Techniques Of Functional Analysis For Differential And Integral Equations

Author : Paul Sacks
Publisher : Academic Press
ISBN 13 : 0128114576
Total Pages : 322 pages
Book Rating : 4.75/5 ( download)

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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

Author : Praveen Agarwal
Publisher : CRC Press
ISBN 13 : 1000078566
Total Pages : 371 pages
Book Rating : 4.65/5 ( download)

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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 371 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.

Author : Helmut Florian
Publisher : World Scientific
ISBN 13 : 9814490008
Total Pages : 473 pages
Book Rating : 4.09/5 ( download)

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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

Author : R Precup
Publisher : Springer Science & Business Media
ISBN 13 : 9401599866
Total Pages : 221 pages
Book Rating : 4.63/5 ( download)

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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.

Author : Helmut Florian
Publisher : World Scientific
ISBN 13 : 9812794557
Total Pages : 473 pages
Book Rating : 4.50/5 ( download)

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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. Sample Chapter(s). Hyperbolic Equations, Waves and the Singularity Theory (858 KB). Contents: Boundary Value Problems and Initial Value Problems for Partial Differential Equations; Applications of Functional-Analytic and Complex Methods to Mathematical Physics; Partial Complex Differential Equations in the Plane; Complex Methods in Higher Dimensions. Readership: Researchers, lecturers and graduate students in the fields of analysis & differential equations, applied mathematics and mathematical physics.

Author : Peter J. Collins
Publisher : Oxford University Press
ISBN 13 : 0198533829
Total Pages : 387 pages
Book Rating : 4.25/5 ( download)

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Download or read book Differential and Integral Equations written by Peter J. Collins and published by Oxford University Press. This book was released on 2006-08-03 with total page 387 pages. Available in PDF, EPUB and Kindle. Book excerpt: Differential & integral equations involve important mathematical techniques, & as such will be encountered by mathematicians, & physical & social scientists, in their undergraduate courses. This text provides a clear, comprehensive guide to first- & second- order ordinary & partial differential equations.

Author : G. Micula
Publisher : Springer Science & Business Media
ISBN 13 : 9401580243
Total Pages : 403 pages
Book Rating : 4.43/5 ( download)

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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.

Author : S.S. Kutateladze
Publisher : CRC Press
ISBN 13 : 9781420050127
Total Pages : 408 pages
Book Rating : 4.25/5 ( download)

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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 408 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.

Author : Mark Iosifovich Freidlin
Publisher : Princeton University Press
ISBN 13 : 9780691083629
Total Pages : 566 pages
Book Rating : 4.22/5 ( download)

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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 566 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.

Author : Veli-Matti Hokkanen
Publisher : CRC Press
ISBN 13 : 1420035363
Total Pages : 259 pages
Book Rating : 4.60/5 ( download)

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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