Recent Advances In Integral Equations

Author : Francisco Bulnes
Publisher : BoD – Books on Demand
Page : 102 pages
File Size : 54,9 Mb
Release : 2019-07-24
Category : Computers
ISBN : 9781838806583

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Recent Advances in Integral Equations by Francisco Bulnes Pdf

Integral equations are functional equations in which an unknown function appears under an integral sign. This can involve aspects of function theory and their integral transforms when the unknown function appears with a functional non-degenerated kernel under the integral sign. The close relation between differential and integral equations does that in some functional analysis, and function theory problems may be formulated either way. This book establishes the fundamentals of integral equations and considers some deep research aspects on integral equations of first and second kind, operator theory applied to integral equations, methods to solve some nonlinear integral equations, and singular integral equations, among other things. This is the first volume on this theme, hoping that other volumes of this important functional analysis theme and operator theory to formal functional equations will be realized in the future.

Author : B N Mandal,Nanigopal Mandal
Publisher : CRC Press
Page : 236 pages
File Size : 44,6 Mb
Release : 1998-12-18
Category : Mathematics
ISBN : 0849306175

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Advances in Dual Integral Equations by B N Mandal,Nanigopal Mandal Pdf

The effectiveness of dual integral equations for handling mixed boundary value problems has established them as an important tool for applied mathematicians. Their many applications in mathematical physics have prompted extensive research over the last 25 years, and many researchers have made significant contributions to the methodology of solving and to the applications of dual integral equations. However, until now, much of this work has been available only in the form of research papers scattered throughout different journals. In Advances in Dual Integral Equations, the authors systematically present some of the recent developments in dual integral equations involving various special functions as kernel. They examine dual integral equations with Bessel, Legendre, and trigonometric functions as kernel plus dual integral equations involving inverse Mellin transforms. These can be particularly useful in studying certain mixed boundary value problems involving homogeneous media in continuum mechanics. However, when dealing with problems involving non-homogenous media, the corresponding equations may have different kernels. This application prompts the authors to conclude with a discussion of hybrid dual integral equations-mixed kernels with generalized associated Legendre functions and mixed kernels involving Bessel functions. Researchers in the theory of elasticity, fluid dynamics, and mathematical physics will find Advances in Dual Integral Equations a concise, one-stop resource for recent work addressing special functions as kernel.

Author : C. Corduneanu
Publisher : American Mathematical Soc.
Page : 205 pages
File Size : 55,8 Mb
Release : 2008-05-09
Category : Mathematics
ISBN : 9780821846223

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Principles of Differential and Integral Equations by C. Corduneanu Pdf

In summary, the author has provided an elegant introduction to important topics in the theory of ordinary differential equations and integral equations. -- Mathematical Reviews This book is intended for a one-semester course in differential and integral equations for advanced undergraduates or beginning graduate students, with a view toward preparing the reader for graduate-level courses on more advanced topics. There is some emphasis on existence, uniqueness, and the qualitative behavior of solutions. Students from applied mathematics, physics, and engineering will find much of value in this book. The first five chapters cover ordinary differential equations. Chapter 5 contains a good treatment of the stability of ODEs. The next four chapters cover integral equations, including applications to second-order differential equations. Chapter 7 is a concise introduction to the important Fredholm theory of linear integral equations. The final chapter is a well-selected collection of fascinating miscellaneous facts about differential and integral equations. The prerequisites are a good course in advanced calculus, some preparation in linear algebra, and a reasonable acquaintance with elementary complex analysis. There are exercises throughout the text, with the more advanced of them providing good challenges to the student.

Author : Svetlin G. Georgiev
Publisher : Springer
Page : 402 pages
File Size : 49,7 Mb
Release : 2016-10-30
Category : Mathematics
ISBN : 9789462392281

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Integral Equations on Time Scales by Svetlin G. Georgiev Pdf

This book offers the reader an overview of recent developments of integral equations on time scales. It also contains elegant analytical and numerical methods. This book is primarily intended for senior undergraduate students and beginning graduate students of engineering and science courses. The students in mathematical and physical sciences will find many sections of direct relevance. The book contains nine chapters and each chapter is pedagogically organized. This book is specially designed for those who wish to understand integral equations on time scales without having extensive mathematical background.

