Theory Of Differential Equations Vi Partial Differential Equations Ii
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Theory Of Differential Equations Vi Partial Differential Equations Ii
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Author :
language : en
Publisher:
Release Date : 1906
Theory Of Differential Equations Vi Partial Differential Equations Ii written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1906 with categories.
Partial Differential Equations Ii
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Author : Michael E. Taylor
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-11-02
Partial Differential Equations Ii written by Michael E. Taylor 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 2010-11-02 with Mathematics categories.
This second in the series of three volumes builds upon the basic theory of linear PDE given in volume 1, and pursues more advanced topics. Analytical tools introduced here include pseudodifferential operators, the functional analysis of self-adjoint operators, and Wiener measure. The book also develops basic differential geometrical concepts, centred about curvature. Topics covered include spectral theory of elliptic differential operators, the theory of scattering of waves by obstacles, index theory for Dirac operators, and Brownian motion and diffusion.
Partial Differential Equations Ii
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Author : Michael Taylor
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17
Partial Differential Equations Ii written by Michael Taylor 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.
Partial differential equations is a many-faceted subject. Created to describe the mechanical behavior of objects such as vibrating strings and blowing winds, it has developed into a body of material that interacts with many branches of math ematics, such as differential geometry, complex analysis, and harmonic analysis, as weil as a ubiquitous factor in the description and elucidation of problems in mathematical physics. This work is intended to provide a course of study of some of the major aspects of PDE. It is addressed to readers with a background in the basic introductory grad uate mathematics courses in American universities: elementary real and complex analysis, differential geometry, and measure theory. Chapter 1 provides background material on the theory of ordinary differential equations (ODE). This includes both very basic material-on topics such as the existence and uniqueness of solutions to ODE and explicit solutions to equations with constant coefficients and relations to linear algebra-and more sophisticated results-on flows generated by vector fields, connections with differential geom etry, the calculus of differential forms, stationary action principles in mechanics, and their relation to Hamiltonian systems. We discuss equations of relativistic motion as weIl as equations of c1assical Newtonian mechanics. There are also applications to topological results, such as degree theory, the Brouwer fixed-point theorem, and the Jordan-Brouwer separation theorem. In this chapter we also treat scalar first-order PDE, via Hamilton-Jacobi theory.
Topics In Abstract Differential Equations Ii
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Author : S D Zaidman
language : en
Publisher: CRC Press
Release Date : 1995-03-20
Topics In Abstract Differential Equations Ii written by S D Zaidman and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-03-20 with Mathematics categories.
This looks at a new branch of operator theory and partial differential equations, which in recent years, has become a rapidly growing field of mathematics. Well-posed problems are studied in the context of the theory of operator groups and semigroups as well as the framework of time dependent evolution equations. Non well-posed problems are also considered.
Commutative Harmonic Analysis Ii
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Author : Viktor Petrovich Khavin
language : en
Publisher: Springer Science & Business Media
Release Date : 1998
Commutative Harmonic Analysis Ii written by Viktor Petrovich Khavin 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 1998 with Mathematics categories.
Classical harmonic analysis is an important part of modern physics and mathematics, comparable in its significance with calculus. Created in the 18th and 19th centuries as a distinct mathematical discipline it continued to develop, conquering new unexpected areas and producing impressive applications to a multitude of problems. It is widely understood that the explanation of this miraculous power stems from group theoretic ideas underlying practically everything in harmonic analysis. This book is an unusual combination of the general and abstract group theoretic approach with a wealth of very concrete topics attractive to everybody interested in mathematics. Mathematical literature on harmonic analysis abounds in books of more or less abstract or concrete kind, but the lucky combination as in this volume can hardly be found.
Numerical Solution Of Partial Differential Equations Ii Synspade 1970
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Author : Bert Hubbard
language : en
Publisher: Academic Press
Release Date : 2014-05-10
Numerical Solution Of Partial Differential Equations Ii Synspade 1970 written by Bert Hubbard and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-10 with Mathematics categories.
Numerical Solution of Partial Differential Equations—II: Synspade 1970 provides information pertinent to the fundamental aspects of partial differential equations. This book covers a variety of topics that range from mathematical numerical analysis to numerical methods applied to problems in mechanics, meteorology, and fluid dynamics. Organized into 18 chapters, this book begins with an overview of the methods of the Rayleigh–Ritz–Galerkin type for the approximation of boundary value problems using spline basis functions and Sobolev spaces. This text then analyzes a special approach aimed at solving elliptical equations. Other chapters consider the approximation theoretic study of special sets of approximating functions. This book discusses as well combining the alternating-direction methods with Galerkin methods to obtain highly efficient procedures for the numerical solution of second order parabolic and hyperbolic problems. The final chapter deals with the results concerning Chebyshev rational approximations of reciprocals of certain entire functions. This book is a valuable resource for mathematicians.
