Operator Methods In Ordinary And Partial Differential Equations

Author : Sergio Albeverio,Nils Elander,W. Nirrie Everitt,Pavel Kurasov
Publisher : Birkhäuser
Page : 423 pages
File Size : 45,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034882194

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Operator Methods in Ordinary and Partial Differential Equations by Sergio Albeverio,Nils Elander,W. Nirrie Everitt,Pavel Kurasov Pdf

CO«i»b.H BaCHJIbeBHa lU>BaJIeBcR8JI (Sonja Kovalevsky) was born in Moscow in 1850 and died in Stockholm in 1891. Between these years, in the then changing and turbulent circumstances for Europe, lies the all too brief life of this remarkable woman. This life was lived out within the great European centers of power and learning in Russia, France, Germany, Switzerland, England and Sweden. To this day, now 150 years after her birth, her influence for and contribution to mathe matics, science, literature, women's rights and democratic government are recorded and reviewed, not only in Europe but now in countries far removed in time and distance from the lands of her birth and being. This volume, dedicated to her memory and to her achievements, records the Proceedings of the Marcus Wallenberg Symposium held, in memory of Sonja Kovalevsky, at Stockholm University from 18 to 22 June 2000. The symposium was held at the Department of Mathematics with its excellent library and lecture halls providing favourable working conditions. Within these pages are contained a curriculum vitae for Sonja Kovalevsky, a list of all her scientific publications, together with a copy of the moving and elegant obituary notice written by her friend and protector Gosta Mittag-Leffler. These papers are followed by a leading article entitled Sonja Kovalevsky: Her life and professorship in Stockholm, written especially for this volume by Jan-Erik Bjork in preparation for his major address to the Symposium.

Author : Randall J. LeVeque
Publisher : SIAM
Page : 356 pages
File Size : 45,8 Mb
Release : 2007-01-01
Category : Mathematics
ISBN : 0898717833

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Finite Difference Methods for Ordinary and Partial Differential Equations by Randall J. LeVeque Pdf

This book introduces finite difference methods for both ordinary differential equations (ODEs) and partial differential equations (PDEs) and discusses the similarities and differences between algorithm design and stability analysis for different types of equations. A unified view of stability theory for ODEs and PDEs is presented, and the interplay between ODE and PDE analysis is stressed. The text emphasizes standard classical methods, but several newer approaches also are introduced and are described in the context of simple motivating examples.

Author : László Székelyhidi
Publisher : World Scientific Publishing Company
Page : 256 pages
File Size : 44,6 Mb
Release : 2016-05-24
Category : Mathematics
ISBN : 9789814725019

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Ordinary and Partial Differential Equations for the Beginner by László Székelyhidi Pdf

This textbook is intended for college, undergraduate and graduate students, emphasizing mainly on ordinary differential equations. However, the theory of characteristics for first order partial differential equations and the classification of second order linear partial differential operators are also included. It contains the basic material starting from elementary solution methods for ordinary differential equations to advanced methods for first order partial differential equations. In addition to the theoretical background, solution methods are strongly emphasized. Each section is completed with problems and exercises, and the solutions are also provided. There are special sections devoted to more applied tools such as implicit equations, Laplace transform, Fourier method, etc. As a novelty, a method for finding exponential polynomial solutions is presented which is based on the author's work in spectral synthesis. The presentation is self-contained, provided the reader has general undergraduate knowledge.

Author : Prem Kythe
Publisher : Springer Science & Business Media
Page : 448 pages
File Size : 44,9 Mb
Release : 1996-07-30
Category : Mathematics
ISBN : 0817638695

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Fundamental Solutions for Differential Operators and Applications by Prem Kythe Pdf

A self-contained and systematic development of an aspect of analysis which deals with the theory of fundamental solutions for differential operators, and their applications to boundary value problems of mathematical physics, applied mathematics, and engineering, with the related computational aspects.