Author : Christian Constanda,Matteo Dalla Riva,Pier Domenico Lamberti,Paolo Musolino
Publisher : Birkhäuser
Page : 340 pages
File Size : 54,9 Mb
Release : 2017-09-08
Category : Mathematics
ISBN : 9783319593845

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Integral Methods in Science and Engineering, Volume 1 by Christian Constanda,Matteo Dalla Riva,Pier Domenico Lamberti,Paolo Musolino Pdf

This contributed volume contains a collection of articles on the most recent advances in integral methods. The first of two volumes, this work focuses on the construction of theoretical integral methods. Written by internationally recognized researchers, the chapters in this book are based on talks given at the Fourteenth International Conference on Integral Methods in Science and Engineering, held July 25-29, 2016, in Padova, Italy. A broad range of topics is addressed, such as:• Integral equations• Homogenization• Duality methods• Optimal design• Conformal techniques This collection will be of interest to researchers in applied mathematics, physics, and mechanical and electrical engineering, as well as graduate students in these disciplines, and to other professionals who use integration as an essential tool in their work.

Author : B.G. Pachpatte
Publisher : Springer Science & Business Media
Page : 245 pages
File Size : 53,7 Mb
Release : 2011-07-26
Category : Mathematics
ISBN : 9789491216176

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Multidimensional Integral Equations and Inequalities by B.G. Pachpatte Pdf

Since from more than a century, the study of various types of integral equations and inequalities has been focus of great attention by many researchers, interested both in theory and its applications. In particular, there exists a very rich literature related to the integral equations and inequalities and their applications. The present monograph is an attempt to organize recent progress related to the Multidimensional integral equations and inequalities, which we hope will widen the scope of their new applications. The field to be covered is extremely wide and it is nearly impossible to treat all of them here. The material included in the monograph is recent and hard to find in other books. It is accessible to any reader with reasonable background in real analysis and acquaintance with its related areas. All results are presented in an elementary way and the book could also serve as a textbook for an advanced graduate course. The book deserves a warm welcome to those who wish to learn the subject and it will also be most valuable as a source of reference in the field. It will be an invaluable reading for mathematicians, physicists and engineers and also for graduate students, scientists and scholars wishing to keep abreast of this important area of research.

Author : John A. Nohel
Publisher : Unknown
Page : 232 pages
File Size : 53,8 Mb
Release : 1969
Category : Mathematics
ISBN : UCAL:$B17663

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Advances in Differential and Integral Equations by John A. Nohel Pdf

Author : Deuflhard,Hairer
Publisher : Springer Science & Business Media
Page : 369 pages
File Size : 51,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781468473247

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Numerical Treatment of Inverse Problems in Differential and Integral Equations by Deuflhard,Hairer Pdf

In many scientific or engineering applications, where ordinary differen tial equation (OOE),partial differential equation (POE), or integral equation (IE) models are involved, numerical simulation is in common use for prediction, monitoring, or control purposes. In many cases, however, successful simulation of a process must be preceded by the solution of the so-called inverse problem, which is usually more complex: given meas ured data and an associated theoretical model, determine unknown para meters in that model (or unknown functions to be parametrized) in such a way that some measure of the "discrepancy" between data and model is minimal. The present volume deals with the numerical treatment of such inverse probelms in fields of application like chemistry (Chap. 2,3,4, 7,9), molecular biology (Chap. 22), physics (Chap. 8,11,20), geophysics (Chap. 10,19), astronomy (Chap. 5), reservoir simulation (Chap. 15,16), elctrocardiology (Chap. 14), computer tomography (Chap. 21), and control system design (Chap. 12,13). In the actual computational solution of inverse problems in these fields, the following typical difficulties arise: (1) The evaluation of the sen sitivity coefficients for the model. may be rather time and storage con suming. Nevertheless these coefficients are needed (a) to ensure (local) uniqueness of the solution, (b) to estimate the accuracy of the obtained approximation of the solution, (c) to speed up the iterative solution of nonlinear problems. (2) Often the inverse problems are ill-posed. To cope with this fact in the presence of noisy or incomplete data or inev itable discretization errors, regularization techniques are necessary.

