# krainaksiazek qualitative theory of differential equations 20106996

- znaleziono 17 produktów w 2 sklepach

### The Qualitative Theory of Ordinary Differential Equations Dover Publications

**Książki / Literatura obcojęzyczna**

Preface Chapter 1. Systems of Differential Equations 1.1 A Simple Mass-Spring System 1.2 Coupled Mass-Spring Systems 1.3 Systems of First-Order Equations 1.4 Vector-Matrix Notation for Systems 1.5 The Need for a Theory 1.6 Existence, Uniqueness, and Continuity 1.7 The Gronwall Inequality Chapter 2. Linear Systems, with an Introduction to Phase Space Analysis 2.1 Introduction 2.2 Existence and Uniqueness for Linear Systems 2.3 Linear Homogeneous Systems 2.4 Linear Nonhomogeneous Systems 2.5 Linear Systems with Constant Coefficients 2.6 Similarity of Matrices and the Jordan Canonical Form 2.7 Asymptotic Behavior of Solutions of Linear Systems with Constant Coefficients 2.8 Autonomous Systems--Phase Space--Two-Dimensional Systems 2.9 Linear Systems with Periodic Coefficients; Miscellaneous Exercises Chapter 3. Existence Theory 3.1 Existence in the Scalar Case 3.2 Existence Theory for Systems of First-Order Equations 3.3 Uniqueness of Solutions 3.4 Continuation of Solutions 3.5 Dependence on Initial Conditions and Parameters; Miscellaneous Exercises Chapter 4. Stability of Linear and Almost Linear Systems 4.1 Introduction 4.2 Definitions of Stability 4.3 Linear Systems 4.4 Almost Linear Systems 4.5 Conditional Stability 4.6 Asymptotic Equivalence 4.7 Stability of Periodic Solutions Chapter 5. Lyapunov's Second Method 5.1 Introductory Remarks 5.2 Lyapunov's Theorems 5.3 Proofs of Lyapunov's Theorems 5.4 Invariant Sets and Stability 5.5 The Extent of Asymptotic Stability--Global Asymptotic Stability 5.6 Nonautonomous Systems Chapter 6. Some Applications 6.1 Introduction 6.2 The Undamped Oscillator 6.3 The Pendulum 6.4 Self-Excited Oscillations--Periodic Solutions of the Liénard Equation 6.5 The Regulator Problem 6.6 Absolute Stability of the Regulator System Appendix 1. Generalized Eigenvectors, Invariant Subspaces, and Canonical Forms of Matrices Appendix 2. Canonical Forms of 2 x 2 Matrices Appendix 3. The Logarithm of a Matrix Appendix 4. Some Results from Matrix Theory Bibliography; Index

Sklep: Libristo.pl

### Ordinary Differential Equations Springer-Verlag New York Inc.

**Książki / Literatura obcojęzyczna**

This book develops the theory of ordinary differential equations (ODEs), starting from an introductory level through to a graduate-level treatment of the qualitative theory, including bifurcation theory (but not chaos). While proofs are rigorous, the exposition is reader-friendly, aiming for the informality of face-to-face interactions.§§A unique feature of this book is the integration of rigorous theory with numerous applications of scientific interest. Besides providing motivation, this synthesis clarifies the theory and enhances scientific literacy. Other features include: (i) a wealth of exercises at various levels, along with commentary that explains why they matter and (ii) a dedicated website with software templates, problem solutions, and other resources supporting the text and (iii) a large number and variety of illustrations.§§Given its many applications, the book is suitable for senior undergraduates and graduate students in mathematics and science and engineering courses. The thoughtful presentation, which anticipates many confusions of beginning students, makes the book suitable for a teaching environment that emphasizes self-directed, active learning (including the so-called inverted classroom).§

Sklep: Libristo.pl

### Differential Equations and Dynamical Systems Springer

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This textbook, ideal for students and lecturers alike, is a systematic study of the qualitative and geometric theory of nonlinear differential equations and dynamical systems. It includes a thorough treatment of linear systems.