Dynamical Systems Ix
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Author : D.V. Anosov
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14
Dynamical Systems Ix written by D.V. Anosov 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 2013-03-14 with Mathematics categories.
This volume is devoted to the "hyperbolic theory" of dynamical systems (DS), that is, the theory of smooth DS's with hyperbolic behaviour of the tra jectories (generally speaking, not the individual trajectories, but trajectories filling out more or less "significant" subsets in the phase space. Hyperbolicity the property that under a small displacement of any of a trajectory consists in point of it to one side of the trajectory, the change with time of the relative positions of the original and displaced points resulting from the action of the DS is reminiscent of the mot ion next to a saddle. If there are "sufficiently many" such trajectories and the phase space is compact, then although they "tend to diverge from one another" as it were, they "have nowhere to go" and their behaviour acquires a complicated intricate character. (In the physical literature one often talks about "chaos" in such situations. ) This type of be haviour would appear to be the opposite of the more customary and simple type of behaviour characterized by its own kind of stability and regularity of the motions (these words are for the moment not being used as a strict ter 1 minology but rather as descriptive informal terms). The ergodic properties of DS's with hyperbolic behaviour of trajectories (Bunimovich et al. 1985) have already been considered in Volume 2 of this series. In this volume we therefore consider mainly the properties of a topological character (see below 2 for further details).
Recent Trends In Nonlinear Partial Differential Equations Ii
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Author : James Serrin
language : en
Publisher: American Mathematical Soc.
Release Date : 2013
Recent Trends In Nonlinear Partial Differential Equations Ii written by James Serrin 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 2013 with Mathematics categories.
This book is the second of two volumes which contain the proceedings of the Workshop on Nonlinear Partial Differential Equations, held from May 28-June 1, 2012, at the University of Perugia in honour of Patrizia Pucci's 60th birthday. The workshop brought together leading experts and researchers in nonlinear partial differential equations to promote research and to stimulate interactions among the participants.
Foundations Of Arithmetic Differential Geometry
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Author : Alexandru Buium
language : en
Publisher: American Mathematical Society
Release Date : 2023-11-20
Foundations Of Arithmetic Differential Geometry written by Alexandru Buium and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-11-20 with Mathematics categories.
The aim of this book is to introduce and develop an arithmetic analogue of classical differential geometry. In this new geometry the ring of integers plays the role of a ring of functions on an infinite dimensional manifold. The role of coordinate functions on this manifold is played by the prime numbers. The role of partial derivatives of functions with respect to the coordinates is played by the Fermat quotients of integers with respect to the primes. The role of metrics is played by symmetric matrices with integer coefficients. The role of connections (respectively curvature) attached to metrics is played by certain adelic (respectively global) objects attached to the corresponding matrices. One of the main conclusions of the theory is that the spectrum of the integers is “intrinsically curved”; the study of this curvature is then the main task of the theory. The book follows, and builds upon, a series of recent research papers. A significant part of the material has never been published before.
Nonlinear Dispersive Partial Differential Equations And Inverse Scattering
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Author : Peter D. Miller
language : en
Publisher: Springer Nature
Release Date : 2019-11-14
Nonlinear Dispersive Partial Differential Equations And Inverse Scattering written by Peter D. Miller and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-11-14 with Mathematics categories.
This volume contains lectures and invited papers from the Focus Program on "Nonlinear Dispersive Partial Differential Equations and Inverse Scattering" held at the Fields Institute from July 31-August 18, 2017. The conference brought together researchers in completely integrable systems and PDE with the goal of advancing the understanding of qualitative and long-time behavior in dispersive nonlinear equations. The program included Percy Deift’s Coxeter lectures, which appear in this volume together with tutorial lectures given during the first week of the focus program. The research papers collected here include new results on the focusing nonlinear Schrödinger (NLS) equation, the massive Thirring model, and the Benjamin-Bona-Mahoney equation as dispersive PDE in one space dimension, as well as the Kadomtsev-Petviashvili II equation, the Zakharov-Kuznetsov equation, and the Gross-Pitaevskii equation as dispersive PDE in two space dimensions. The Focus Program coincided with the fiftieth anniversary of the discovery by Gardner, Greene, Kruskal and Miura that the Korteweg-de Vries (KdV) equation could be integrated by exploiting a remarkable connection between KdV and the spectral theory of Schrodinger's equation in one space dimension. This led to the discovery of a number of completely integrable models of dispersive wave propagation, including the cubic NLS equation, and the derivative NLS equation in one space dimension and the Davey-Stewartson, Kadomtsev-Petviashvili and Novikov-Veselov equations in two space dimensions. These models have been extensively studied and, in some cases, the inverse scattering theory has been put on rigorous footing. It has been used as a powerful analytical tool to study global well-posedness and elucidate asymptotic behavior of the solutions, including dispersion, soliton resolution, and semiclassical limits.