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Author: S. Leela
Publisher: Springer Science & Business Media
ISBN: 9491216252
Category : Mathematics
Languages : en
Pages : 218
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Book Description
The problems of modern society are both complex and inter-disciplinary. Despite the - parent diversity of problems, however, often tools developed in one context are adaptable to an entirely different situation. For example, consider the well known Lyapunov’s second method. This interesting and fruitful technique has gained increasing signi?cance and has given decisive impetus for modern development of stability theory of discrete and dynamic system. It is now recognized that the concept of Lyapunov function and theory of diff- ential inequalities can be utilized to investigate qualitative and quantitative properties of a variety of nonlinear problems. Lyapunov function serves as a vehicle to transform a given complicated system into a simpler comparison system. Therefore, it is enough to study the properties of the simpler system to analyze the properties of the complicated system via an appropriate Lyapunov function and the comparison principle. It is in this perspective, the present monograph is dedicated to the investigation of the theory of causal differential equations or differential equations with causal operators, which are nonanticipative or abstract Volterra operators. As we shall see in the ?rst chapter, causal differential equations include a variety of dynamic systems and consequently, the theory developed for CDEs (Causal Differential Equations) in general, covers the theory of several dynamic systems in a single framework.
Author: S. Leela
Publisher: Springer Science & Business Media
ISBN: 9491216252
Category : Mathematics
Languages : en
Pages : 218
Get Book Here
Book Description
The problems of modern society are both complex and inter-disciplinary. Despite the - parent diversity of problems, however, often tools developed in one context are adaptable to an entirely different situation. For example, consider the well known Lyapunov’s second method. This interesting and fruitful technique has gained increasing signi?cance and has given decisive impetus for modern development of stability theory of discrete and dynamic system. It is now recognized that the concept of Lyapunov function and theory of diff- ential inequalities can be utilized to investigate qualitative and quantitative properties of a variety of nonlinear problems. Lyapunov function serves as a vehicle to transform a given complicated system into a simpler comparison system. Therefore, it is enough to study the properties of the simpler system to analyze the properties of the complicated system via an appropriate Lyapunov function and the comparison principle. It is in this perspective, the present monograph is dedicated to the investigation of the theory of causal differential equations or differential equations with causal operators, which are nonanticipative or abstract Volterra operators. As we shall see in the ?rst chapter, causal differential equations include a variety of dynamic systems and consequently, the theory developed for CDEs (Causal Differential Equations) in general, covers the theory of several dynamic systems in a single framework.
Author: V. Lakshmikantham
Publisher: Atlantis Studies in Mathematic
ISBN: 9789078677321
Category : Mathematics
Languages : en
Pages : 0
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Book Description
The theory of causal differential equations (CDE) includes several types of dynamic systems such as ordinary differential equations, functional differential equations, integro-differential equations (with or without memory), differential equations with anticipation and retardation. This is the first book which describes the theory of CDE as an independent discipline, incorporating the recent general theory of CDE and introducing several new ideas. This book is a timely introduction to the subject in a more generalised frame work. The present monograph collects recent works in this broad area and provides possible extensions to other dynamic systems involving causal operators such as CDE in abstract spaces, CDE with memory, CDE with fractional derivatives and causal set differential equations-giving initial apparatus, for further study in this important branch of nonlinear analysis.
Author: S. Leela
Publisher:
ISBN: 9781282749054
Category : Differential equations
Languages : en
Pages :
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Book Description
The theory of causal differential equations (CDE) includes several types of dynamic systems such as ordinary differential equations, functional differential equations, integro-differential equations (with or without memory), differential equations with anticipation and retardation. This is the first book which describes the theory of CDE as an independent discipline, incorporating the recent general theory of CDE and introducing several new ideas. This book is a timely introduction to the subject in a more generalised frame work. The present monograph collects recent works in this broad area and provides possible extensions to other dynamic systems involving causal operators such as CDE in abstract spaces, CDE with memory, CDE with fractional derivatives and causal set differential equations-giving initial apparatus, for further study in this important branch of nonlinear analysis.
Author: C. Corduneanu
Publisher: CRC Press
ISBN: 020316637X
Category : Mathematics
Languages : en
Pages : 185
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Book Description
Functional equations encompass most of the equations used in applied science and engineering: ordinary differential equations, integral equations of the Volterra type, equations with delayed argument, and integro-differential equations of the Volterra type. The basic theory of functional equations includes functional differential equations with cau
Author: Andrew Russell Forsyth
Publisher: CUP Archive
ISBN:
Category : Differential equations
Languages : en
Pages : 364
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Book Description
Author: Stanley A. Mulaik
Publisher: CRC Press
ISBN: 1439800391
Category : Mathematics
Languages : en
Pages : 470
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Book Description
Emphasizing causation as a functional relationship between variables, this book provides comprehensive coverage on the basics of SEM. It takes readers through the process of identifying, estimating, analyzing, and evaluating a range of models. The author discusses the history and philosophy of causality and its place in science and presents graph theory as a tool for the design and analysis of causal models. He explains how the algorithms in SEM are derived and how they work, covers various indices and tests for evaluating the fit of structural equation models to data, and explores recent research in graph theory, path tracing rules, and model evaluation.
Author: Mario Bunge
Publisher: Courier Corporation
ISBN: 0486144879
Category : Philosophy
Languages : en
Pages : 450
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Book Description
"I regard it as a truly seminal work in this field." — Professor William A. Wallace, author of Causality and Scientific ExplanationThis third edition of a distinguished book on the subject of causality is clear evidence that this principle continues to be an important area of philosophic enquiry.Non-technical and clearly written, this book focuses on the ontological problem of causality, with specific emphasis on the place of the causal principle in modern science. The author first defines the terminology employed and describes various formulations on the causal principle. He then examines the two primary critiques of causality, the empiricist and the romantic, as a prelude to the detailed explanation of the actual assertions of causal determination. Finally, Dr. Bunge analyzes the function of the causal principle in science, touching on such subjects as scientific law, scientific explanation, and scientific prediction. Included, also, is an appendix that offers specific replies to questions and criticisms raised upon the publication of the first edition.Now professor of philosophy and head of the Foundation and Philosophy of Science Unit at McGill University in Montreal, Dr. Mario Bunge has formerly been a full professor of theoretical physics. His observations on causality are of great interest to both scientists and humanists, as well as the general scientific and philosophic reader.
Author: Andrew Russell Forsyth
Publisher:
ISBN:
Category : Differential equations
Languages : en
Pages : 508
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Book Description
Author: E. J. Post
Publisher:
ISBN:
Category : Differential equations
Languages : en
Pages : 38
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Book Description
A mathematical procedure is given for singling out the causal solutions from the general set of solutions of self-adjoint differential equations. It consists in splitting the self-adjoint equation into a pair of adjoint equations whose solutions are purely causal and purely anti-causal, respectively. A subsequent merging of the equations then generates in full detail, including singularities, the causal and anti-causal :olutions of the original self -adjoint equation. As an important example, it is shown that the d'Alembertian with point source has a legitimate causal solution involving both retarded and advanced potentials at the source point itself, while at all other points, the retarded potential alone satisfies causality. Within the context of the formalism some recent attempts at modifying classical radiation theory can now be reassessed and more clearly categorized. In particular, the Dirac and Wheeler-Feynman approaches are examined in this light.
Author: Andrew Russell Forsyth
Publisher:
ISBN:
Category : Differential equations
Languages : en
Pages : 357
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Book Description
