Global Analysis In Linear Differential Equations

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Global Analysis in Linear Differential Equations

M. Kohno
Global Analysis in Linear Differential Equations Book PDF

Author : M. Kohno
Publisher : Springer Science & Business Media
Page : 539 pages
File Size : 49,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789401146050

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Global Analysis in Linear Differential Equations by M. Kohno Pdf

Since the initiative works for global analysis of linear differential equations by G.G. Stokes and B. Riemann in 1857, the Airy function and the Gauss hypergeometric function became the most important and the greatest practical special functions, which have a variety of applications to mathematical science, physics and engineering. The cffcctivity of these functions is essentially due to their "behavior in the large" . For instance, the Airy function plays a basic role in the asymptotic analysis of many functions arising as solutions of differential equations in several problems of applied math ematics. In case of the employment of its behavior, one should always pay attention to the Stokes phenomenon. On the other hand, as is well-known, the Gauss hypergeometric function arises in all fields of mathematics, e.g., in number theory, in the theory of groups and in analysis itself. It is not too much to say that all power series are special or extended cases of the hypergeometric series. For the full use of its properties, one needs connection formulas or contiguous relations.

Handbook of Global Analysis

Demeter Krupka,David Saunders
Handbook of Global Analysis Book PDF

Author : Demeter Krupka,David Saunders
Publisher : Elsevier
Page : 1243 pages
File Size : 42,6 Mb
Release : 2011-08-11
Category : Mathematics
ISBN : 9780080556734

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Handbook of Global Analysis by Demeter Krupka,David Saunders Pdf

This is a comprehensive exposition of topics covered by the American Mathematical Society’s classification “Global Analysis , dealing with modern developments in calculus expressed using abstract terminology. It will be invaluable for graduate students and researchers embarking on advanced studies in mathematics and mathematical physics.This book provides a comprehensive coverage of modern global analysis and geometrical mathematical physics, dealing with topics such as; structures on manifolds, pseudogroups, Lie groupoids, and global Finsler geometry; the topology of manifolds and differentiable mappings; differential equations (including ODEs, differential systems and distributions, and spectral theory); variational theory on manifolds, with applications to physics; function spaces on manifolds; jets, natural bundles and generalizations; and non-commutative geometry. - Comprehensive coverage of modern global analysis and geometrical mathematical physics- Written by world-experts in the field- Up-to-date contents

Microlocal Methods in Mathematical Physics and Global Analysis

Daniel Grieser,Stefan Teufel,Andras Vasy
Microlocal Methods in Mathematical Physics and Global Analysis Book PDF

Author : Daniel Grieser,Stefan Teufel,Andras Vasy
Publisher : Springer Science & Business Media
Page : 148 pages
File Size : 50,9 Mb
Release : 2012-12-13
Category : Mathematics
ISBN : 9783034804660

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Microlocal Methods in Mathematical Physics and Global Analysis by Daniel Grieser,Stefan Teufel,Andras Vasy Pdf

Microlocal analysis is a field of mathematics that was invented in the mid-20th century for the detailed investigation of problems from partial differential equations, which incorporated and made rigorous many ideas that originated in physics. Since then it has grown to a powerful machine which is used in global analysis, spectral theory, mathematical physics and other fields, and its further development is a lively area of current mathematical research. In this book extended abstracts of the conference 'Microlocal Methods in Mathematical Physics and Global Analysis', which was held at the University of Tübingen from the 14th to the 18th of June 2011, are collected.​

Nonlinear Dispersive Equations

Terence Tao
Nonlinear Dispersive Equations Book PDF

Author : Terence Tao
Publisher : American Mathematical Soc.
Page : 394 pages
File Size : 53,9 Mb
Release : 2006
Category : Differential equations, Partial
ISBN : 9780821841433

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Nonlinear Dispersive Equations by Terence Tao Pdf

"Starting only with a basic knowledge of graduate real analysis and Fourier analysis, the text first presents basic nonlinear tools such as the bootstrap method and perturbation theory in the simpler context of nonlinear ODE, then introduces the harmonic analysis and geometric tools used to control linear dispersive PDE. These methods are then combined to study four model nonlinear dispersive equations. Through extensive exercises, diagrams, and informal discussion, the book gives a rigorous theoretical treatment of the material, the real-world intuition and heuristics that underlie the subject, as well as mentioning connections with other areas of PDE, harmonic analysis, and dynamical systems.".

