Techniques of Functional Analysis for Differential and Integral Equations

Techniques of Functional Analysis for Differential and Integral Equations describes a variety of powerful and modern tools from mathematical analysis, for graduate study and further research in ordinary differential equations, integral equations and partial differential equations. Knowledge of these techniques is particularly useful as preparation for graduate courses and PhD research in differential equations and numerical analysis, and more specialized topics such as fluid dynamics and control theory. Striking a balance between mathematical depth and accessibility, proofs involving more technical aspects of measure and integration theory are avoided, but clear statements and precise alternative references are given . The work provides many examples and exercises drawn from the literature. Provides an introduction to mathematical techniques widely used in applied mathematics and needed for advanced research in ordinary and partial differential equations, integral equations, numerical analysis, fluid dynamics and other areas Establishes the advanced background needed for sophisticated literature review and research in differential equations and integral equations Suitable for use as a textbook for a two semester graduate level course for M.S. and Ph.D. students in Mathematics and Applied Mathematics

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  • Author : Paul Sacks
  • Publisher : Academic Press
  • Pages : 320 pages
  • ISBN : 0128114576
  • Rating : 4/5 from 21 reviews
CLICK HERE TO GET THIS BOOKTechniques of Functional Analysis for Differential and Integral Equations

Techniques of Functional Analysis for Differential and Integral Equations

Techniques of Functional Analysis for Differential and Integral Equations
  • Author : Paul Sacks
  • Publisher : Academic Press
  • Release : 16 May 2017
GET THIS BOOKTechniques of Functional Analysis for Differential and Integral Equations

Techniques of Functional Analysis for Differential and Integral Equations describes a variety of powerful and modern tools from mathematical analysis, for graduate study and further research in ordinary differential equations, integral equations and partial differential equations. Knowledge of these techniques is particularly useful as preparation for graduate courses and PhD research in differential equations and numerical analysis, and more specialized topics such as fluid dynamics and control theory. Striking a balance between mathematical depth and accessibility, proofs involving more technical

Stationary Oscillations of Elastic Plates

Stationary Oscillations of Elastic Plates
  • Author : Gavin R. Thomson,Christian Constanda
  • Publisher : Springer Science & Business Media
  • Release : 28 June 2011
GET THIS BOOKStationary Oscillations of Elastic Plates

Many problems in mathematical physics rely heavily on the use of elliptical partial differential equations, and boundary integral methods play a significant role in solving these equations. Stationary Oscillations of Elastic Plates studies the latter in the context of stationary vibrations of thin elastic plates. The techniques presented here reduce the complexity of classical elasticity to a system of two independent variables, modeling problems of flexural-vibrational elastic body deformation with the aid of eigenfrequencies and simplifying them to manageable, uniquely

Theoretical Numerical Analysis

Theoretical Numerical Analysis
  • Author : Kendall Atkinson,Weimin Han
  • Publisher : Springer Science & Business Media
  • Release : 07 June 2007
GET THIS BOOKTheoretical Numerical Analysis

Mathematics is playing an ever more important role in the physical and biological sciences, provoking a blurring of boundaries between scienti?c disciplines and a resurgence of interest in the modern as well as the cl- sical techniques of applied mathematics. This renewal of interest, both in research and teaching, has led to the establishment of the series: Texts in Applied Mathematics (TAM). Thedevelopmentofnewcoursesisanaturalconsequenceofahighlevelof excitement on the research frontier as newer techniques, such as numerical and symbolic computer systems, dynamical

Special Functions and Analysis of Differential Equations

Special Functions and Analysis of Differential Equations
  • Author : Praveen Agarwal,Ravi P Agarwal,Michael Ruzhansky
  • Publisher : CRC Press
  • Release : 08 September 2020
GET THIS BOOKSpecial Functions and Analysis of Differential Equations

