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Author : Yurii Vladimirovich Egorov,Mikhail Aleksandrovich Shubin
Publisher : Unknown
Page : 0 pages
File Size : 43,9 Mb
Release : 1993
Category : Electronic
ISBN : OCLC:1123553835
Author : Walter A. Strauss
Publisher : John Wiley & Sons
Page : 467 pages
File Size : 49,9 Mb
Release : 2007-12-21
Category : Mathematics
ISBN : 9780470054567
Our understanding of the fundamental processes of the natural world is based to a large extent on partial differential equations (PDEs). The second edition of Partial Differential Equations provides an introduction to the basic properties of PDEs and the ideas and techniques that have proven useful in analyzing them. It provides the student a broad perspective on the subject, illustrates the incredibly rich variety of phenomena encompassed by it, and imparts a working knowledge of the most important techniques of analysis of the solutions of the equations. In this book mathematical jargon is minimized. Our focus is on the three most classical PDEs: the wave, heat and Laplace equations. Advanced concepts are introduced frequently but with the least possible technicalities. The book is flexibly designed for juniors, seniors or beginning graduate students in science, engineering or mathematics.
Author : Yu.V. Egorov,M.A. Shubin
Publisher : Springer
Page : 244 pages
File Size : 54,7 Mb
Release : 2012-12-22
Category : Mathematics
ISBN : 3662092085
A two-part monograph covering recent research in an important field, previously scattered in numerous journals, including the latest results in the theory of mixed problems for hyperbolic operators. The book is hence of immense value to graduate students and researchers in partial differential equations and theoretical physics.
Author : Lars Hörmander
Publisher : Springer Science & Business Media
Page : 352 pages
File Size : 52,5 Mb
Release : 2009-04-28
Category : Mathematics
ISBN : 9783642001369
From the reviews: "Volumes III and IV complete L. Hörmander's treatise on linear partial differential equations. They constitute the most complete and up-to-date account of this subject, by the author who has dominated it and made the most significant contributions in the last decades.....It is a superb book, which must be present in every mathematical library, and an indispensable tool for all - young and old - interested in the theory of partial differential operators." L. Boutet de Monvel in Bulletin of the American Mathematical Society, 1987 "This treatise is outstanding in every respect and must be counted among the great books in mathematics. It is certainly no easy reading (...) but a careful study is extremely rewarding for its wealth of ideas and techniques and the beauty of presentation." J. Brüning in Zentralblatt MATH, 1987 Honours awarded to Lars Hörmander: Fields Medal 1962, Speaker at International Congress 1970, Wolf Prize 1988, AMS Steele Prize 2006
Author : Fritz John
Publisher : Springer Science & Business Media
Page : 230 pages
File Size : 52,7 Mb
Release : 2013-11-11
Category : Mathematics
ISBN : 9781461599661
These Notes grew out of a course given by the author in 1952-53. Though the field of Partial Differential Equations has changed considerably since those days, particularly under the impact of methods taken from Functional Analysis, the author feels that the introductory material offered here still is basic for an understanding of the subject. It supplies the necessary intuitive foundation which motivates and anticipates abstract formulations of the questions and relates them to the description of natual phenomena. In the present edition, only minor corrections have been made in the text. An Index and up-to-date listing of books recommended for further study have been added. Fritz John New York November 19, 1970 v TABLE OF CONTENTS Introduetion 1 CHAPl'ER I - TEE SINGLE FIRST ORDER EQUATION 1. The linear and quasi-linear equations. 6 The general first order equation for a funetion 2. of two variables. • • • • • • • • • 15 The general first order equation for a funetion 3. of n independent variables. • • • • • 37 CHAPl'ER II - TEE CAUCIIT PROBLEM FOR HIGEER ORDER EQUATIONS 1. Analytie funetions of several real variables • Formulation of the Cauehy problem. The not ion 2. of eharaeteristies. • • • 54 3. The Cauehy problem for the general non-linear equation. 71 4. The Cauehy-Kowalewsky theorem. 76 CHAPl'ER 111 - SECOND ORDER EQUATIONS WITH CONSTANT COEFFICIENTS 1. Equations in two independent variables.
Author : Yu.V. Egorov,M.A. Shubin
Publisher : Springer
Page : 244 pages
File Size : 43,7 Mb
Release : 2010-12-15
Category : Mathematics
ISBN : 3642080995
A two-part monograph covering recent research in an important field, previously scattered in numerous journals, including the latest results in the theory of mixed problems for hyperbolic operators. The book is hence of immense value to graduate students and researchers in partial differential equations and theoretical physics.
Author : Marcus Pivato
Publisher : Cambridge University Press
Page : 631 pages
File Size : 47,5 Mb
Release : 2010-01-07
Category : Mathematics
ISBN : 9780521199704
This highly visual introductory textbook provides a rigorous mathematical foundation for all solution methods and reinforces ties to physical motivation.
Author : Haim Brezis
Publisher : Springer Science & Business Media
Page : 600 pages
File Size : 48,6 Mb
Release : 2010-11-02
Category : Mathematics
ISBN : 9780387709147
This textbook is a completely revised, updated, and expanded English edition of the important Analyse fonctionnelle (1983). In addition, it contains a wealth of problems and exercises (with solutions) to guide the reader. Uniquely, this book presents in a coherent, concise and unified way the main results from functional analysis together with the main results from the theory of partial differential equations (PDEs). Although there are many books on functional analysis and many on PDEs, this is the first to cover both of these closely connected topics. Since the French book was first published, it has been translated into Spanish, Italian, Japanese, Korean, Romanian, Greek and Chinese. The English edition makes a welcome addition to this list.
