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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: Walter A. Strauss
Publisher: John Wiley & Sons
ISBN: 0470054565
Category : Mathematics
Languages : en
Pages : 467
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Book Description
Our understanding of the fundamental processes of the natural world is based to a large extent on partial differential equations (PDEs). The second edition of Partial Differential Equations provides an introduction to the basic properties of PDEs and the ideas and techniques that have proven useful in analyzing them. It provides the student a broad perspective on the subject, illustrates the incredibly rich variety of phenomena encompassed by it, and imparts a working knowledge of the most important techniques of analysis of the solutions of the equations. In this book mathematical jargon is minimized. Our focus is on the three most classical PDEs: the wave, heat and Laplace equations. Advanced concepts are introduced frequently but with the least possible technicalities. The book is flexibly designed for juniors, seniors or beginning graduate students in science, engineering or mathematics.
Author: Vangipuram Lakshmikantham
Publisher: World Scientific
ISBN: 9814507261
Category : Mathematics
Languages : en
Pages : 287
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Book Description
Many evolution processes are characterized by the fact that at certain moments of time they experience a change of state abruptly. These processes are subject to short-term perturbations whose duration is negligible in comparison with the duration of the process. Consequently, it is natural to assume that these perturbations act instantaneously, that is, in the form of impulses. It is known, for example, that many biological phenomena involving thresholds, bursting rhythm models in medicine and biology, optimal control models in economics, pharmacokinetics and frequency modulated systems, do exhibit impulsive effects. Thus impulsive differential equations, that is, differential equations involving impulse effects, appear as a natural description of observed evolution phenomena of several real world problems.
Author: John Losee
Publisher: Routledge
ISBN: 1351472291
Category : Philosophy
Languages : en
Pages : 219
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Book Description
What types of entities qualify as causes and effects? What is the relationship between cause and effect? How are causal claims to be assessed? The first question deals with the structure of the world; the second is about theories that interpret the relationship of causes to effects; while the third has to do with proper procedure in science and everyday life. This volume is a wide-ranging history of answers that have been given to these three questions, and their relationship to scientific understanding.Losee presents a number of theories of causality within a historical survey that emphasizes the interrelationship between these theories and developments in science. His analysis displays the strengths and weaknesses of these theories so as to contribute to our present understanding of causal relatedness.Among the positions discussed are those of Aristotle, Hume, Kant, Mill, Salmon, Lewis, and Woodward. Losee's analysis displays the strengths and weaknesses of theories that identify causal relatedness with regularity of sequence, probability increase, energy transfer, exchange of a conserved quantity, counterfactual dependence, and inferability.These theories are judged, in part,by their ability to resolvedifficulties posed by instances of overdetermination,causation by omission, preventive causation, and causation by disconnection. Since applications of the theories to these instances disagree, a strategy of employing multiple concepts of causation is examined.Theories of Causality also describes the particular difficulties for causal analysis posed by quantum mechanics. One such difficulty is the prohibition against combining a causal analysis of a quantum process with a spatio-temporal description of that process.
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: Chin-Yuan Lin
Publisher: World Scientific
ISBN: 9814307122
Category : Mathematics
Languages : en
Pages : 555
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Book Description
This book presents a complete theory of ordinary differential equations, with many illustrative examples and interesting exercises. A rigorous treatment is offered in this book with clear proofs for the theoretical results and with detailed solutions for the examples and problems. This book is intended for undergraduate students who major in mathematics and have acquired a prerequisite knowledge of calculus and partly the knowledge of a complex variable, and are now reading advanced calculus and linear algebra. Additionally, the comprehensive coverage of the theory with a wide array of examples and detailed solutions, would appeal to mathematics graduate students and researchers as well as graduate students in majors of other disciplines. As a handy reference, advanced knowledge is provided in this book with details developed beyond the basics; optional sections, where main results are extended, offer an understanding of further applications of ordinary differential equations.
Author: Demetrios Christodoulou
Publisher: Princeton University Press
ISBN: 9780691049571
Category : Mathematics
Languages : en
Pages : 332
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Book Description
This book introduces new methods in the theory of partial differential equations derivable from a Lagrangian. These methods constitute, in part, an extension to partial differential equations of the methods of symplectic geometry and Hamilton-Jacobi theory for Lagrangian systems of ordinary differential equations. A distinguishing characteristic of this approach is that one considers, at once, entire families of solutions of the Euler-Lagrange equations, rather than restricting attention to single solutions at a time. The second part of the book develops a general theory of integral identities, the theory of "compatible currents," which extends the work of E. Noether. Finally, the third part introduces a new general definition of hyperbolicity, based on a quadratic form associated with the Lagrangian, which overcomes the obstacles arising from singularities of the characteristic variety that were encountered in previous approaches. On the basis of the new definition, the domain-of-dependence theorem and stability properties of solutions are derived. Applications to continuum mechanics are discussed throughout the book. The last chapter is devoted to the electrodynamics of nonlinear continuous media.
Author: William Jones
Publisher: Springer Science & Business Media
ISBN: 1475702116
Category : Science
Languages : en
Pages : 320
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Book Description
Modern plasma physics, encompassing wave-particle interactions and collec tive phenomena characteristic of the collision-free nature of hot plasmas, was founded in 1946 when 1. D. Landau published his analysis of linear (small amplitude) waves in such plasmas. It was not until some ten to twenty years later, however, with impetus from the then rapidly developing controlled fusion field, that sufficient attention was devoted, in both theoretical and experimental research, to elucidate the importance and ramifications of Landau's original work. Since then, with advances in laboratory, fusion, space, and astrophysical plasma research, we have witnessed important devel opments toward the understanding of a variety of linear as well as nonlinear plasma phenomena, including plasma turbulence. Today, plasma physics stands as a well-developed discipline containing a unified body of powerful theoretical and experimental techniques and including a wide range of appli cations. As such, it is now frequently introduced in university physics and engineering curricula at the senior and first-year-graduate levels. A necessary prerequisite for all of modern plasma studies is the under standing oflinear waves in a temporally and spatially dispersive medium such as a plasma, including the kinetic (Landau) theory description of such waves. Teaching experience has usually shown that students (seniors and first-year graduates), when first exposed to the kinetic theory of plasma waves, have difficulties in dealing with the required sophistication in multidimensional complex variable (singular) integrals and transforms.