Introduction to Global Analysis

Donald W. Kahn
Introduction to Global Analysis Book PDF

Author : Donald W. Kahn
Publisher : Courier Corporation
Page : 352 pages
File Size : 54,6 Mb
Release : 2013-11-07
Category : Mathematics
ISBN : 0486152294

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Introduction to Global Analysis by Donald W. Kahn Pdf

This text introduces the methods of mathematical analysis as applied to manifolds, including the roles of differentiation and integration, infinite dimensions, Morse theory, Lie groups, and dynamical systems. 1980 edition.

Global and Stochastic Analysis with Applications to Mathematical Physics

Yuri E. Gliklikh
Global and Stochastic Analysis with Applications to Mathematical Physics Book PDF

Author : Yuri E. Gliklikh
Publisher : Springer Science & Business Media
Page : 454 pages
File Size : 46,7 Mb
Release : 2010-12-07
Category : Mathematics
ISBN : 9780857291639

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Global and Stochastic Analysis with Applications to Mathematical Physics by Yuri E. Gliklikh Pdf

Methods of global analysis and stochastic analysis are most often applied in mathematical physics as separate entities, thus forming important directions in the field. However, while combination of the two subject areas is rare, it is fundamental for the consideration of a broader class of problems. This book develops methods of Global Analysis and Stochastic Analysis such that their combination allows one to have a more or less common treatment for areas of mathematical physics that traditionally are considered as divergent and requiring different methods of investigation. Global and Stochastic Analysis with Applications to Mathematical Physics covers branches of mathematics that are currently absent in monograph form. Through the demonstration of new topics of investigation and results, both in traditional and more recent problems, this book offers a fresh perspective on ordinary and stochastic differential equations and inclusions (in particular, given in terms of Nelson's mean derivatives) on linear spaces and manifolds. Topics covered include classical mechanics on non-linear configuration spaces, problems of statistical and quantum physics, and hydrodynamics. A self-contained book that provides a large amount of preliminary material and recent results which will serve to be a useful introduction to the subject and a valuable resource for further research. It will appeal to researchers, graduate and PhD students working in global analysis, stochastic analysis and mathematical physics.

Global Analysis

Ilka Agricola,Thomas Friedrich
Global Analysis Book PDF

Author : Ilka Agricola,Thomas Friedrich
Publisher : American Mathematical Soc.
Page : 362 pages
File Size : 53,9 Mb
Release : 2002
Category : Differential forms
ISBN : 9780821829516

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Global Analysis by Ilka Agricola,Thomas Friedrich Pdf

The final third of the book applies the mathematical ideas to important areas of physics: Hamiltonian mechanics, statistical mechanics, and electrodynamics." "There are many classroom-tested exercises and examples with excellent figures throughout. The book is ideal as a text for a first course in differential geometry, suitable for advanced undergraduates or graduate students in mathematics or physics."--BOOK JACKET.

Basic Global Relative Invariants for Homogeneous Linear Differential Equations

Roger Chalkley
Basic Global Relative Invariants for Homogeneous Linear Differential Equations Book PDF

Author : Roger Chalkley
Publisher : American Mathematical Soc.
Page : 223 pages
File Size : 43,9 Mb
Release : 2002
Category : Differential equations, Linear
ISBN : 9780821827819

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Basic Global Relative Invariants for Homogeneous Linear Differential Equations by Roger Chalkley Pdf

Given any fixed integer $m \ge 3$, the author presents simple formulas for $m - 2$ algebraically independent polynomials over $\mathbb{Q}$ having the remarkable property, with respect to transformations of homogeneous linear differential equations of order $m$, that each polynomial is both a semi-invariant of the first kind (with respect to changes of the dependent variable) and a semi-invariant of the second kind (with respect to changes of the independent variable). These relative invariants are suitable for global studies in several different contexts and do not require Laguerre-Forsyth reductions for their evaluation. In contrast, all of the general formulas for basic relative invariants that have been proposed by other researchers during the last 113 years are merely local ones that are either much too complicated or require a Laguerre-Forsyth reduction for each evaluation.