Author : Yu.V. Egorov,M.A. Shubin
Publisher : Springer Science & Business Media
Page : 247 pages
File Size : 49,8 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9783662092071
A two-part monograph covering recent research in an important field, previously scattered in numerous journals, including the latest results in the theory of mixed problems for hyperbolic operators. The book is hence of immense value to graduate students and researchers in partial differential equations and theoretical physics.
Author : Michael Griebel,Marc Alexander Schweitzer
Publisher : Springer Science & Business Media
Page : 404 pages
File Size : 53,5 Mb
Release : 2008-10-16
Category : Mathematics
ISBN : 9783540799948
The numerical treatment of partial differential equations with particle methods and meshfree discretization techniques is a active research field both in the mathematics and engineering community. This volume of LNCSE is a collection of the proceedings papers of the Fourth International Workshop on Meshfree Methods held in September 2007 in Bonn.
Author : Michael Shearer,Rachel Levy
Publisher : Princeton University Press
Page : 287 pages
File Size : 40,5 Mb
Release : 2015-03-01
Category : Mathematics
ISBN : 9781400866601
An accessible yet rigorous introduction to partial differential equations This textbook provides beginning graduate students and advanced undergraduates with an accessible introduction to the rich subject of partial differential equations (PDEs). It presents a rigorous and clear explanation of the more elementary theoretical aspects of PDEs, while also drawing connections to deeper analysis and applications. The book serves as a needed bridge between basic undergraduate texts and more advanced books that require a significant background in functional analysis. Topics include first order equations and the method of characteristics, second order linear equations, wave and heat equations, Laplace and Poisson equations, and separation of variables. The book also covers fundamental solutions, Green's functions and distributions, beginning functional analysis applied to elliptic PDEs, traveling wave solutions of selected parabolic PDEs, and scalar conservation laws and systems of hyperbolic PDEs. Provides an accessible yet rigorous introduction to partial differential equations Draws connections to advanced topics in analysis Covers applications to continuum mechanics An electronic solutions manual is available only to professors An online illustration package is available to professors
Author : Lothar Collatz
Publisher : Unknown
Page : 596 pages
File Size : 50,5 Mb
Release : 1966
Category : Differential equations
ISBN : UCAL:B4406383
I Mathematical preliminaries and some general principles.- II Initial-value problems in ordinary differential equations.- III Boundary-value problems in ordinary differential equations.- IV Initial- and initial-/boundary-value problems in partial differential equations.- V Boundary-value problems in partial differential equations.- VI Integral and functional equations.- Table III. Finite-difference expressions for ordinary differential equations.- Table IV. Euler expressions for functions of one independent variable.- Table V. Euler expressions for functions of two independent variables.- Table VII. Catalogue of examples treated.- Author index.
Author : Lars Hörmander
Publisher : Springer
Page : 460 pages
File Size : 47,8 Mb
Release : 1990-08-10
Category : Mathematics
ISBN : 354052343X
The main change in this edition is the inclusion of exercises with answers and hints. This is meant to emphasize that this volume has been written as a general course in modern analysis on a graduate student level and not only as the beginning of a specialized course in partial differen tial equations. In particular, it could also serve as an introduction to harmonic analysis. Exercises are given primarily to the sections of gen eral interest; there are none to the last two chapters. Most of the exercises are just routine problems meant to give some familiarity with standard use of the tools introduced in the text. Others are extensions of the theory presented there. As a rule rather complete though brief solutions are then given in the answers and hints. To a large extent the exercises have been taken over from courses or examinations given by Anders Melin or myself at the University of Lund. I am grateful to Anders Melin for letting me use the problems originating from him and for numerous valuable comments on this collection. As in the revised printing of Volume II, a number of minor flaws have also been corrected in this edition. Many of these have been called to my attention by the Russian translators of the first edition, and I wish to thank them for our excellent collaboration.
Author : James M. Ortega,Robert G. Voigt
Publisher : SIAM
Page : 99 pages
File Size : 43,8 Mb
Release : 1985-09-01
Category : Mathematics
ISBN : 9780898710557
Mathematics of Computing -- Parallelism.
Author : F. John
Publisher : Springer Science & Business Media
Page : 258 pages
File Size : 53,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461599791
These Notes grew out of a course given by the author in 1952-53. Though the field of Partial Differential Equations has changed considerably since those days, particularly under the impact of methods taken from Functional Analysis, the author feels that the introductory material offered here still is basic for an understanding of the subject. It supplies the necessary intuitive foundation which motivates and anticipates abstract formulations of the questions and relates them to the description of natual phenomena. Added to this second corrected edition is a collection of problems and solutions, which illustrate and supplement the theories developed in the text. Fritz John New York September, 1974 vii TABLE OF CONTENTS Introd uction 1 CHAPrER I - THE SINGLE FIRST ORDER EQUATION 1. The linear and quasi-linear equations. 6 2. The general first order equation for a function of two variables. • • • • • • • • • 15 The general first order equation for a function 3. of n independent variables. • • • • • 37 CHAPrER II - THE CAUCHY PROBLEM FOR HIGHER ORDER EQUATIONS 1. Analytic functions of several real variables • 48 2. Formulation of the Cauchy problem. The notion of characteristics. • • • 54 3. The Cauchy problem for the general non-linear equation ••• 71 4. The Cauchy-Kowalewsky theorem. 76 CHAPTER III - SECOND ORDER EQUATIONS WITH CONSTANT COEFFICIENTS 1. Equations in two independent variables.