Introduction To Hilbert Space Methods In Partial Differential Equations
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Introduction To Partial Differential Equations And Hilbert Space Methods
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Author : Karl E. Gustafson
language : en
Publisher: Courier Corporation
Release Date : 2012-04-26
Introduction To Partial Differential Equations And Hilbert Space Methods written by Karl E. Gustafson and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-04-26 with Mathematics categories.
Easy-to-use text examines principal method of solving partial differential equations, 1st-order systems, computation methods, and much more. Over 600 exercises, with answers for many. Ideal for a 1-semester or full-year course.
Hilbert Space Methods In Partial Differential Equations
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Author : Ralph E. Showalter
language : en
Publisher: Courier Corporation
Release Date : 2011-09-12
Hilbert Space Methods In Partial Differential Equations written by Ralph E. Showalter and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-09-12 with Mathematics categories.
This graduate-level text opens with an elementary presentation of Hilbert space theory sufficient for understanding the rest of the book. Additional topics include boundary value problems, evolution equations, optimization, and approximation.1979 edition.
Hilbert Space Methods For Partial Differential Equations
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Author : Ralph E. Showalter
language : en
Publisher:
Release Date : 1979
Hilbert Space Methods For Partial Differential Equations written by Ralph E. Showalter and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1979 with categories.
Partial Differential Equations
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Author : Wolfgang Arendt
language : en
Publisher: Springer Nature
Release Date : 2023-01-01
Partial Differential Equations written by Wolfgang Arendt and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-01-01 with Mathematics categories.
This textbook introduces the study of partial differential equations using both analytical and numerical methods. By intertwining the two complementary approaches, the authors create an ideal foundation for further study. Motivating examples from the physical sciences, engineering, and economics complete this integrated approach. A showcase of models begins the book, demonstrating how PDEs arise in practical problems that involve heat, vibration, fluid flow, and financial markets. Several important characterizing properties are used to classify mathematical similarities, then elementary methods are used to solve examples of hyperbolic, elliptic, and parabolic equations. From here, an accessible introduction to Hilbert spaces and the spectral theorem lay the foundation for advanced methods. Sobolev spaces are presented first in dimension one, before being extended to arbitrary dimension for the study of elliptic equations. An extensive chapter on numerical methods focuses on finite difference and finite element methods. Computer-aided calculation with MapleTM completes the book. Throughout, three fundamental examples are studied with different tools: Poisson’s equation, the heat equation, and the wave equation on Euclidean domains. The Black–Scholes equation from mathematical finance is one of several opportunities for extension. Partial Differential Equations offers an innovative introduction for students new to the area. Analytical and numerical tools combine with modeling to form a versatile toolbox for further study in pure or applied mathematics. Illuminating illustrations and engaging exercises accompany the text throughout. Courses in real analysis and linear algebra at the upper-undergraduate level are assumed.
Hilbert Space Methods For Partial Differential Equations
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Author : R. E. Showalter
language : en
Publisher:
Release Date : 1977
Hilbert Space Methods For Partial Differential Equations written by R. E. Showalter and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1977 with Differential equations, Partial categories.
Modern Methods In Partial Differential Equations
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Author : Martin Schechter
language : en
Publisher:
Release Date : 1977
Modern Methods In Partial Differential Equations written by Martin Schechter and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1977 with Mathematics categories.
Second Order Partial Differential Equations In Hilbert Spaces
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Author : Giuseppe Da Prato
language : en
Publisher: Cambridge University Press
Release Date : 2002-07-25
Second Order Partial Differential Equations In Hilbert Spaces written by Giuseppe Da Prato 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 2002-07-25 with Mathematics categories.
State of the art treatment of a subject which has applications in mathematical physics, biology and finance. Includes discussion of applications to control theory. There are numerous notes and references that point to further reading. Coverage of some essential background material helps to make the book self contained.
Reduced Basis Methods For Partial Differential Equations
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Author : Alfio Quarteroni
language : en
Publisher: Springer
Release Date : 2015-08-19
Reduced Basis Methods For Partial Differential Equations written by Alfio Quarteroni and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-08-19 with Mathematics categories.
This book provides a basic introduction to reduced basis (RB) methods for problems involving the repeated solution of partial differential equations (PDEs) arising from engineering and applied sciences, such as PDEs depending on several parameters and PDE-constrained optimization. The book presents a general mathematical formulation of RB methods, analyzes their fundamental theoretical properties, discusses the related algorithmic and implementation aspects, and highlights their built-in algebraic and geometric structures. More specifically, the authors discuss alternative strategies for constructing accurate RB spaces using greedy algorithms and proper orthogonal decomposition techniques, investigate their approximation properties and analyze offline-online decomposition strategies aimed at the reduction of computational complexity. Furthermore, they carry out both a priori and a posteriori error analysis. The whole mathematical presentation is made more stimulating by the use of representative examples of applicative interest in the context of both linear and nonlinear PDEs. Moreover, the inclusion of many pseudocodes allows the reader to easily implement the algorithms illustrated throughout the text. The book will be ideal for upper undergraduate students and, more generally, people interested in scientific computing. All these pseudocodes are in fact implemented in a MATLAB package that is freely available at https://github.com/redbkit
Partial Differential Equations
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Author : Rainer Picard
language : en
Publisher: Walter de Gruyter
Release Date : 2011-06-30
Partial Differential Equations written by Rainer Picard and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-06-30 with Mathematics categories.
This book presents a systematic approach to a solution theory for linear partial differential equations developed in a Hilbert space setting based on a Sobolev lattice structure, a simple extension of the well-established notion of a chain (or scale) of Hilbert spaces. The focus on a Hilbert space setting (rather than on an apparently more general Banach space) is not a severe constraint, but rather a highly adaptable and suitable approach providing a more transparent framework for presenting the main issues in the development of a solution theory for partial differential equations. In contrast to other texts on partial differential equations, which consider either specific equation types or apply a collection of tools for solving a variety of equations, this book takes a more global point of view by focusing on the issues involved in determining the appropriate functional analytic setting in which a solution theory can be naturally developed. Applications to many areas of mathematical physics are also presented. The book aims to be largely self-contained. Full proofs to all but the most straightforward results are provided, keeping to a minimum references to other literature for essential material. It is therefore highly suitable as a resource for graduate courses and also for researchers, who will find new results for particular evolutionary systems from mathematical physics.
Applied Analysis By The Hilbert Space Method
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Author : Samuel S. Holland
language : en
Publisher: Courier Corporation
Release Date : 2012-05-04
Applied Analysis By The Hilbert Space Method written by Samuel S. Holland and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-05-04 with Mathematics categories.
Numerous worked examples and exercises highlight this unified treatment. Simple explanations of difficult subjects make it accessible to undergraduates as well as an ideal self-study guide. 1990 edition.