Techniques Of Functional Analysis For Differential And Integral Equations

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Techniques of Functional Analysis for Differential and Integral Equations

Author : Paul Sacks
Publisher : Academic Press
ISBN 13 : 0128114576
Total Pages : 322 pages
Book Rating : 4.1/5 (281 download)

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Book Synopsis Techniques of Functional Analysis for Differential and Integral Equations by : Paul Sacks

Download or read book Techniques of Functional Analysis for Differential and Integral Equations written by Paul Sacks and published by Academic Press. This book was released on 2017-05-16 with total page 322 pages. Available in PDF, EPUB and Kindle. Book 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

Special Functions and Analysis of Differential Equations

Author : Praveen Agarwal
Publisher : CRC Press
ISBN 13 : 1000078582
Total Pages : 349 pages
Book Rating : 4.0/5 ( download)

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Book Synopsis Special Functions and Analysis of Differential Equations by : Praveen Agarwal

Download or read book Special Functions and Analysis of Differential Equations written by Praveen Agarwal and published by CRC Press. This book was released on 2020-09-08 with total page 349 pages. Available in PDF, EPUB and Kindle. Book 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 Operational method in fractional calculus Functional analysis and operator theory Mathematical physics Applications of numerical analysis and applied mathematics Computational mathematics Mathematical modeling This book provides the recent developments in special functions and differential equations and publishes high-quality, peer-reviewed book chapters in the area of nonlinear analysis, ordinary differential equations, partial differential equations, and related applications.

Integral Equations

Author : Wolfgang Hackbusch
Publisher : Birkhäuser
ISBN 13 : 3034892152
Total Pages : 377 pages
Book Rating : 4.0/5 (348 download)

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Book Synopsis Integral Equations by : Wolfgang Hackbusch

Download or read book Integral Equations written by Wolfgang Hackbusch and published by Birkhäuser. This book was released on 2012-12-06 with total page 377 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 mathematics. The contents of the first six chapters correspond to an intensive lecture course of four hours per week for a semester. Readers of the book require background from analysis and the foundations of numeri cal mathematics. Knowledge of functional analysis is helpful, but to begin with some basic facts about Banach and Hilbert spaces are sufficient. The theoretical part of this book is reduced to a minimum; in Chapters 2, 4, and 5 more importance is attached to the numerical treatment of the integral equations than to their theory. Important parts of functional analysis (e. g. , the Riesz-Schauder theory) are presented without proof. We expect the reader either to be already familiar with functional analysis or to become motivated by the practical examples given here to read a book about this topic. We recall that also from a historical point of view, functional analysis was initially stimulated by the investigation of integral equations.

Differential and Integral Equations

Author : Peter J. Collins
Publisher : OUP Oxford
ISBN 13 : 019152400X
Total Pages : 392 pages
Book Rating : 4.1/5 (915 download)

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Book Synopsis Differential and Integral Equations by : Peter J. Collins

Download or read book Differential and Integral Equations written by Peter J. Collins and published by OUP Oxford. This book was released on 2006-08-03 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: Differential and integral equations involve important mathematical techniques, and as such will be encountered by mathematicians, and physical and social scientists, in their undergraduate courses. This text provides a clear, comprehensive guide to first- and second-order ordinary and partial differential equations, whilst introducing important and useful basic material on integral equations. Readers will encounter detailed discussion of the wave, heat and Laplace equations, of Green's functions and their application to the Sturm-Liouville equation, and how to use series solutions, transform methods and phase-plane analysis. The calculus of variations will take them further into the world of applied analysis. Providing a wealth of techniques, but yet satisfying the needs of the pure mathematician, and with numerous carefully worked examples and exercises, the text is ideal for any undergraduate with basic calculus to gain a thorough grounding in 'analysis for applications'.

Differential and Integral Equations through Practical Problems and Exercises

Author : G. Micula
Publisher : Springer Science & Business Media
ISBN 13 : 9401580243
Total Pages : 403 pages
Book Rating : 4.4/5 (15 download)

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Book Synopsis Differential and Integral Equations through Practical Problems and Exercises by : G. Micula

Download or read book Differential and Integral Equations through Practical Problems and Exercises written by G. Micula and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 403 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many important phenomena are described and modeled by means of differential and integral equations. To understand these phenomena necessarily implies being able to solve the differential and integral equations that model them. Such equations, and the development of techniques for solving them, have always held a privileged place in the mathematical sciences. Today, theoretical advances have led to more abstract and comprehensive theories which are increasingly more complex in their mathematical concepts. Theoretical investigations along these lines have led to even more abstract and comprehensive theories, and to increasingly complex mathematical concepts. Long-standing teaching practice has, however, shown that the theory of differential and integral equations cannot be studied thoroughly and understood by mere contemplation. This can only be achieved by acquiring the necessary techniques; and the best way to achieve this is by working through as many different exercises as possible. The eight chapters of this book contain a large number of problems and exercises, selected on the basis of long experience in teaching students, which together with the author's original problems cover the whole range of current methods employed in solving the integral, differential equations, and the partial differential equations of order one, without, however, renouncing the classical problems. Every chapter of this book begins with the succinct theoretical exposition of the minimum of knowledge required to solve the problems and exercises therein.

