Techniques of Functional Analysis for Differential and Integral Equations Book

Techniques of Functional Analysis for Differential and Integral Equations


  • Author : Paul Sacks
  • Publisher : Academic Press
  • Release Date : 2017-05-16
  • Genre: Mathematics
  • Pages : 320
  • ISBN 10 : 9780128114575

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Techniques of Functional Analysis for Differential and Integral Equations Excerpt :

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

Techniques of Functional Analysis for Differential and Integral Equations Book

Techniques of Functional Analysis for Differential and Integral Equations


  • Author : Paul Sacks
  • Publisher : Academic Press
  • Release Date : 2017-03-24
  • Genre: Uncategoriezed
  • Pages : 324
  • ISBN 10 : 0128114266

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Techniques of Functional Analysis for Differential and Integral Equations Excerpt :

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 especially partial differential equations. Knowledge of these techniques is particularly useful as preparation for graduate courses and as PhD research preparation 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 are limited, and their sources precisely identifie d, 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 the mathematical techniques widely used in applied mathematics and needed for advanced research Establishes the advanced background needed for sophisticated literature review and research in both differential 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

Special Functions and Analysis of Differential Equations Book

Special Functions and Analysis of Differential Equations


  • Author : Praveen Agarwal
  • Publisher : CRC Press
  • Release Date : 2020-09-08
  • Genre: Mathematics
  • Pages : 349
  • ISBN 10 : 9781000078589

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Special Functions and Analysis of Differential Equations Excerpt :

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 unified presentation and extensive development of special functions associated with fractional calculus are necessary tools, being related to the theory of differentiation and integration of arbitrary order (i.e., fractional calculus) and to the fractional order (or multi-order) differential and integral equations. This book provides learners with the opportunity to develop an understanding of advancements of special functions and the skills needed to apply advanced mathematical techniques to solve complex differential equations and Partial Differential Equations (PDEs). Subject matters should be strongly related to special functions involving mathematical analysis and its numerous applications. The main objective of this book is to highlight the importance of fundamental results and techniques of the theory of complex analysis for differential equations and PDEs and emphasizes articles devoted to the mathematical treatment of questions arising in physics, chemistry, biology, and engineering, particularly those that stress analytical aspects and novel problems and their solutions. Specific topics include but are not limited to Partial differential equations Least squares on first-order system Sequence and series in functional analysis Special functions related to fractional (non-integer) order control systems and equations Various special functions related to generalized fractional calculus Operatio

Functional Analysis  Sobolev Spaces and Partial Differential Equations Book

Functional Analysis Sobolev Spaces and Partial Differential Equations


  • Author : Haim Brezis
  • Publisher : Springer Science & Business Media
  • Release Date : 2010-11-02
  • Genre: Mathematics
  • Pages : 600
  • ISBN 10 : 9780387709147

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Functional Analysis Sobolev Spaces and Partial Differential Equations 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.

Functional Analysis for the Applied Sciences Book

Functional Analysis for the Applied Sciences


  • Author : Gheorghe Moroşanu
  • Publisher : Springer Nature
  • Release Date : 2019-12-27
  • Genre: Mathematics
  • Pages : 432
  • ISBN 10 : 9783030271534

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Functional Analysis for the Applied Sciences Excerpt :

This advanced graduate textbook presents main results and techniques in Functional Analysis and uses them to explore other areas of mathematics and applications. Special attention is paid to creating appropriate frameworks towards solving significant problems involving differential and integral equations. Exercises at the end of each chapter help the reader to understand the richness of ideas and methods offered by Functional Analysis. Some of the exercises supplement theoretical material, while others relate to the real world. This textbook, with its friendly exposition, focuses on different problems in physics and other applied sciences and uniquely provides solutions to most of the exercises. The text is aimed toward graduate students and researchers in applied mathematics, physics, and neighboring fields of science.

