Aspects of Integrability of Differential Systems and Fields
A Mathematical Primer for Physicists
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Beschreibung
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.
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
Autor*in
Costas J. Papachristou
Themen in »Aspects of Integrability of Differential Systems and Fields«
Integrability Condition Conservation of Mechanical Energy Autonomous System Conservative Force Field Homogeneous Linear System of ODEs Irrotational Vector Field Bäcklund Transformation ordinary differential equations partial differential equations