Sklep: Libristo.pl

### Essential Partial Differential Equations Springer, Berlin

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This volume provides an introduction to the analytical and numerical aspects of partial differential equations (PDEs). It unifies an analytical and computational approach for these; the qualitative behaviour of solutions being established using classical concepts: maximum principles and energy methods.§§Notable inclusions are the treatment of irregularly shaped boundaries, polar coordinates and the use of flux-limiters when approximating hyperbolic conservation laws. The numerical analysis of difference schemes is rigorously developed using discrete maximum principles and discrete Fourier analysis. A novel feature is the inclusion of a chapter containing projects, intended for either individual or group study, that cover a range of topics such as parabolic smoothing, travelling waves, isospectral matrices, and the approximation of multidimensional advection-diffusion problems.§§The underlying theory is illustrated by numerous examples and there are around 300 exercises, designed to promote and test understanding. They are starred according to level of difficulty. Solutions to odd-numbered exercises are available to all readers while even-numbered solutions are available to authorised instructors.§§Written in an informal yet rigorous style, Essential Partial Differential Equations is designed for mathematics undergraduates in their final or penultimate year of university study, but will be equally useful for students following other scientific and engineering disciplines in which PDEs are of practical importance. The only prerequisite is a familiarity with the basic concepts of calculus and linear algebra.§

Sklep: Libristo.pl

### Dynamics of Partial Differential Equations Springer, Berlin

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This book contains two review articles on the dynamics of partial differential equations that deal with closely related topics but can be read independently.§§Wayne reviews recent results on the global dynamics of the two-dimensional Navier-Stokes equations. This system exhibits stable vortex solutions: the topic of Wayne's contribution is how solutions that start from arbitrary initial conditions evolve towards stable vortices. Weinstein considers the dynamics of localized states in nonlinear Schrodinger and Gross-Pitaevskii equations that describe many optical and quantum systems. In this contribution, Weinstein reviews recent bifurcations results of solitary waves, their linear and nonlinear stability properties and results about radiation damping where waves lose energy through radiation.§§The articles, written independently, are combined into one volume to showcase the tools of dynamical systems theory at work in explaining qualitative phenomena associated with two classes of partial differential equations with very different physical origins and mathematical properties.§

Sklep: Libristo.pl

### Differential Equations And Dynamical Systems

**Książki Obcojęzyczne>Angielskie>Mathematics & science>Mathematics>Calculus & mathematical analysis>Differential calculus & equationsKsi...**

This Textbook, Ideal For Students And Lecturers Alike, Is A Systematic Study Of The Qualitative And Geometric Theory Of Nonlinear Differential Equations And Dynamical Systems. It Includes A Thorough Treatment Of Linear Systems.

Sklep: Gigant.pl

### Stochastic Equations in Infinite Dimensions Cambridge University Press

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Now in its second edition, this book gives a systematic and self-contained presentation of basic results on stochastic evolution equations in infinite dimensional, typically Hilbert and Banach, spaces. In the first part the authors give a self-contained exposition of the basic properties of probability measure on separable Banach and Hilbert spaces, as required later; they assume a reasonable background in probability theory and finite dimensional stochastic processes. The second part is devoted to the existence and uniqueness of solutions of a general stochastic evolution equation, and the third concerns the qualitative properties of those solutions. Appendices gather together background results from analysis that are otherwise hard to find under one roof. This revised edition includes two brand new chapters surveying recent developments in the area and an even more comprehensive bibliography, making this book an essential and up-to-date resource for all those working in stochastic differential equations.

