Global Analysis In Linear Differential Equations
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Global Analysis In Linear Differential Equations
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Author : M. Kohno
language : en
Publisher:
Release Date : 1999-04-30
Global Analysis In Linear Differential Equations written by M. Kohno and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-04-30 with categories.
Global Properties Of Linear Ordinary Differential Equations
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Author : Frantisek Neuman
language : en
Publisher: Springer
Release Date : 1991
Global Properties Of Linear Ordinary Differential Equations written by Frantisek Neuman and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991 with Mathematics categories.
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
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Author : Odile Pons
language : en
Publisher: World Scientific Publishing Company
Release Date : 2015-01-19
Analysis And Differential Equations written by Odile Pons and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-01-19 with Mathematics categories.
This book presents advanced methods of integral calculus and the classical theory of the ordinary and partial differential equations. It provides explicit solutions of linear and nonlinear differential equations and implicit solutions with discrete approximations. Differential equations that could not be explicitly solved are discussed with special functions such as Bessel functions. New functions are defined from differential equations. Laguerre, Hermite and Legendre orthonormal polynomials as well as several extensions are also considered.It is illustrated by examples and graphs of functions, with each chapter containing exercises solved in the last chapter.
Nonlinear Dispersive Equations
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Author : Terence Tao
language : en
Publisher: American Mathematical Soc.
Release Date : 2006
Nonlinear Dispersive Equations written by Terence Tao and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Mathematics categories.
"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.".
Global Analysis
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Author : Donald Clayton Spencer
language : en
Publisher: Princeton University Press
Release Date : 2015-03-08
Global Analysis written by Donald Clayton Spencer and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-03-08 with Mathematics categories.
Global analysis describes diverse yet interrelated research areas in analysis and algebraic geometry, particularly those in which Kunihiko Kodaira made his most outstanding contributions to mathematics. The eminent contributors to this volume, from Japan, the United States, and Europe, have prepared original research papers that illustrate the progress and direction of current research in complex variables and algebraic and differential geometry. The authors investigate, among other topics, complex manifolds, vector bundles, curved 4-dimensional space, and holomorphic mappings. Bibliographies facilitate further reading in the development of the various studies. Originally published in 1970. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.
The Collected Papers Of Stephen Smale
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Author : Stephen Smale
language : en
Publisher: World Scientific
Release Date : 2000
The Collected Papers Of Stephen Smale written by Stephen Smale and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Mathematics categories.
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.
Generalized Ordinary Differential Equations
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Author : ?tefan Schwabik
language : en
Publisher: World Scientific
Release Date : 1992
Generalized Ordinary Differential Equations written by ?tefan Schwabik and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992 with Mathematics categories.
The contemporary approach of J Kurzweil and R Henstock to the Perron integral is applied to the theory of ordinary differential equations in this book. It focuses mainly on the problems of continuous dependence on parameters for ordinary differential equations. For this purpose, a generalized form of the integral based on integral sums is defined. The theory of generalized differential equations based on this integral is then used, for example, to cover differential equations with impulses or measure differential equations. Solutions of generalized differential equations are found to be functions of bounded variations.The book may be used for a special undergraduate course in mathematics or as a postgraduate text. As there are currently no other special research monographs or textbooks on this topic in English, this book is an invaluable reference text for those interested in this field.
The Convenient Setting Of Global Analysis
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Author : Andreas Kriegl
language : en
Publisher: American Mathematical Soc.
Release Date : 1997
The Convenient Setting Of Global Analysis written by Andreas Kriegl and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with Mathematics categories.
For graduate students and research mathematicians interested in global analysis and the analysis of manifolds, lays the foundations for a differential calculus in infinite dimensions and discusses applications in infinite-dimension differential geometry and global analysis not involving Sobolev completions and fixed-point theory. Shows how the notion of smoothness as mapping smooth curves to smooth curves coincides with all known reasonable concepts up to Frechet spaces. Then develops a calculus of holomorphic mappings, and another of real analytical mapping. Emphasizes regular infinite dimensional Lie groups. Annotation copyrighted by Book News, Inc., Portland, OR
Differential Equations And Linear Algebra Global Edition
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Author : C. HENRY. PENNEY EDWARDS (DAVID E.. CALVIS, DAVID.)
language : en
Publisher:
Release Date : 2020-07-08
Differential Equations And Linear Algebra Global Edition written by C. HENRY. PENNEY EDWARDS (DAVID E.. CALVIS, DAVID.) and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-07-08 with categories.
Existence Theory For Nonlinear Ordinary Differential Equations
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Author : Donal O'Regan
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17
Existence Theory For Nonlinear Ordinary Differential Equations written by Donal O'Regan and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-17 with Mathematics categories.
We begin our applications of fixed point methods with existence of solutions to certain first order initial initial value problems. This problem is relatively easy to treat, illustrates important methods, and in the end will carry us a good deal further than may first meet the eye. Thus, we seek solutions to Y'. = I(t,y) (1. 1 ) { yeO) = r n where I: I X R n ---+ R and I = [0, b]. We shall seek solutions that are de fined either locally or globally on I, according to the assumptions imposed on I. Notice that (1. 1) is a system of first order equations because I takes its values in Rn. In section 3. 2 we will first establish some basic existence theorems which guarantee that a solution to (1. 1) exists for t > 0 and near zero. Familiar examples show that the interval of existence can be arbi trarily short, depending on the initial value r and the nonlinear behaviour of I. As a result we will also examine in section 3. 2 the dependence of the interval of existence on I and r. We mention in passing that, in the results which follow, the interval I can be replaced by any bounded interval and the initial value can be specified at any point in I. The reasoning needed to cover this slightly more general situation requires minor modifications on the arguments given here.