Download or read book Introduction to Partial Differential Equations and Hilbert Space Methods written by Karl E. Gustafson and published by Courier Corporation. This book was released on 2012-04-26 with total page 500 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Hilbert Space Methods in Partial Differential Equations written by Ralph E. Showalter and published by Courier Corporation. This book was released on 2011-09-12 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Hilbert Space Methods for Partial Differential Equations written by Ralph E. Showalter and published by . This book was released on 1979 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Second Order Partial Differential Equations in Hilbert Spaces written by Giuseppe Da Prato and published by Cambridge University Press. This book was released on 2002-07-25 with total page 397 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Hilbert Space Methods for Partial Differential Equations written by R. E. Showalter and published by . This book was released on 1977 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Partial Differential Equations written by Wolfgang Arendt and published by Springer Nature. This book was released on 2023-01-01 with total page 463 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Applied Analysis by the Hilbert Space Method written by Samuel S. Holland and published by Courier Corporation. This book was released on 2012-05-04 with total page 578 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Partial Differential Equations written by Rainer Picard and published by Walter de Gruyter. This book was released on 2011-06-30 with total page 489 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Modern Methods in Partial Differential Equations written by Martin Schechter and published by . This book was released on 1977 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book An Introduction to Hilbert Space written by N. Young and published by Cambridge University Press. This book was released on 1988-07-21 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook is an introduction to the theory of Hilbert space and its applications. The notion of Hilbert space is central in functional analysis and is used in numerous branches of pure and applied mathematics. Dr Young has stressed applications of the theory, particularly to the solution of partial differential equations in mathematical physics and to the approximation of functions in complex analysis. Some basic familiarity with real analysis, linear algebra and metric spaces is assumed, but otherwise the book is self-contained. It is based on courses given at the University of Glasgow and contains numerous examples and exercises (many with solutions). Thus it will make an excellent first course in Hilbert space theory at either undergraduate or graduate level and will also be of interest to electrical engineers and physicists, particularly those involved in control theory and filter design.
Download or read book Functional Analysis Sobolev Spaces and Partial Differential Equations written by Haim Brezis and published by Springer Science & Business Media. This book was released on 2010-11-02 with total page 600 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Reduced Basis Methods for Partial Differential Equations written by Alfio Quarteroni and published by Springer. This book was released on 2015-08-19 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Download or read book Introduction to Hilbert Spaces with Applications written by Lokenath Debnath and published by Elsevier. This book was released on 2005-09-29 with total page 599 pages. Available in PDF, EPUB and Kindle. Book excerpt: Building on the success of the two previous editions, Introduction to Hilbert Spaces with Applications, Third Edition, offers an overview of the basic ideas and results of Hilbert space theory and functional analysis. It acquaints students with the Lebesgue integral, and includes an enhanced presentation of results and proofs. Students and researchers will benefit from the wealth of revised examples in new, diverse applications as they apply to optimization, variational and control problems, and problems in approximation theory, nonlinear instability, and bifurcation. The text also includes a popular chapter on wavelets that has been completely updated. Students and researchers agree that this is the definitive text on Hilbert Space theory. Updated chapter on wavelets Improved presentation on results and proof Revised examples and updated applications Completely updated list of references
Download or read book Partial Differential Equations written by Joseph Wloka and published by Cambridge University Press. This book was released on 1987-05-21 with total page 536 pages. Available in PDF, EPUB and Kindle. Book excerpt: A rigorous introduction to the abstract theory of partial differential equations progresses from the theory of distribution and Sobolev spaces to Fredholm operations, the Schauder fixed point theorem and Bochner integrals.
Download or read book Partial Differential Equations written by Aleksei A. Dezin and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 175 pages. Available in PDF, EPUB and Kindle. Book excerpt: Let me begin by explaining the meaning of the title of this book. In essence, the book studies boundary value problems for linear partial differ ential equations in a finite domain in n-dimensional Euclidean space. The problem that is investigated is the question of the dependence of the nature of the solvability of a given equation on the way in which the boundary conditions are chosen, i.e. on the supplementary requirements which the solution is to satisfy on specified parts of the boundary. The branch of mathematical analysis dealing with the study of boundary value problems for partial differential equations is often called mathematical physics. Classical courses in this subject usually consider quite restricted classes of equations, for which the problems have an immediate physical context, or generalizations of such problems. With the expanding domain of application of mathematical methods at the present time, there often arise problems connected with the study of partial differential equations that do not belong to any of the classical types. The elucidation of the correct formulation of these problems and the study of the specific properties of the solutions of similar equations are closely related to the study of questions of a general nature.
Download or read book An Introduction to the Mathematical Theory of Finite Elements written by J. T. Oden and published by Courier Corporation. This book was released on 2012-05-23 with total page 450 pages. Available in PDF, EPUB and Kindle. Book excerpt: This introduction to the theory of Sobolev spaces and Hilbert space methods in partial differential equations is geared toward readers of modest mathematical backgrounds. It offers coherent, accessible demonstrations of the use of these techniques in developing the foundations of the theory of finite element approximations. J. T. Oden is Director of the Institute for Computational Engineering & Sciences (ICES) at the University of Texas at Austin, and J. N. Reddy is a Professor of Engineering at Texas A&M University. They developed this essentially self-contained text from their seminars and courses for students with diverse educational backgrounds. Their effective presentation begins with introductory accounts of the theory of distributions, Sobolev spaces, intermediate spaces and duality, the theory of elliptic equations, and variational boundary value problems. The second half of the text explores the theory of finite element interpolation, finite element methods for elliptic equations, and finite element methods for initial boundary value problems. Detailed proofs of the major theorems appear throughout the text, in addition to numerous examples.
Download or read book Functional Spaces for the Theory of Elliptic Partial Differential Equations written by Françoise Demengel and published by Springer Science & Business Media. This book was released on 2012-01-24 with total page 480 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of elliptic boundary problems is fundamental in analysis and the role of spaces of weakly differentiable functions (also called Sobolev spaces) is essential in this theory as a tool for analysing the regularity of the solutions. This book offers on the one hand a complete theory of Sobolev spaces, which are of fundamental importance for elliptic linear and non-linear differential equations, and explains on the other hand how the abstract methods of convex analysis can be combined with this theory to produce existence results for the solutions of non-linear elliptic boundary problems. The book also considers other kinds of functional spaces which are useful for treating variational problems such as the minimal surface problem. The main purpose of the book is to provide a tool for graduate and postgraduate students interested in partial differential equations, as well as a useful reference for researchers active in the field. Prerequisites include a knowledge of classical analysis, differential calculus, Banach and Hilbert spaces, integration and the related standard functional spaces, as well as the Fourier transformation on the Schwartz space. There are complete and detailed proofs of almost all the results announced and, in some cases, more than one proof is provided in order to highlight different features of the result. Each chapter concludes with a range of exercises of varying levels of difficulty, with hints to solutions provided for many of them.