Differential Equations are very important tools in Mathematical Analysis. They are widely found in mathematics itself and in its applications to statistics, computing, electrical circuit analysis, dynamical systems, economics, biology, and so on. Recently there has been an increasing interest in and widely-extended use of differential equations and systems of fractional order (that is, of arbitrary order) as better models of phenomena in various physics, engineering, automatization, biology and biomedicine, chemistry, earth science, economics, nature, and so on. Now, new

Integral Equations

Integral Equations
  • Author : Wolfgang Hackbusch
  • Publisher : Birkhäuser
  • Release : 06 December 2012
GET THIS BOOKIntegral Equations

The theory of integral equations has been an active research field for many years and is based on analysis, function theory, and functional analysis. On the other hand, integral equations are of practical interest because of the «boundary integral equation method», which transforms partial differential equations on a domain into integral equations over its boundary. This book grew out of a series of lectures given by the author at the Ruhr-Universitat Bochum and the Christian-Albrecht-Universitat zu Kiel to students of

Functional Analysis and Numerical Mathematics

Functional Analysis and Numerical Mathematics
  • Author : Lothar Collatz
  • Publisher : Academic Press
  • Release : 12 May 2014
GET THIS BOOKFunctional Analysis and Numerical Mathematics

Functional Analysis and Numerical Mathematics focuses on the structural changes which numerical analysis has undergone, including iterative methods, vectors, integral equations, matrices, and boundary value problems. The publication first examines the foundations of functional analysis and applications, including various types of spaces, convergence and completeness, operators in Hilbert spaces, vector and matrix norms, eigenvalue problems, and operators in pseudometric and other special spaces. The text then elaborates on iterative methods. Topics include the fixed-point theorem for a general iterative method

Linear Integral Equations

Linear Integral Equations
  • Author : Rainer Kress
  • Publisher : Springer Science & Business Media
  • Release : 06 December 2012
GET THIS BOOKLinear Integral Equations

The result of the author's fascination with the mathematical beauty of integral equations, this book combines theory, applications, and numerical methods, and covers each of these fields with the same weight. In order to make the book accessible to mathematicians, physicists, and engineers alike, the author has made it as self-contained as possible, requiring only a solid foundation in differential and integral calculus. The functional analysis which is necessary for an adequate treatment of the theory and the numerical solution

Functional Analysis, Sobolev Spaces and Partial Differential Equations

Functional Analysis, Sobolev Spaces and Partial Differential Equations
  • Author : Haim Brezis
  • Publisher : Springer Science & Business Media
  • Release : 02 November 2010
GET THIS BOOKFunctional Analysis, Sobolev Spaces and Partial Differential Equations

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

Green's Functions and Boundary Value Problems

Green's Functions and Boundary Value Problems
  • Author : Ivar Stakgold,Michael J. Holst
  • Publisher : John Wiley & Sons
  • Release : 01 March 2011
GET THIS BOOKGreen's Functions and Boundary Value Problems

Praise for the Second Edition "This book is an excellent introduction to the wide field of boundary value problems."—Journal of Engineering Mathematics "No doubt this textbook will be useful for both students and research workers."—Mathematical Reviews A new edition of the highly-acclaimed guide to boundary value problems, now featuring modern computational methods and approximation theory Green's Functions and Boundary Value Problems, Third Edition continues the tradition of the two prior editions by providing mathematical techniques for the use

Partial Differential and Integral Equations

Partial Differential and Integral Equations
  • Author : Heinrich Begehr,R.P. Gilbert,Wen-Chung Guo
  • Publisher : Springer Science & Business Media
  • Release : 01 December 2013
GET THIS BOOKPartial Differential and Integral Equations

This volume of the Proceedings of the congress ISAAC '97 collects the con tributions of the four sections 1. Function theoretic and functional analytic methods for pde, 2. Applications of function theory of several complex variables to pde, 3. Integral equations and boundary value problems, 4. Partial differential equations. Most but not all of the authors have participated in the congress. Unfortunately some from Eastern Europe and Asia have not managed to come because of lack of financial support. Nevertheless their manuscripts of the

