Advanced Partial Differential Equations

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Advanced Topics In Computational Partial Differential Equations

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Author : Hans Petter Langtangen
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-09-22

Advanced Topics In Computational Partial Differential Equations written by Hans Petter Langtangen 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 2012-09-22 with Mathematics categories.

This book is about solving partial differential equations (PDEs). Such equa tions are used to model a wide range ofphenomena in virtually all fields ofsci ence and technology. Inthe last decade, the general availability of extremely powerful computers has shifted the focus in computational mathematics from simplified model problems to much more sophisticated models resembling in tricate features of real life. This change challenges our knowledge in computer science and in numerical analysis. The main objective ofthe present book is to teach modern,advanced tech niques for numerical PDE solution. The book also introduces several models arising in fields likefinance, medicine, material technology, and geology. Inor der to read this book, you must have a basic knowledge of partial differential equations and numerical methods for solving such equations. Furthermore, some background in finite element methods is required. You do not need to know Diffpack, although this programming environment is used in examples throughout the text. Basically, this book is about models, methods, and how to implement the methods. For the implementation part it is natural for us to use Diffpack as the programming environment, because making a PDE solver in Diffpack requires little amount of programming and because Diff pack has support for the advanced numerical methods treated in this book. Most chapters have a part on models and methods, and a part on imple mentation and Diffpack programming. The exposition is designed such that readers can focus only on the first part, if desired.

Numerical Solutions Of Partial Differential Equations

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Author : Silvia Bertoluzza
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-03-13

Numerical Solutions Of Partial Differential Equations written by Silvia Bertoluzza 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 2009-03-13 with Mathematics categories.

This book presents some of the latest developments in numerical analysis and scientific computing. Specifically, it covers central schemes, error estimates for discontinuous Galerkin methods, and the use of wavelets in scientific computing.

Partial Differential Equations In Action

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Author : Sandro Salsa
language : en
Publisher: Springer
Release Date : 2015-04-24

Partial Differential Equations In Action written by Sandro Salsa and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-04-24 with Mathematics categories.

The book is intended as an advanced undergraduate or first-year graduate course for students from various disciplines, including applied mathematics, physics and engineering. It has evolved from courses offered on partial differential equations (PDEs) over the last several years at the Politecnico di Milano. These courses had a twofold purpose: on the one hand, to teach students to appreciate the interplay between theory and modeling in problems arising in the applied sciences, and on the other to provide them with a solid theoretical background in numerical methods, such as finite elements. Accordingly, this textbook is divided into two parts. The first part, chapters 2 to 5, is more elementary in nature and focuses on developing and studying basic problems from the macro-areas of diffusion, propagation and transport, waves and vibrations. In turn the second part, chapters 6 to 11, concentrates on the development of Hilbert spaces methods for the variational formulation and the analysis of (mainly) linear boundary and initial-boundary value problems.

Partial Differential Equations

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Author : Lawrence C. Evans
language : en
Publisher: American Mathematical Society
Release Date : 2022-03-22

Partial Differential Equations written by Lawrence C. Evans 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 2022-03-22 with Mathematics categories.

This is the second edition of the now definitive text on partial differential equations (PDE). It offers a comprehensive survey of modern techniques in the theoretical study of PDE with particular emphasis on nonlinear equations. Its wide scope and clear exposition make it a great text for a graduate course in PDE. For this edition, the author has made numerous changes, including a new chapter on nonlinear wave equations, more than 80 new exercises, several new sections, a significantly expanded bibliography. About the First Edition: I have used this book for both regular PDE and topics courses. It has a wonderful combination of insight and technical detail. … Evans' book is evidence of his mastering of the field and the clarity of presentation. —Luis Caffarelli, University of Texas It is fun to teach from Evans' book. It explains many of the essential ideas and techniques of partial differential equations … Every graduate student in analysis should read it. —David Jerison, MIT I usePartial Differential Equationsto prepare my students for their Topic exam, which is a requirement before starting working on their dissertation. The book provides an excellent account of PDE's … I am very happy with the preparation it provides my students. —Carlos Kenig, University of Chicago Evans' book has already attained the status of a classic. It is a clear choice for students just learning the subject, as well as for experts who wish to broaden their knowledge … An outstanding reference for many aspects of the field. —Rafe Mazzeo, Stanford University

Fourier Analysis And Partial Differential Equations

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Author : Jose Garcia-Cuerva
language : en
Publisher: CRC Press
Release Date : 2018-01-18

Fourier Analysis And Partial Differential Equations written by Jose Garcia-Cuerva and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-01-18 with Mathematics categories.