Theoretical Numerical Analysis Book

Theoretical Numerical Analysis


  • Author : Kendall Atkinson
  • Publisher : Springer Science & Business Media
  • Release Date : 2007-06-07
  • Genre: Mathematics
  • Pages : 576
  • ISBN 10 : 9780387287690

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Theoretical Numerical Analysis Excerpt :

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 systems, and chaos, mix with and reinforce the traditional methods of applied mathematics. Thus, the purpose of this textbook series is to meet the current and future needs of these advances and to encourage the teaching of new courses. TAM will publish textbooks suitable for use in advanced undergraduate and beginning graduate courses, and will complement the Applied Ma- ematical Sciences (AMS) series, which will focus on advanced textbooks and research-level monographs.

Wavelet Based Approximation Schemes for Singular Integral Equations Book

Wavelet Based Approximation Schemes for Singular Integral Equations


  • Author : Madan Mohan Panja
  • Publisher : CRC Press
  • Release Date : 2020-09-25
  • Genre: Mathematics
  • Pages : 290
  • ISBN 10 : 9780429534287

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Wavelet Based Approximation Schemes for Singular Integral Equations Excerpt :

Many mathematical problems in science and engineering are defined by ordinary or partial differential equations with appropriate initial-boundary conditions. Among the various methods, boundary integral equation method (BIEM) is probably the most effective. It’s main advantage is that it changes a problem from its formulation in terms of unbounded differential operator to one for an integral/integro-differential operator, which makes the problem tractable from the analytical or numerical point of view. Basically, the review/study of the problem is shifted to a boundary (a relatively smaller domain), where it gives rise to integral equations defined over a suitable function space. Integral equations with singular kernels areamong the most important classes in the fields of elasticity, fluid mechanics, electromagnetics and other domains in applied science and engineering. With the advancesin computer technology, numerical simulations have become important tools in science and engineering. Several methods have been developed in numerical analysis for equations in mathematical models of applied sciences. Widely used methods include: Finite Difference Method (FDM), Finite Element Method (FEM), Finite Volume Method (FVM) and Galerkin Method (GM). Unfortunately, none of these are versatile. Each has merits and limitations. For example, the widely used FDM and FEM suffers from difficulties in problem solving when rapid changes appear in singularities. Even with the modern computing machines, analysis of shock-wave or crack propagations in three dimensional solids by the existing classical numerical schemes is challenging (computational time/memory requirements). Therefore, with the availability of faster computing machines, research into the development of new efficient schemes for approximate solutions/numerical simulations is an ongoing parallel activity. Numerical methods based on wavelet basis (multiresolution analysis) may be regarded as a confluence of widely used n

Methods in Nonlinear Integral Equations Book

Methods in Nonlinear Integral Equations


  • Author : R Precup
  • Publisher : Springer Science & Business Media
  • Release Date : 2013-03-09
  • Genre: Mathematics
  • Pages : 218
  • ISBN 10 : 9789401599863

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Methods in Nonlinear Integral Equations Excerpt :

Methods in Nonlinear Integral Equations presents several extremely fruitful methods for the analysis of systems and nonlinear integral equations. They include: fixed point methods (the Schauder and Leray-Schauder principles), variational methods (direct variational methods and mountain pass theorems), and iterative methods (the discrete continuation principle, upper and lower solutions techniques, Newton's method and the generalized quasilinearization method). Many important applications for several classes of integral equations and, in particular, for initial and boundary value problems, are presented to complement the theory. Special attention is paid to the existence and localization of solutions in bounded domains such as balls and order intervals. The presentation is essentially self-contained and leads the reader from classical concepts to current ideas and methods of nonlinear analysis.

Computational Functional Analysis Book

Computational Functional Analysis


  • Author : Ramon E Moore
  • Publisher : Elsevier
  • Release Date : 2007-06-01
  • Genre: Technology & Engineering
  • Pages : 212
  • ISBN 10 : 9780857099433

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Computational Functional Analysis Excerpt :

This course text fills a gap for first-year graduate-level students reading applied functional analysis or advanced engineering analysis and modern control theory. Containing 100 problem-exercises, answers, and tutorial hints, the first edition is often cited as a standard reference. Making a unique contribution to numerical analysis for operator equations, it introduces interval analysis into the mainstream of computational functional analysis, and discusses the elegant techniques for reproducing Kernel Hilbert spaces. There is discussion of a successful ‘‘hybrid’’ method for difficult real-life problems, with a balance between coverage of linear and non-linear operator equations. The authors successful teaching philosophy: ‘‘We learn by doing’’ is reflected throughout the book. Contains 100 problem-exercises, answers and tutorial hints for students reading applied functional analysis Introduces interval analysis into the mainstream of computational functional analysis

