Stability: Elements of the Theory and Applications with Examples:
This book is intended to familiarize the readers with basic concepts, and classic results of stability theory stated in a way as required by the rigorous rules of contemporary mathematics and, simultaneously, to introduce the learners to broad elds of not only the stability theory but also applicati...
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| Hauptverfasser: | , , |
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Warsaw ; Berlin
Sciendo
[2021]
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| Online-Zugang: | FAB01 FAW01 FCO01 FHA01 FKE01 FLA01 UPA01 Volltext |
| Zusammenfassung: | This book is intended to familiarize the readers with basic concepts, and classic results of stability theory stated in a way as required by the rigorous rules of contemporary mathematics and, simultaneously, to introduce the learners to broad elds of not only the stability theory but also applications involved. The emphasis is put on various dynamical systems which are defined by different branches of science and through diverse areas of human activity but always with care not to exceed the basic classical approach in the presentation. All in all, the authors plan to combine the textbook-like with encyclopaedia-like content. Another special goal of the authors is to attract the reader's attention to those aspects of theories whose incomplete understanding may lead to inaccuracies or errors. Sometimes, anyway just as designed, the offered information is limited to the pure statements of facts without any proofs. The reader should consult the references to find out missing pieces of information. This book also makes use of numerical (computer) computations. Most of the material contained in the book has already been published, a large part in various works of the authors. Fragments of several chapters come from published works of other authors - some excerpts, particularly relating to basic concepts, and some classic results are taken from outside sources. The book is offered as a textbook for the college-level students or as an aid to the PhD students interested in practical problems of the stability theory. The prerequisites are not demanding - the basic knowledge of calculus, complex functions, and linear algebra which are covered in the suitable, elementary courses is required. The first two chapters include what is typically covered in most introductory courses for students. The first chapter contains definitions of various types of stability; the second commences classic stability theorems regarding ordinary differential equations, but the most basic, applicable in technical sciences. The linear equations are treated more broadly, which creates a foundation for the linear approximation of differential equations in the stability research. Chapter three deals with integral inequalities and their application to the stability studies. Integral inequalities, both linear and nonlinear, are effectively applied in the development of the direct Lyapunov method when the boundedness and stability of motion of nonlinear weakly coupled systems are studied. Chapter four is predominantly dedicated to the Lyapunov direct method. Still, some attention is also paid to the method of limiting equations because it can be used to study motion stability even in hopeless cases when other methods fail. |
| Beschreibung: | Description based on online resource; title from PDF title page (publisher's Web site, viewed 25. Feb 2021) |
| Beschreibung: | 1 online resource (328 pages) |
| ISBN: | 9788366675285 |
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| 520 | |a This book is intended to familiarize the readers with basic concepts, and classic results of stability theory stated in a way as required by the rigorous rules of contemporary mathematics and, simultaneously, to introduce the learners to broad elds of not only the stability theory but also applications involved. The emphasis is put on various dynamical systems which are defined by different branches of science and through diverse areas of human activity but always with care not to exceed the basic classical approach in the presentation. All in all, the authors plan to combine the textbook-like with encyclopaedia-like content. Another special goal of the authors is to attract the reader's attention to those aspects of theories whose incomplete understanding may lead to inaccuracies or errors. Sometimes, anyway just as designed, the offered information is limited to the pure statements of facts without any proofs. | ||
| 520 | |a The reader should consult the references to find out missing pieces of information. This book also makes use of numerical (computer) computations. Most of the material contained in the book has already been published, a large part in various works of the authors. Fragments of several chapters come from published works of other authors - some excerpts, particularly relating to basic concepts, and some classic results are taken from outside sources. The book is offered as a textbook for the college-level students or as an aid to the PhD students interested in practical problems of the stability theory. The prerequisites are not demanding - the basic knowledge of calculus, complex functions, and linear algebra which are covered in the suitable, elementary courses is required. The first two chapters include what is typically covered in most introductory courses for students. | ||
