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Author : L. Nirenberg
Publisher : American Mathematical Soc.
Page : 70 pages
File Size : 51,9 Mb
Release : 1973
Category : Mathematics
ISBN : 0821888668
Author : Grigoriĭ Ilʹich Eskin
Publisher : American Mathematical Soc.
Page : 432 pages
File Size : 43,7 Mb
Release : 2011
Category : Differential equations, Elliptic
ISBN : 9780821852842
This is a reader-friendly, relatively short introduction to the modern theory of linear partial differential equations. An effort has been made to present complete proofs in an accessible and self-contained form. The first three chapters are on elementary distribution theory and Sobolev spaces. The following chapters study the Cauchy problem for parabolic and hyperbolic equations, boundary value problems for elliptic equations, heat trace asymptotics, and scattering theory.
Author : Jacques Hadamard
Publisher : Courier Corporation
Page : 320 pages
File Size : 50,5 Mb
Release : 2014-08-25
Category : Mathematics
ISBN : 9780486781488
Would well repay study by most theoretical physicists." — Physics Today "An overwhelming influence on subsequent work on the wave equation." — Science Progress "One of the classical treatises on hyperbolic equations." — Royal Naval Scientific Service Delivered at Columbia University and the Universities of Rome and Zürich, these lectures represent a pioneering investigation. Jacques Hadamard based his research on prior studies by Riemann, Kirchhoff, and Volterra. He extended and improved Volterra's work, applying its theories relating to spherical and cylindrical waves to all normal hyperbolic equations instead of only to one. Topics include the general properties of Cauchy's problem, the fundamental formula and the elementary solution, equations with an odd number of independent variables, and equations with an even number of independent variables and the method of descent.
Author : Grigoriĭ Ilʹich Eskin
Publisher : American Mathematical Soc.
Page : 410 pages
File Size : 47,6 Mb
Release : 2011
Category : Mathematics
ISBN : 1470411849
This book offers a reader-friendly and relatively concise introduction to the modern theory of linear partial differential equations. The author takes a modern approach to the subject based on the distribution theory and the Fourier transforms. Problems at the end of each chapter range from simple exercises to difficult problems on more advanced topics.
Author : L. Nirenberg
Publisher : Unknown
Page : 58 pages
File Size : 52,7 Mb
Release : 1973
Category : Differential equations, Partial
ISBN : 0821816675
Author : Alberto Valli
Publisher : Springer Nature
Page : 267 pages
File Size : 49,6 Mb
Release : 2023-09-30
Category : Mathematics
ISBN : 9783031359767
This textbook is devoted to second order linear partial differential equations. The focus is on variational formulations in Hilbert spaces. It contains elliptic equations, including the biharmonic problem, some useful notes on functional analysis, a brief presentation of Sobolev spaces and their properties, some basic results on Fredholm alternative and spectral theory, saddle point problems, parabolic and linear Navier-Stokes equations, and hyperbolic and Maxwell equations. Almost 80 exercises are added, and the complete solution of all of them is included. The work is mainly addressed to students in Mathematics, but also students in Engineering with a good mathematical background should be able to follow the theory presented here. This second edition has been enriched by some new sections and new exercises; in particular, three important equations are now included: the biharmonic equation, the linear Navier-Stokes equations and the Maxwell equations.
Author : I. G. Petrovsky
Publisher : Courier Corporation
Page : 261 pages
File Size : 48,9 Mb
Release : 2012-12-13
Category : Mathematics
ISBN : 9780486155081
Graduate-level exposition by noted Russian mathematician offers rigorous, readable coverage of classification of equations, hyperbolic equations, elliptic equations, and parabolic equations. Translated from the Russian by A. Shenitzer.
Author : Alberto Bressan
Publisher : American Mathematical Soc.
Page : 250 pages
File Size : 47,9 Mb
Release : 2013
Category : Mathematics
ISBN : 9780821887714
This textbook is addressed to graduate students in mathematics or other disciplines who wish to understand the essential concepts of functional analysis and their applications to partial differential equations. The book is intentionally concise, presenting all the fundamental concepts and results but omitting the more specialized topics. Enough of the theory of Sobolev spaces and semigroups of linear operators is included as needed to develop significant applications to elliptic, parabolic, and hyperbolic PDEs. Throughout the book, care has been taken to explain the connections between theorems in functional analysis and familiar results of finite-dimensional linear algebra. The main concepts and ideas used in the proofs are illustrated with a large number of figures. A rich collection of homework problems is included at the end of most chapters. The book is suitable as a text for a one-semester graduate course.