Sklep: Libristo.pl

### Some Quantitative Methods Models in Economic Theory Nova Science Publishers Inc

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This book takes an intermediate place between monographs and textbooks: on the one hand, it contains known, yet unusually portrayed facts, and on the other hand, the author brings his own results corresponding to the field of research. It is already obvious from the title that while reading the book, attention and concentration are required, as it is always necessary when studying books with mathematical content. Mathematical models and methods in the economic theory are very various. They are as follows: econometrics, the game theory, operation research, nonlinear and chaotic dynamics and many other aspects as well. The book will be interesting only to those who are already familiar with corresponding tasks as well as to students at all levels specializing in economic dynamics, in decision-making methods, in forecasting effects of management and in the analysis of interaction of economic agents. In terms of the most interesting and new models of economic dynamics, the authors emphasize multidimensional nonlinear systems of the differential equations of Lotka-Volterra type. These models have been constructed and analyzed, and scopes of their application and various methods of coefficients identification have been offered for them. The analysis of the competition between various economic agents (i.e. branches of economy, rival companies and sellers in the market) has been made. Another fact unusual to similar monographs is the inclusion of the theory of differential equations with the retarded argument. In economic theory, there are numerous examples of models being used with discrete time (they also have been given attention here) and with time lags (concentrated or distributed). Such an approach gives more adequate models without lags, but in the differential equations with continuous time, the introduction of delay complicates systems while the growth of delay the qualitative behavior of trajectories is changed. Additionally, there appear fluctuations such as stability being changed by instability, etc. As the author has belonged to the St. Petersburg Mathematical School for more than thirty-five years, the list of references contains many Russian names which may be unknown to Western readers. However, the list also includes world classical scientists who devoted their works to mathematical methods in economics. In this monograph, an attentive reader will find numerous points for further analysis which can become a subject of publications or theses. In some cases, the text is conducted in a polemic manner that is, the author is always open for discussions and does not consider his work to be the ultimate truth.

Sklep: Libristo.pl

### Global Attractors of Non-Autonomous Dynamical and Control Systems World Scientific Publishing Co Pte Ltd

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The study of attractors of dynamical systems occupies an important position in the modern qualitative theory of differential equations. This engaging volume presents an authoritative overview of both autonomous and non-autonomous dynamical systems, including the global compact attractor. From an in-depth introduction to the different types of dissipativity and attraction, the book takes a comprehensive look at the connections between them, and critically discusses applications of general results to different classes of differential equations.The new Chapters 15-17 added to this edition include some results concerning Control Dynamical Systems - the global attractors, asymptotic stability of switched systems, absolute asymptotic stability of differential/difference equations and inclusions - published in the works of author in recent years.

Sklep: Libristo.pl

### Elliptic Boundary Value Problems of Second Order in Piecewise Smooth Domains Elsevier Science Ltd

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The book contains a systematic treatment of the qualitative theory of elliptic boundary value problems for linear and quasilinear second order equations in non-smooth domains. The authors concentrate on the following fundamental results: sharp estimates for strong and weak solutions, solvability of the boundary value problems, regularity assertions for solutions near singular points. The book contains the Hardy Friedrichs Wirtinger type inequalities as well as new integral inequalities related to the Cauchy problem for a differential equation. It covers the precise exponents of the solution decreasing rate near boundary singular points and best possible conditions for this. It answers the question about the influence of the coefficients smoothness on the regularity of solutions. It has new existence theorems for the Dirichlet problem for linear and quasilinear equations in domains with conical points. It covers: the precise power modulus of continuity at singular boundary point for solutions of the Dirichlet, mixed and the Robin problems; the behaviour of weak solutions near conical point for the Dirichlet problem for m Laplacian; the behaviour of weak solutions near a boundary edge for the Dirichlet and mixed problem for elliptic quasilinear equations with triple degeneration; and, the behaviour of weak solutions near a boundary edge for the Dirichlet and mixed problem for elliptic quasilinear equations with triple degeneration.

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### A Short Course on Operator Semigroups Springer, Berlin

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The book offers a direct and up-to-date introduction to the theory of one-parameter semigroups of linear operators on Banach spaces It contains the fundamental results of the theory such as the Hille-Yoshida generation theorem, the bounded perturbation theorem, and the Trotter-Kato approximation theorem, but also treats the spectral theory of semigroups and its consequences for the qualitative behavior.The book is intended for students and researchers who want to become acquainted with the concept of semigroups in order to work with it in fields like partial and functional differential equations, stochastic processes, infinite dimensional control theory, or dynamical systems coming from physics or biology.