Author : Yakov Yakubov,Sasun Yakubov
Publisher : CRC Press
Page : 586 pages
File Size : 43,8 Mb
Release : 1999-11-24
Category : Mathematics
ISBN : 1584881399

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Differential-Operator Equations by Yakov Yakubov,Sasun Yakubov Pdf

The theory of differential-operator equations is one of two modern theories for the study of both ordinary and partial differential equations, with numerous applications in mechanics and theoretical physics. Although a number of published works address differential-operator equations of the first and second orders, to date none offer a treatment of the higher orders. In Differential-Operator Equations, the authors present a systematic treatment of the theory of differential-operator equations of higher order, with applications to partial differential equations. They construct a theory that allows application to both regular and irregular differential problems. In particular, they study problems that cannot be solved by various known methods and irregular problems not addressed in existing monographs. These include Birkhoff-irregularity, non-local boundary value conditions, and non-smoothness of the boundary of the domains. Among this volume's other points of interest are: The Abel basis property of a system of root functions Irregular boundary value problems The theory of hyperbolic equations in Gevrey space The theory of boundary value problems for elliptic differential equations with a parameter

Author : Stefan Bergman
Publisher : Springer Science & Business Media
Page : 155 pages
File Size : 51,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642649851

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Integral Operators in the Theory of Linear Partial Differential Equations by Stefan Bergman Pdf

The present book deals with the construction of solutions of linear partial differential equations by means of integral operators which transform analytic functions of a complex variable into such solutions. The theory of analytic functions has achieved a high degree of deve lopment and simplicity, and the operator method permits us to exploit this theory in the study of differential equations. Although the study of existence and uniqueness of solutions has been highly developed, much less attention has been paid to the investigation of function theo retical properties and to the explicit construction of regular and singular solutions using a unified general procedure. This book attempts to fill in the gap in this direction. Integral operators of various types have been used for a long time in the mathematical literature. In this connection one needs only to mention Euler and Laplace. The author has not attempted to give a complete account of all known operators, but rather has aimed at developing a unified approach. For this purpose he uses special operators which preserve various function theoretical properties of analytic functions, such as domains of regularity, validity of series development, connection between the coefficients of these developments and location and character of singularities, etc. However, all efforts were made to give a complete bibliography to help the reader to find more detailed information.

Author : K. W. Bauer,S. Ruscheweyh
Publisher : Springer
Page : 264 pages
File Size : 51,7 Mb
Release : 2007-02-08
Category : Mathematics
ISBN : 9783540392118

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Differential Operators for Partial Differential Equations and Function Theoretic Applications by K. W. Bauer,S. Ruscheweyh Pdf

Author : Cornelius Lanczos
Publisher : SIAM
Page : 581 pages
File Size : 48,8 Mb
Release : 1997-12-01
Category : Mathematics
ISBN : 1611971187

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Linear Differential Operators by Cornelius Lanczos Pdf

Originally published in 1961, this Classics edition continues to be appealing because it describes a large number of techniques still useful today. Although the primary focus is on the analytical theory, concrete cases are cited to forge the link between theory and practice. Considerable manipulative skill in the practice of differential equations is to be developed by solving the 350 problems in the text. The problems are intended as stimulating corollaries linking theory with application and providing the reader with the foundation for tackling more difficult problems. Lanczos begins with three introductory chapters that explore some of the technical tools needed later in the book, and then goes on to discuss interpolation, harmonic analysis, matrix calculus, the concept of the function space, boundary value problems, and the numerical solution of trajectory problems, among other things. The emphasis is constantly on one question: "What are the basic and characteristic properties of linear differential operators?" In the author's words, this book is written for those "to whom a problem in ordinary or partial differential equations is not a problem of logical acrobatism, but a problem in the exploration of the physical universe. To get an explicit solution of a given boundary value problem is in this age of large electronic computers no longer a basic question. But of what value is the numerical answer if the scientist does not understand the peculiar analytical properties and idiosyncrasies of the given operator? The author hopes that this book will help in this task by telling something about the manifold aspects of a fascinating field."

Author : Johannes Elschner
Publisher : Springer
Page : 199 pages
File Size : 46,7 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540392941

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Singular Ordinary Differential Operators and Pseudodifferential Equations by Johannes Elschner Pdf

Author : Sasun Yakubov
Publisher : Chapman and Hall/CRC
Page : 280 pages
File Size : 51,6 Mb
Release : 1994
Category : Mathematics
ISBN : 0582236924

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Completeness of Root Functions of Regular Differential Operators by Sasun Yakubov Pdf

This book is the first monograph to treat systematically the general non-self-adjoint case, including all the questions connected with the completeness of elementary solutions of mathematical physics problems. In particular, the completeness problem of eigenvectors and associated vectors (root vectors) of unbounded polynomial operator pencils, and the coercive solvability and completeness of root functions of boundary value problems for both ordinary and partial differential equations are investigated.