Contains easy access to four actual and active areas of research in Fourier Analysis and PDE Covers a wide spectrum of topics in present research Provides a complete picture of state-of-the-art methods in the field Contains 200 tables allowing the reader speedy access to precise data

Advanced Differential Equations

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Author : M.D.Raisinghania
language : en
Publisher: S. Chand Publishing
Release Date : 1995-03

Advanced Differential Equations written by M.D.Raisinghania and has been published by S. Chand Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-03 with Mathematics categories.

This book is especially prepared for B.A., B.Sc. and honours (Mathematics and Physics), M.A/M.Sc. (Mathematics and Physics), B.E. Students of Various Universities and for I.A.S., P.C.S., AMIE, GATE, and other competitve exams.Almost all the chapters have been rewritten so that in the present form, the reader will not find any difficulty in understanding the subject matter.The matter of the previous edition has been re-organised so that now each topic gets its proper place in the book.More solved examples have been added so that now each topic gets its proper place in the book. References to the latest papers of various universities and I.A.S. examination have been made at proper places.

An Introduction To Partial Differential Equations

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Author : Michael Renardy
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-04-18

An Introduction To Partial Differential Equations written by Michael Renardy 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 2006-04-18 with Mathematics categories.

Partial differential equations are fundamental to the modeling of natural phenomena, arising in every field of science. Consequently, the desire to understand the solutions of these equations has always had a prominent place in the efforts of mathematicians; it has inspired such diverse fields as complex function theory, functional analysis and algebraic topology. Like algebra, topology, and rational mechanics, partial differential equations are a core area of mathematics. This book aims to provide the background necessary to initiate work on a Ph.D. thesis in PDEs for beginning graduate students. Prerequisites include a truly advanced calculus course and basic complex variables. Lebesgue integration is needed only in Chapter 10, and the necessary tools from functional analysis are developed within the course. The book can be used to teach a variety of different courses. This new edition features new problems throughout and the problems have been rearranged in each section from simplest to most difficult. New examples have also been added. The material on Sobolev spaces has been rearranged and expanded. A new section on nonlinear variational problems with "Young-measure" solutions appears. The reference section has also been expanded.

Fourier Analysis And Partial Differential Equations

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Author : Iorio Júnior Iorio Jr.
language : en
Publisher: Cambridge University Press
Release Date : 2001-03-15

Fourier Analysis And Partial Differential Equations written by Iorio Júnior Iorio Jr. and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-03-15 with Mathematics categories.

This book was first published in 2001. It provides an introduction to Fourier analysis and partial differential equations and is intended to be used with courses for beginning graduate students. With minimal prerequisites the authors take the reader from fundamentals to research topics in the area of nonlinear evolution equations. The first part of the book consists of some very classical material, followed by a discussion of the theory of periodic distributions and the periodic Sobolev spaces. The authors then turn to the study of linear and nonlinear equations in the setting provided by periodic distributions. They assume only some familiarity with Banach and Hilbert spaces and the elementary properties of bounded linear operators. After presenting a fairly complete discussion of local and global well-posedness for the nonlinear Schrödinger and the Korteweg-de Vries equations, they turn their attention, in the two final chapters, to the non-periodic setting, concentrating on problems that do not occur in the periodic case.

Partial Differential Equations And Complex Analysis

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Author : Steven G. Krantz
language : en
Publisher: CRC Press
Release Date : 2018-05-04

Partial Differential Equations And Complex Analysis written by Steven G. Krantz and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-05-04 with Mathematics categories.

Ever since the groundbreaking work of J.J. Kohn in the early 1960s, there has been a significant interaction between the theory of partial differential equations and the function theory of several complex variables. Partial Differential Equations and Complex Analysis explores the background and plumbs the depths of this symbiosis. The book is an excellent introduction to a variety of topics and presents many of the basic elements of linear partial differential equations in the context of how they are applied to the study of complex analysis. The author treats the Dirichlet and Neumann problems for elliptic equations and the related Schauder regularity theory, and examines how those results apply to the boundary regularity of biholomorphic mappings. He studies the ?-Neumann problem, then considers applications to the complex function theory of several variables and to the Bergman projection.

Partial Differential Equations In Action

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Author : Sandro Salsa
language : en
Publisher:
Release Date : 2015

Partial Differential Equations In Action written by Sandro Salsa and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015 with categories.

This textbook presents problems and exercises at various levels of difficulty in the following areas: Classical Methods in PDEs (diffusion, waves, transport, potential equations); Basic Functional Analysis and Distribution Theory; Variational Formulation of Elliptic Problems; and Weak Formulation for Parabolic Problems and for the Wave Equation. Thanks to the broad variety of exercises with complete solutions, it can be used in all basic and advanced PDE courses.