The Collected Papers of Stephen Smale

Stephen Smale,Roderick Wong
The Collected Papers of Stephen Smale Book PDF

Author : Stephen Smale,Roderick Wong
Publisher : World Scientific
Page : 564 pages
File Size : 41,8 Mb
Release : 2000
Category : Mathematics
ISBN : 9810249926

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The Collected Papers of Stephen Smale by Stephen Smale,Roderick Wong Pdf

This invaluable book contains the collected papers of Stephen Smale. These are divided into eight groups: topology; calculus of variations; dynamics; mechanics; economics; biology, electric circuits and mathematical programming; theory of computation; miscellaneous. In addition, each group contains one or two articles by world leaders on its subject which comment on the influence of Smale's work, and another article by Smale with his own retrospective views.

Global Properties of Linear Ordinary Differential Equations

Frantisek Neuman
Global Properties of Linear Ordinary Differential Equations Book PDF

Author : Frantisek Neuman
Publisher : Springer
Page : 344 pages
File Size : 45,9 Mb
Release : 1991
Category : Mathematics
ISBN : UOM:39015029206920

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Global Properties of Linear Ordinary Differential Equations by Frantisek Neuman Pdf

This volume presents an authoritative, unified overview of the methods and results concerning the global properties of linear differential equations of order n (n>=2). It does not, however, seek to be comprehensive. Rather, it contains a selection of results which richly illustrate the unified approach presented. By making use of recent methods and results from many different areas of mathematics and by introducing several original methods, global solutions of problems previously studied only locally are given. The structure of global transformations is described algebraically, and a new geometrical approach is introduced which leads to global canonical forms suitable for Cartan's moving frame-of-reference method. The theory discussed also provides effective tools for solving some open problems, especially relating to the distribution of zeros of solutions. In addition, the theory of functional equations plays an important role in studying the asymptotic behaviour of solutions. Applications to differential geometry and functional equations are also described. The volume is largely self-contained. This book is for mathematicians, computer scientists, physicists, chemists, engineers, and others whose work involves the use of linear differential equations.

Analysis And Differential Equations (Second Edition)

Odile Pons
Analysis And Differential Equations Second Edition Book PDF

Author : Odile Pons
Publisher : World Scientific
Page : 305 pages
File Size : 52,8 Mb
Release : 2022-12-19
Category : Mathematics
ISBN : 9789811268588

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Analysis And Differential Equations (Second Edition) by Odile Pons Pdf

The book presents advanced methods of integral calculus and optimization, the classical theory of ordinary and partial differential equations and systems of dynamical equations. It provides explicit solutions of linear and nonlinear differential equations, and implicit solutions with discrete approximations.The main changes of this second edition are: the addition of theoretical sections proving the existence and the unicity of the solutions for linear differential equations on real and complex spaces and for nonlinear differential equations defined by locally Lipschitz functions of the derivatives, as well as the approximations of nonlinear parabolic, elliptic, and hyperbolic equations with locally differentiable operators which allow to prove the existence of their solutions; furthermore, the behavior of the solutions of differential equations under small perturbations of the initial condition or of the differential operators is studied.

Recent Trends in Differential Equations

R P Agarwal
Recent Trends in Differential Equations Book PDF

Author : R P Agarwal
Publisher : World Scientific
Page : 600 pages
File Size : 42,6 Mb
Release : 1992-05-07
Category : Mathematics
ISBN : 9789814505628

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Recent Trends in Differential Equations by R P Agarwal Pdf

This series aims at reporting new developments of a high mathematical standard and of current interest. Each volume in the series shall be devoted to mathematical analysis that has been applied, or potentially applicable to the solutions of scientific, engineering, and social problems. The first volume of WSSIAA contains 42 research articles on differential equations by leading mathematicians from all over the world. This volume has been dedicated to V Lakshmikantham on his 65th birthday for his significant contributions in the field of differential equations. Contents:Semilinear and Quasilinear Stochastic Differential Equations in Banach Spaces (N U Ahmed)Asymptotic Behaviour of the Nonoscillating Solutions of First Order Linear Nonautonomous Neutral Equations (D Bainov & V Petrov)Boundary and Angular Layer Behavior in Singularly Perturbed Quasilinear Systems (K W Chang & G X Liu)Singular Perturbation for a System of Differential-Difference Equations (S-N Chow & W Huang)Bounds for Solutions Sets of Multivalued ODES (K Deimling)Comparison of Eigenvalues for a Class of Multipoint Boundary Value Problems (P W Eloe & J Henderson)A Solution to the General Bessel Moment Problem (W D Evans et al.)Boundedness in Linear Functional Differential Equations with Infinite Delay (J Kato)Foundation of Invariant Manifold Theory for Ordinary Differential Equations (H W Knobloch)and other papers Readership: Mathematicians and engineers. keywords:Differential Equations