Author : Ali Mason
Publisher : Scientific e-Resources
Page : 284 pages
File Size : 49,9 Mb
Release : 2018-10-20
Category : Electronic
ISBN : 9781839473289

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Ordinary Differential Equations with Applications by Ali Mason Pdf

Ordinary differential equations (ODEs) arise in many contexts of mathematics and science (social as well as natural). Mathematical descriptions of change use differentials and derivatives. Various differentials, derivatives, and functions become related to each other via equations, and thus a differential equation is a result that describes dynamically changing phenomena, evolution, and variation. Often, quantities are defined as the rate of change of other quantities (for example, derivatives of displacement with respect to time), or gradients of quantities, which is how they enter differential equations. Ordinary differential equations are equations to be solved in which the unknown element is a function, rather than a number, and in which the known information relates that function to its derivatives. Few such equations admit an explicit answer, but there is a wealth of qualitative information describing the solutions and their dependence on the defining equation. Systems of differential equations form the basis of mathematical models in a wide range of fields - from engineering and physical sciences to finance and biological sciences. Differential equations are relations between unknown functions and their derivatives. Computing numerical solutions to differential equations is one of the most important tasks in technical computing, and one of the strengths of MATLAB. The book explains the origins of various types of differential equations. The scope of the book is limited to linear differential equations of the first order, linear differential equation of higher order, partial differential equations and special methods of solution of differential equations of second order, keeping in view the requirement of students.

Author : Jiri Lebl
Publisher : Unknown
Page : 468 pages
File Size : 48,8 Mb
Release : 2019-11-13
Category : Electronic
ISBN : 1706230230

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Notes on Diffy Qs by Jiri Lebl Pdf

Version 6.0. An introductory course on differential equations aimed at engineers. The book covers first order ODEs, higher order linear ODEs, systems of ODEs, Fourier series and PDEs, eigenvalue problems, the Laplace transform, and power series methods. It has a detailed appendix on linear algebra. The book was developed and used to teach Math 286/285 at the University of Illinois at Urbana-Champaign, and in the decade since, it has been used in many classrooms, ranging from small community colleges to large public research universities. See https: //www.jirka.org/diffyqs/ for more information, updates, errata, and a list of classroom adoptions.

Author : Sofʹi͡a Vasilʹevna Kovalevskai͡a
Publisher : Birkhauser
Page : 422 pages
File Size : 43,9 Mb
Release : 2002-01-01
Category : Differential equations
ISBN : 0817667903

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Operator Methods in Ordinary and Partial Differential Equations by Sofʹi͡a Vasilʹevna Kovalevskai͡a Pdf

Author : Karel Rektorys
Publisher : CRC Press
Page : 218 pages
File Size : 49,7 Mb
Release : 1998-10-20
Category : Mathematics
ISBN : 0849325528

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Solving Ordinary and Partial Boundary Value Problems in Science and Engineering by Karel Rektorys Pdf

This book provides an elementary, accessible introduction for engineers and scientists to the concepts of ordinary and partial boundary value problems, acquainting readers with fundamental properties and with efficient methods of constructing solutions or satisfactory approximations. Discussions include: ordinary differential equations classical theory of partial differential equations Laplace and Poisson equations heat equation variational methods of solution of corresponding boundary value problems methods of solution for evolution partial differential equations The author presents special remarks for the mathematical reader, demonstrating the possibility of generalizations of obtained results and showing connections between them. For the non-mathematician, the author provides profound functional-analytical results without proofs and refers the reader to the literature when necessary. Solving Ordinary and Partial Boundary Value Problems in Science and Engineering contains essential functional analytical concepts, explaining its subject without excessive abstraction.

Author : Zalman Rubinstein
Publisher : Academic Press
Page : 488 pages
File Size : 41,7 Mb
Release : 2014-05-12
Category : Mathematics
ISBN : 9781483262628

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A Course in Ordinary and Partial Differential Equations by Zalman Rubinstein Pdf

A Course in Ordinary and Partial Differential Equations discusses ordinary differential equations and partial differential equations. The book reviews the solution of elementary first-order differential equations, existence theorems, singular solutions, and linear equations of arbitrary order. It explains the solutions of linear equations with constant coefficients, operational calculus, and the solutions of linear differential equations. It also explores the techniques of computing for the solution of systems of linear differential equations, which is similar to the solutions of linear equations of arbitrary order. The text proves that if the coefficients of some differential equations possess certain restricted types of singularities, the solution will have Taylor series expansions about the singular points. The investigator can calculate a divergent series whose partial sums numerically approximate the solution for large x if the point in question is infinity, of which the series will be a Taylor series of negative powers of x. The book also explains the Fourier transform, its applications to partial differential equations, as well as the Hilbert space approach to partial differential equations. The book is a stimulating material for mathematicians, for professors, or for students of pure and applied mathematics, physics, or engineering.