received a Ph.D. in Theoretical Physics from Brigham Young University, USA, and spent another year at BYU as a research faculty in Physics. At the HNA he teaches freshman- and sophomore-level Physics. His research interests are mainly in Theoretical and Mathematical Physics (in particular, symmetry and integrability properties of classical field equations, classical electromagnetism) but he is also active in Physics Education. He is an amateur musician and a columnist for Greek newspapers and magazines.

Table of contents (6 chapters)

Table of contents (6 chapters)

Buy this book

eBook $44.99
price for USA in USD (gross)
  • ISBN 978-3-030-35002-4
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $59.99
price for USA in USD
  • ISBN 978-3-030-35001-7
  • Free shipping for individuals worldwide
  • Immediate ebook access, if available*, with your print order
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Aspects of Integrability of Differential Systems and Fields
Book Subtitle
A Mathematical Primer for Physicists
Authors
Series Title
SpringerBriefs in Physics
Copyright
2019
Publisher
Springer International Publishing
Copyright Holder
The Author(s), under exclusive license to Springer Nature Switzerland AG
eBook ISBN
978-3-030-35002-4
DOI
10.1007/978-3-030-35002-4
Softcover ISBN
978-3-030-35001-7
Series ISSN
2191-5423
Edition Number
1
Number of Pages
VIII, 94
Number of Illustrations
20 b/w illustrations
Topics

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