Functional-analytic And Complex Methods, Their Interactions, And Applications To Partial Differential Equations - Proceedings Of The International Graz Workshop

Download Functional-analytic And Complex Methods, Their Interactions, And Applications To Partial Differential Equations - Proceedings Of The International Graz Workshop PDF Online Free

Author : Helmut Florian
Publisher : World Scientific
ISBN 13 : 9814490008
Total Pages : 473 pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Functional-analytic And Complex Methods, Their Interactions, And Applications To Partial Differential Equations - Proceedings Of The International Graz Workshop by : Helmut Florian

Download or read book Functional-analytic And Complex Methods, Their Interactions, And Applications To Partial Differential Equations - Proceedings Of The International Graz Workshop written by Helmut Florian and published by World Scientific. This book was released on 2001-11-12 with total page 473 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 Clifford analysis. New interesting problems in the field of partial differential equations concern, for instance, the Dirichlet problem for hyperbolic equations. Applications to mathematical physics address mainly Maxwell's equations, crystal optics, dynamical problems for cusped bars, and conservation laws. remove /a remove

Functional Integration and Partial Differential Equations

Author : Mark Iosifovich Freidlin
Publisher : Princeton University Press
ISBN 13 : 0691083622
Total Pages : 556 pages
Book Rating : 4.6/5 (91 download)

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Book Synopsis Functional Integration and Partial Differential Equations by : Mark Iosifovich Freidlin

Download or read book Functional Integration and Partial Differential Equations written by Mark Iosifovich Freidlin and published by Princeton University Press. This book was released on 1985-08-21 with total page 556 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This book discusses some aspects of the theory of partial differential equations from the viewpoint of probability theory. It is intended not only for specialists in partial differential equations or probability theory but also for specialists in asymptotic methods and in functional analysis. It is also of interest to physicists who use functional integrals in their research. The work contains results that have not previously appeared in book form, including research contributions of the author"--Publisher description.

History of Functional Analysis

Author : J. Dieudonne
Publisher : Elsevier
ISBN 13 : 0080871607
Total Pages : 319 pages
Book Rating : 4.0/5 (88 download)

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Book Synopsis History of Functional Analysis by : J. Dieudonne

Download or read book History of Functional Analysis written by J. Dieudonne and published by Elsevier. This book was released on 1983-01-01 with total page 319 pages. Available in PDF, EPUB and Kindle. Book 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.

Functional Analysis and Numerical Mathematics

Author : Lothar Collatz
Publisher : Academic Press
ISBN 13 : 1483264009
Total Pages : 494 pages
Book Rating : 4.4/5 (832 download)

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Book Synopsis Functional Analysis and Numerical Mathematics by : Lothar Collatz

Download or read book Functional Analysis and Numerical Mathematics written by Lothar Collatz and published by Academic Press. This book was released on 2014-05-12 with total page 494 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 in pseudometric spaces; special cases of the fixed-point theorem and change of operator; iterative methods for differential and integral equations; and systems of equations and difference methods. The manuscript takes a look at monotonicity, inequalities, and other topics, including monotone operators, applications of Schauder's theorem, matrices and boundary value problems of monotone kind, discrete Chebyshev approximation and exchange methods, and approximation of functions. The publication is a valuable source of data for mathematicians and researchers interested in functional analysis and numerical mathematics.

Applied Functional Analysis. Approximation Methods and Computers

Author : S.S. Kutateladze
Publisher : CRC Press
ISBN 13 : 1420050125
Total Pages : 400 pages
Book Rating : 4.4/5 (2 download)

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Book Synopsis Applied Functional Analysis. Approximation Methods and Computers by : S.S. Kutateladze

Download or read book Applied Functional Analysis. Approximation Methods and Computers written by S.S. Kutateladze and published by CRC Press. This book was released on 2010-12-12 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains the most remarkable papers of L.V. Kantorovich in applied and numerical mathematics. It explores the principal directions of Kantorovich's research in approximate methods. The book covers descriptive set theory and functional analysis in semi-ordered vector spaces.