Functional-Analytic and Complex Methods, Their Interactions, and Applications to Partial Differential Equations

Functional-Analytic and Complex Methods, Their Interactions, and Applications to Partial Differential Equations
  • Author : H Florian,W Tutschke,N Ortner,F J Schnitzer
  • Publisher : World Scientific
  • Release : 12 November 2001
GET THIS BOOKFunctional-Analytic and Complex Methods, Their Interactions, and Applications to Partial Differential Equations

Functional analysis is not only a tool for unifying mathematical analysis, but it also provides the background for today's rapid development of the theory of partial differential equations. Using concepts of functional analysis, the field of complex analysis has developed methods (such as the theory of generalized analytic functions) for solving very general classes of partial differential equations. This book is aimed at promoting further interactions of functional analysis, partial differential equations, and complex analysis including its generalizations such as

Variational, Topological, and Partial Order Methods with Their Applications

Variational, Topological, and Partial Order Methods with Their Applications
  • Author : Zhitao Zhang
  • Publisher : Springer Science & Business Media
  • Release : 18 September 2012
GET THIS BOOKVariational, Topological, and Partial Order Methods with Their Applications

Nonlinear functional analysis is an important branch of contemporary mathematics. It's related to topology, ordinary differential equations, partial differential equations, groups, dynamical systems, differential geometry, measure theory, and more. In this book, the author presents some new and interesting results on fundamental methods in nonlinear functional analysis, namely variational, topological and partial order methods, which have been used extensively to solve existence of solutions for elliptic equations, wave equations, Schrödinger equations, Hamiltonian systems etc., and are also used to

History of Functional Analysis

History of Functional Analysis
  • Author : J. Dieudonne
  • Publisher : Elsevier
  • Release : 01 January 1983
GET THIS BOOKHistory of Functional Analysis

History of Functional Analysis presents functional analysis as a rather complex blend of algebra and topology, with its evolution influenced by the development of these two branches of mathematics. The book adopts a narrower definition—one that is assumed to satisfy various algebraic and topological conditions. A moment of reflections shows that this already covers a large part of modern analysis, in particular, the theory of partial differential equations. This volume comprises nine chapters, the first of which focuses on

Advanced Numerical Methods for Differential Equations

Advanced Numerical Methods for Differential Equations
  • Author : Harendra Singh,Jagdev Singh,Sunil Dutt Purohit,Devendra Kumar
  • Publisher : Unknown Publisher
  • Release : 24 January 2022
GET THIS BOOKAdvanced Numerical Methods for Differential Equations

Mathematical models are used to convert real-life problems using mathematical concepts and language. These models are governed by differential equations whose solutions make it easy to understand real-life problems and can be applied to engineering and science disciplines. This book presents numerical methods for solving various mathematical models. This book offers real-life applications, includes research problems on numerical treatment, and shows how to develop the numerical methods for solving problems. The book also covers theory and applications in engineering and

Scientific and Technical Revolution: Yesterday, Today and Tomorrow

Scientific and Technical Revolution: Yesterday, Today and Tomorrow
  • Author : Elena G. Popkova,Bruno S. Sergi
  • Publisher : Springer Nature
  • Release : 05 June 2020
GET THIS BOOKScientific and Technical Revolution: Yesterday, Today and Tomorrow

This book presents a system view of the digital scientific and technological revolution, including its genesis and prerequisites, current trends, as well as current and potential issues and future prospects. It gathers selected research papers presented at the 12th International Scientific and Practical Conference, organized by the Institute of Scientific Communications. The conference “Artificial Intelligence: Anthropogenic Nature vs. Social Origin” took place on December 5–7, 2019 in Krasnoyarsk, Russia. The book is intended for academic researchers and independent experts studying the social