Author : G. B. Folland
Publisher : Springer
Page : 182 pages
File Size : 40,9 Mb
Release : 1983
Category : Mathematics
ISBN : UOM:39015016362363
Author : Vladimir I. Arnold
Publisher : Springer Science & Business Media
Page : 168 pages
File Size : 45,7 Mb
Release : 2013-06-29
Category : Mathematics
ISBN : 9783662054413
Choice Outstanding Title! (January 2006) This richly illustrated text covers the Cauchy and Neumann problems for the classical linear equations of mathematical physics. A large number of problems are sprinkled throughout the book, and a full set of problems from examinations given in Moscow are included at the end. Some of these problems are quite challenging! What makes the book unique is Arnold's particular talent at holding a topic up for examination from a new and fresh perspective. He likes to blow away the fog of generality that obscures so much mathematical writing and reveal the essentially simple intuitive ideas underlying the subject. No other mathematical writer does this quite so well as Arnold.
Author : Philip L. Korman
Publisher : American Mathematical Soc.
Page : 399 pages
File Size : 49,6 Mb
Release : 2019-08-30
Category : Differential equations
ISBN : 9781470451738
Lectures on Differential Equations provides a clear and concise presentation of differential equations for undergraduates and beginning graduate students. There is more than enough material here for a year-long course. In fact, the text developed from the author's notes for three courses: the undergraduate introduction to ordinary differential equations, the undergraduate course in Fourier analysis and partial differential equations, and a first graduate course in differential equations. The first four chapters cover the classical syllabus for the undergraduate ODE course leavened by a modern awareness of computing and qualitative methods. The next two chapters contain a well-developed exposition of linear and nonlinear systems with a similarly fresh approach. The final two chapters cover boundary value problems, Fourier analysis, and the elementary theory of PDEs. The author makes a concerted effort to use plain language and to always start from a simple example or application. The presentation should appeal to, and be readable by, students, especially students in engineering and science. Without being excessively theoretical, the book does address a number of unusual topics: Massera's theorem, Lyapunov's inequality, the isoperimetric inequality, numerical solutions of nonlinear boundary value problems, and more. There are also some new approaches to standard topics including a rethought presentation of series solutions and a nonstandard, but more intuitive, proof of the existence and uniqueness theorem. The collection of problems is especially rich and contains many very challenging exercises. Philip Korman is professor of mathematics at the University of Cincinnati. He is the author of over one hundred research articles in differential equations and the monograph Global Solution Curves for Semilinear Elliptic Equations. Korman has served on the editorial boards of Communications on Applied Nonlinear Analysis, Electronic Journal of Differential Equations, SIAM Review, an\ d Differential Equations and Applications.
Author : Walter Craig
Publisher : American Mathematical Soc.
Page : 205 pages
File Size : 55,6 Mb
Release : 2018-12-12
Category : Differential equations, Partial
ISBN : 9781470442927
Does entropy really increase no matter what we do? Can light pass through a Big Bang? What is certain about the Heisenberg uncertainty principle? Many laws of physics are formulated in terms of differential equations, and the questions above are about the nature of their solutions. This book puts together the three main aspects of the topic of partial differential equations, namely theory, phenomenology, and applications, from a contemporary point of view. In addition to the three principal examples of the wave equation, the heat equation, and Laplace's equation, the book has chapters on dispersion and the Schrödinger equation, nonlinear hyperbolic conservation laws, and shock waves. The book covers material for an introductory course that is aimed at beginning graduate or advanced undergraduate level students. Readers should be conversant with multivariate calculus and linear algebra. They are also expected to have taken an introductory level course in analysis. Each chapter includes a comprehensive set of exercises, and most chapters have additional projects, which are intended to give students opportunities for more in-depth and open-ended study of solutions of partial differential equations and their properties.
Author : Anonim
Publisher : Unknown
Page : 128 pages
File Size : 54,6 Mb
Release : 1923
Category : Electronic
ISBN : OCLC:999419190
Author : Alberto Bressan
Publisher : American Mathematical Society
Page : 250 pages
File Size : 43,8 Mb
Release : 2021-12-03
Category : Mathematics
ISBN : 9781470465728
This textbook is addressed to graduate students in mathematics or other disciplines who wish to understand the essential concepts of functional analysis and their applications to partial differential equations. The book is intentionally concise, presenting all the fundamental concepts and results but omitting the more specialized topics. Enough of the theory of Sobolev spaces and semigroups of linear operators is included as needed to develop significant applications to elliptic, parabolic, and hyperbolic PDEs. Throughout the book, care has been taken to explain the connections between theorems in functional analysis and familiar results of finite-dimensional linear algebra. The main concepts and ideas used in the proofs are illustrated with a large number of figures. A rich collection of homework problems is included at the end of most chapters. The book is suitable as a text for a one-semester graduate course.
Author : Jacques Hadamard
Publisher : Forgotten Books
Page : 332 pages
File Size : 48,7 Mb
Release : 2017-09-18
Category : Mathematics
ISBN : 1528484924
Excerpt from Lectures on Cauchy's Problem in Linear Partial Differential Equations Picard's researches - which we shall quote in their place - are also essential in several parts of the present work. Such is also the case for Le Roux. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.