Green s Functions and Boundary Value Problems Book
Score: 4
From 1 Ratings

Green s Functions and Boundary Value Problems


  • Author : Ivar Stakgold
  • Publisher : John Wiley & Sons
  • Release Date : 2011-03-01
  • Genre: Mathematics
  • Pages : 736
  • ISBN 10 : 9780470906521

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Green s Functions and Boundary Value Problems Excerpt :

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 of differential and integral equations to tackle important problems in applied mathematics, the physical sciences, and engineering. This new edition presents mathematical concepts and quantitative tools that are essential for effective use of modern computational methods that play a key role in the practical solution of boundary value problems. With a careful blend of theory and applications, the authors successfully bridge the gap between real analysis, functional analysis, nonlinear analysis, nonlinear partial differential equations, integral equations, approximation theory, and numerical analysis to provide a comprehensive foundation for understanding and analyzing core mathematical and computational modeling problems. Thoroughly updated and revised to reflect recent developments, the book includes an extensive new chapter on the modern tools of computational mathematics for boundary value problems. The Third Edition features numerous new topics, including: Nonlinear analysis tools for Banach spaces Finite element and related discretizations Best and near-best approximation in Banach spaces Iterative methods for discretized equations Overview of Sobolev and Besov space linear Methods for nonlinear equations Applications to nonlinear elliptic equations In addition, various topics have been substantially expanded, and new material on weak derivatives and Sobolev spaces, the Hahn-Banach theorem, reflexive Banach spaces,

Integral Equations  A Practical Treatment  from Spectral Theory to Applications Book

Integral Equations A Practical Treatment from Spectral Theory to Applications


  • Author : David Porter
  • Publisher : Cambridge University Press
  • Release Date : 1990-09-28
  • Genre: Mathematics
  • Pages : 388
  • ISBN 10 : 0521337429

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Integral Equations A Practical Treatment from Spectral Theory to Applications Excerpt :

The book aims to tackle the solution of integral equations using a blend of abstract 'structural' results and more direct, down-to-earth mathematics.

History of Functional Analysis Book

History of Functional Analysis


  • Author : J. Dieudonne
  • Publisher : Elsevier
  • Release Date : 1983-01-01
  • Genre: Mathematics
  • Pages : 311
  • ISBN 10 : 0080871607

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History of Functional Analysis Excerpt :

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 linear differential equations and the Sturm-Liouville problem. The succeeding chapters go on to discuss the ""crypto-integral"" equations, including the Dirichlet principle and the Beer-Neumann method; the equation of vibrating membranes, including the contributions of Poincare and H.A. Schwarz's 1885 paper; and the idea of infinite dimension. Other chapters cover the crucial years and the definition of Hilbert space, including Fredholm's discovery and the contributions of Hilbert; duality and the definition of normed spaces, including the Hahn-Banach theorem and the method of the gliding hump and Baire category; spectral theory after 1900, including the theories and works of F. Riesz, Hilbert, von Neumann, Weyl, and Carleman; locally convex spaces and the theory of distributions; and applications of functional analysis to differential and partial differential equations. This book will be of interest to practitioners in the fields of mathematics and statistics.

Computational Methods for Integral Equations Book

Computational Methods for Integral Equations


  • Author : L. M. Delves
  • Publisher : CUP Archive
  • Release Date : 1988-03-31
  • Genre: Mathematics
  • Pages : 392
  • ISBN 10 : 0521357969

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Computational Methods for Integral Equations Excerpt :

This textbook provides a readable account of techniques for numerical solutions.

Volterra Integral and Functional Equations Book

Volterra Integral and Functional Equations


  • Author : G. Gripenberg
  • Publisher : Cambridge University Press
  • Release Date : 1990-03-30
  • Genre: Mathematics
  • Pages : 727
  • ISBN 10 : 9780521372893

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Volterra Integral and Functional Equations Excerpt :

This book looks at the theories of Volterra integral and functional equations.