| 520 | |a The first chapter contains definitions of various types of stability; the second commences classic stability theorems regarding ordinary differential equations, but the most basic, applicable in technical sciences. The linear equations are treated more broadly, which creates a foundation for the linear approximation of differential equations in the stability research. Chapter three deals with integral inequalities and their application to the stability studies. Integral inequalities, both linear and nonlinear, are effectively applied in the development of the direct Lyapunov method when the boundedness and stability of motion of nonlinear weakly coupled systems are studied. Chapter four is predominantly dedicated to the Lyapunov direct method. Still, some attention is also paid to the method of limiting equations because it can be used to study motion stability even in hopeless cases when other methods fail. | ||
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| 700 | 1 | |a Szadkowski, Andrzej |4 aut | |
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Datensatz im Suchindex
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| illustrated | Not Illustrated |
| index_date | 2024-07-03T16:50:14Z |
| indexdate | 2024-07-10T09:05:25Z |
| institution | BVB |
| isbn | 9788366675285 |
| language | English |
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| spelling | Martynyuk, Anatoliy A. Verfasser aut Stability: Elements of the Theory and Applications with Examples Anatoliy A. Martynyuk, Bogusław Radziszewski, Andrzej Szadkowski Warsaw ; Berlin Sciendo [2021] © 2020 1 online resource (328 pages) txt rdacontent c rdamedia cr rdacarrier Description based on online resource; title from PDF title page (publisher's Web site, viewed 25. Feb 2021) This book is intended to familiarize the readers with basic concepts, and classic results of stability theory stated in a way as required by the rigorous rules of contemporary mathematics and, simultaneously, to introduce the learners to broad elds of not only the stability theory but also applications involved. The emphasis is put on various dynamical systems which are defined by different branches of science and through diverse areas of human activity but always with care not to exceed the basic classical approach in the presentation. All in all, the authors plan to combine the textbook-like with encyclopaedia-like content. Another special goal of the authors is to attract the reader's attention to those aspects of theories whose incomplete understanding may lead to inaccuracies or errors. Sometimes, anyway just as designed, the offered information is limited to the pure statements of facts without any proofs. The reader should consult the references to find out missing pieces of information. This book also makes use of numerical (computer) computations. Most of the material contained in the book has already been published, a large part in various works of the authors. Fragments of several chapters come from published works of other authors - some excerpts, particularly relating to basic concepts, and some classic results are taken from outside sources. The book is offered as a textbook for the college-level students or as an aid to the PhD students interested in practical problems of the stability theory. The prerequisites are not demanding - the basic knowledge of calculus, complex functions, and linear algebra which are covered in the suitable, elementary courses is required. The first two chapters include what is typically covered in most introductory courses for students. The first chapter contains definitions of various types of stability; the second commences classic stability theorems regarding ordinary differential equations, but the most basic, applicable in technical sciences. The linear equations are treated more broadly, which creates a foundation for the linear approximation of differential equations in the stability research. Chapter three deals with integral inequalities and their application to the stability studies. Integral inequalities, both linear and nonlinear, are effectively applied in the development of the direct Lyapunov method when the boundedness and stability of motion of nonlinear weakly coupled systems are studied. Chapter four is predominantly dedicated to the Lyapunov direct method. Still, some attention is also paid to the method of limiting equations because it can be used to study motion stability even in hopeless cases when other methods fail. In English Technology & Engineering / General bisacsh Radziszewski, Bogusław aut Szadkowski, Andrzej aut Erscheint auch als Druck-Ausgabe 9788366675278 https://www.degruyter.com/isbn/9788366675285 Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Martynyuk, Anatoliy A. Radziszewski, Bogusław Szadkowski, Andrzej Stability: Elements of the Theory and Applications with Examples Technology & Engineering / General bisacsh |
| title | Stability: Elements of the Theory and Applications with Examples |
| title_auth | Stability: Elements of the Theory and Applications with Examples |
| title_exact_search | Stability: Elements of the Theory and Applications with Examples |
| title_exact_search_txtP | Stability: Elements of the Theory and Applications with Examples |
| title_full | Stability: Elements of the Theory and Applications with Examples Anatoliy A. Martynyuk, Bogusław Radziszewski, Andrzej Szadkowski |
| title_fullStr | Stability: Elements of the Theory and Applications with Examples Anatoliy A. Martynyuk, Bogusław Radziszewski, Andrzej Szadkowski |
| title_full_unstemmed | Stability: Elements of the Theory and Applications with Examples Anatoliy A. Martynyuk, Bogusław Radziszewski, Andrzej Szadkowski |
| title_short | Stability: Elements of the Theory and Applications with Examples |
| title_sort | stability elements of the theory and applications with examples |
| topic | Technology & Engineering / General bisacsh |
| topic_facet | Technology & Engineering / General |
| url | https://www.degruyter.com/isbn/9788366675285 |
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