Non-Linear Differential Equations

G. Sansone,R. Conti
Non Linear Differential Equations Book PDF

Author : G. Sansone,R. Conti
Publisher : Elsevier
Page : 550 pages
File Size : 44,8 Mb
Release : 2016-06-06
Category : Mathematics
ISBN : 9781483135960

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Non-Linear Differential Equations by G. Sansone,R. Conti Pdf

International Series of Monographs in Pure and Applied Mathematics, Volume 67: Non-Linear Differential Equations, Revised Edition focuses on the analysis of the phase portrait of two-dimensional autonomous systems; qualitative methods used in finding periodic solutions in periodic systems; and study of asymptotic properties. The book first discusses general theorems about solutions of differential systems. Periodic solutions, autonomous systems, and integral curves are explained. The text explains the singularities of Briot-Bouquet theory. The selection takes a look at plane autonomous systems. Topics include limiting sets, plane cycles, isolated singular points, index, and the torus as phase space. The text also examines autonomous plane systems with perturbations and autonomous and non-autonomous systems with one degree of freedom. The book also tackles linear systems. Reducible systems, periodic solutions, and linear periodic systems are considered. The book is a vital source of information for readers interested in applied mathematics.

Nonlinear Dispersive Equations

Jaime Angulo Pava
Nonlinear Dispersive Equations Book PDF

Author : Jaime Angulo Pava
Publisher : American Mathematical Soc.
Page : 272 pages
File Size : 45,6 Mb
Release : 2009
Category : Mathematics
ISBN : 9780821848975

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Nonlinear Dispersive Equations by Jaime Angulo Pava Pdf

This book provides a self-contained presentation of classical and new methods for studying wave phenomena that are related to the existence and stability of solitary and periodic travelling wave solutions for nonlinear dispersive evolution equations. Simplicity, concrete examples, and applications are emphasized throughout in order to make the material easily accessible. The list of classical nonlinear dispersive equations studied include Korteweg-de Vries, Benjamin-Ono, and Schrodinger equations. Many special Jacobian elliptic functions play a role in these examples. The author brings the reader to the forefront of knowledge about some aspects of the theory and motivates future developments in this fascinating and rapidly growing field. The book can be used as an instructive study guide as well as a reference by students and mature scientists interested in nonlinear wave phenomena.

Asymptotic Analysis

Mikhail V. Fedoryuk
Asymptotic Analysis Book PDF

Author : Mikhail V. Fedoryuk
Publisher : Springer Science & Business Media
Page : 370 pages
File Size : 51,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642580161

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Asymptotic Analysis by Mikhail V. Fedoryuk Pdf

In this book we present the main results on the asymptotic theory of ordinary linear differential equations and systems where there is a small parameter in the higher derivatives. We are concerned with the behaviour of solutions with respect to the parameter and for large values of the independent variable. The literature on this question is considerable and widely dispersed, but the methods of proofs are sufficiently similar for this material to be put together as a reference book. We have restricted ourselves to homogeneous equations. The asymptotic behaviour of an inhomogeneous equation can be obtained from the asymptotic behaviour of the corresponding fundamental system of solutions by applying methods for deriving asymptotic bounds on the relevant integrals. We systematically use the concept of an asymptotic expansion, details of which can if necessary be found in [Wasow 2, Olver 6]. By the "formal asymptotic solution" (F.A.S.) is understood a function which satisfies the equation to some degree of accuracy. Although this concept is not precisely defined, its meaning is always clear from the context. We also note that the term "Stokes line" used in the book is equivalent to the term "anti-Stokes line" employed in the physics literature.