Sklep: Libristo.pl

### The Mathematics Behind Biological Invasions Springer, Berlin

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This book investigates the mathematical§analysis of biological invasions. Unlike purely qualitative treatments of§ecology, it draws on mathematical theory and methods, equipping the reader with§sharp tools and rigorous methodology.§Subjects include invasion dynamics, species interactions, population§spread, long-distance dispersal, stochastic effects, risk analysis, and optimal§responses to invaders. While based on the theory of dynamical systems,§including partial differential equations and integrodifference equations, the book§also draws on information theory, machine learning, Monte Carlo methods,§optimal control, statistics, and stochastic processes. Applications to real§biological invasions are included throughout. Ultimately, the book imparts a§powerful principle: that by bringing ecology and mathematics together,§researchers can uncover new understanding of, and effective response strategies§to, biological invasions. It is suitable for graduate students and established§researchers in mathematical ecology.§

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### Nonlinear Dynamics and Chaotic Phenomena Springer Netherlands

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FolJowing the formulation of the laws of mechanics by Newton, Lagrange sought to clarify and emphasize their geometrical character. Poincare and Liapunov successfuIJy developed analytical mechanics further along these lines. In this approach, one represents the evolution of all possible states (positions and momenta) by the flow in phase space, or more efficiently, by mappings on manifolds with a symplectic geometry, and tries to understand qualitative features of this problem, rather than solving it explicitly. One important outcome of this line of inquiry is the discovery that vastly different physical systems can actually be abstracted to a few universal forms, like Mandelbrot's fractal and Smale's horse-shoe map, even though the underlying processes are not completely understood. This, of course, implies that much of the observed diversity is only apparent and arises from different ways of looking at the same system. Thus, modern nonlinear dynamics 1 is very much akin to classical thermodynamics in that the ideas and results appear to be applicable to vastly different physical systems. Chaos theory, which occupies a central place in modem nonlinear dynamics, refers to a deterministic development with chaotic outcome. Computers have contributed considerably to progress in chaos theory via impressive complex graphics. However, this approach lacks organization and therefore does not afford complete insight into the underlying complex dynamical behavior. This dynamical behavior mandates concepts and methods from such areas of mathematics and physics as nonlinear differential equations, bifurcation theory, Hamiltonian dynamics, number theory, topology, fractals, and others.

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### Mathematical Modeling and Methods of Option Pricing World Scientific Publishing Co Pte Ltd

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From the unique perspective of partial differential equations (PDE), this self-contained book presents a systematic, advanced introduction to the Black-Scholes-Merton's option pricing theory. A unified approach is used to model various types of option pricing as PDE problems, to derive pricing formulas as their solutions, and to design efficient algorithms from the numerical calculation of PDEs. In particular, the qualitative and quantitative analysis of American option pricing is treated based on free boundary problems, and the implied volatility as an inverse problem is solved in the optimal control framework of parabolic equations.

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### Jacob Palis - Selected Works, 1 Springer, Berlin

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The Theory of Dynamical Systems was first introduced by the great mathematician Henri Poincaré as a qualitative study of differential equations. For more than forty years, Jacob Palis has made outstanding contributions to this area of mathematics. In the 1970s, following in the wake of Stephen Smale, he became one of the major figures in developing the Theory of Hyperbolic Dynamics and Structural Stability.§This volume presents a selection of Jacob Palis mathematical contributions, starting with his PhD thesis and ending with papers on what is widely known as the Palis Conjecture. Most of the papers included in the present volume are inspired by the earlier work of Poincaré and, more recently, by Steve Smale among others. They aim at providing a description of the general structure of dynamical systems.§Jacob Palis, whose work has been distinguished with numerous international prizes, is broadly recognized as the father of the Latin American School of Mathematics in Dynamical Systems and one of the most important scientific personalities on the continent. In 2010 he was awarded the Balzan Prize for his fundamental contributions in the Mathematical Theory of Dynamical Systems, which has been the basis for many applications in various scientific disciplines.§

Sklep: Libristo.pl

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