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

Author : Helmut Florian
Publisher : World Scientific
ISBN 13 : 9810247648
Total Pages : 473 pages
Book Rating : 4.8/5 (12 download)

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Book Synopsis Functional-analytic and Complex Methods, Their Interactions, and Applications to Partial Differential Equations by : Helmut Florian

Download or read book Functional-analytic and Complex Methods, Their Interactions, and Applications to Partial Differential Equations written by Helmut Florian and published by World Scientific. This book was released on 2001 with total page 473 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 Clifford analysis. New interesting problems in the field of partial differential equations concern, for instance, the Dirichlet problem for hyperbolic equations. Applications to mathematical physics address mainly Maxwell's equations, crystal optics, dynamical problems for cusped bars, and conservation laws.

Integral Equations

Author : Harry Hochstadt
Publisher : John Wiley & Sons
ISBN 13 : 1118165934
Total Pages : 282 pages
Book Rating : 4.1/5 (181 download)

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Book Synopsis Integral Equations by : Harry Hochstadt

Download or read book Integral Equations written by Harry Hochstadt and published by John Wiley & Sons. This book was released on 2011-09-09 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: This classic work is now available in an unabridged paperback edition. Hochstatdt's concise treatment of integral equations represents the best compromise between the detailed classical approach and the faster functional analytic approach, while developing the most desirable features of each. The seven chapters present an introduction to integral equations, elementary techniques, the theory of compact operators, applications to boundary value problems in more than dimension, a complete treatment of numerous transform techniques, a development of the classical Fredholm technique, and application of the Schauder fixed point theorem to nonlinear equations.

Functional Analysis, Sobolev Spaces and Partial Differential Equations

Author : Haim Brezis
Publisher : Springer Science & Business Media
ISBN 13 : 0387709142
Total Pages : 600 pages
Book Rating : 4.3/5 (877 download)

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Book Synopsis Functional Analysis, Sobolev Spaces and Partial Differential Equations by : Haim Brezis

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.

Functional Methods in Differential Equations

Author : Veli-Matti Hokkanen
Publisher : CRC Press
ISBN 13 : 1420035363
Total Pages : 259 pages
Book Rating : 4.4/5 (2 download)

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Book Synopsis Functional Methods in Differential Equations by : Veli-Matti Hokkanen

Download or read book Functional Methods in Differential Equations written by Veli-Matti Hokkanen and published by CRC Press. This book was released on 2002-04-26 with total page 259 pages. Available in PDF, EPUB and Kindle. Book excerpt: In recent years, functional methods have become central to the study of theoretical and applied mathematical problems. As demonstrated in this Research Note, functional methods can not only provide more generality, but they can also unify results and techniques and lead to better results than those obtained by classical methods. Presenting

Methods in Nonlinear Integral Equations

Author : R Precup
Publisher : Springer Science & Business Media
ISBN 13 : 9401599866
Total Pages : 221 pages
Book Rating : 4.4/5 (15 download)

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Book Synopsis Methods in Nonlinear Integral Equations by : R Precup

Download or read book Methods in Nonlinear Integral Equations written by R Precup and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 221 pages. Available in PDF, EPUB and Kindle. Book 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.

Functional Analysis for the Applied Sciences

Author : Gheorghe Moroşanu
Publisher : Springer Nature
ISBN 13 : 3030271536
Total Pages : 439 pages
Book Rating : 4.0/5 (32 download)

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Book Synopsis Functional Analysis for the Applied Sciences by : Gheorghe Moroşanu

Download or read book Functional Analysis for the Applied Sciences written by Gheorghe Moroşanu and published by Springer Nature. This book was released on 2019-12-27 with total page 439 pages. Available in PDF, EPUB and Kindle. Book 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.

Stationary Oscillations of Elastic Plates

Author : Gavin R. Thomson
Publisher : Springer Science & Business Media
ISBN 13 : 0817682414
Total Pages : 241 pages
Book Rating : 4.8/5 (176 download)

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Book Synopsis Stationary Oscillations of Elastic Plates by : Gavin R. Thomson

Download or read book Stationary Oscillations of Elastic Plates written by Gavin R. Thomson and published by Springer Science & Business Media. This book was released on 2011-06-28 with total page 241 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 solvable integral equations. The book is intended for an audience with a knowledge of advanced calculus and some familiarity with functional analysis. It is a valuable resource for professionals in pure and applied mathematics, and for theoretical physicists and mechanical engineers whose work involves elastic plates. Graduate students in these fields can also benefit from the monograph as a supplementary text for courses relating to theories of elasticity or flexural vibrations.