Author : Allen C. Pipkin
Publisher : Springer Science & Business Media
Page : 281 pages
File Size : 46,7 Mb
Release : 2013-11-22
Category : Mathematics
ISBN : 9781461244462

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A Course on Integral Equations by Allen C. Pipkin Pdf

Mathematics is playing an ever more important role in the physical and biological sciences, provoking a blurring of boundaries between scientific disciplines and a resurgence of interest in the modern as well as the clas 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). The development of new courses is a natural consequence of a high level of 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 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 Mathe matical Sciences ( AMS) series, which will focus on advanced textbooks and research level monographs. Foreword This book is based on a one-semester course for graduate students in the physical sciences and applied mathematics. No great mathematical back ground is needed, but the student should be familiar with the theory of analytic functions of a complex variable. Since the course is on problem solving rather than theorem-proving, the main requirement is that the stu dent should be willing to work out a large number of specific examples.

Author : Mangey Ram
Publisher : CRC Press
Page : 335 pages
File Size : 44,6 Mb
Release : 2020-03-17
Category : Technology & Engineering
ISBN : 9780429575808

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Recent Advances in Mathematics for Engineering by Mangey Ram Pdf

In recent years, mathematics has experienced amazing growth in the engineering sciences. Mathematics forms the common foundation of all engineering disciplines. This book provides a comprehensive range of mathematics applied in various fields of engineering for different tasks such as civil engineering, structural engineering, computer science, and electrical engineering, among others. It offers chapters that develop the applications of mathematics in engineering sciences, conveys the innovative research ideas, offers real-world utility of mathematics, and has a significance in the life of academics, practitioners, researchers, and industry leaders. Features Focuses on the latest research in the field of engineering applications Includes recent findings from various institutions Identifies the gaps in the knowledge in the field and provides the latest approaches Presents international studies and findings in modeling and simulation Offers various mathematical tools, techniques, strategies, and methods across different engineering fields

Author : Harendra Singh,Hemen Dutta,Marcelo M. Cavalcanti
Publisher : Springer Nature
Page : 255 pages
File Size : 44,7 Mb
Release : 2021-04-16
Category : Technology & Engineering
ISBN : 9783030655099

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Topics in Integral and Integro-Differential Equations by Harendra Singh,Hemen Dutta,Marcelo M. Cavalcanti Pdf

This book includes different topics associated with integral and integro-differential equations and their relevance and significance in various scientific areas of study and research. Integral and integro-differential equations are capable of modelling many situations from science and engineering. Readers should find several useful and advanced methods for solving various types of integral and integro-differential equations in this book. The book is useful for graduate students, Ph.D. students, researchers and educators interested in mathematical modelling, applied mathematics, applied sciences, engineering, etc. Key Features • New and advanced methods for solving integral and integro-differential equations • Contains comparison of various methods for accuracy • Demonstrates the applicability of integral and integro-differential equations in other scientific areas • Examines qualitative as well as quantitative properties of solutions of various types of integral and integro-differential equations

Author : Philip M. Anselone
Publisher : Unknown
Page : 400 pages
File Size : 52,8 Mb
Release : 1964
Category : Mathematics
ISBN : STANFORD:36105031265056

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Nonlinear Integral Equations by Philip M. Anselone Pdf

Author : Matiur Rahman
Publisher : WIT Press
Page : 385 pages
File Size : 42,8 Mb
Release : 2007
Category : Mathematics
ISBN : 9781845641016

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Integral Equations and Their Applications by Matiur Rahman Pdf

The book deals with linear integral equations, that is, equations involving an unknown function which appears under the integral sign and contains topics such as Abel's integral equation, Volterra integral equations, Fredholm integral integral equations, singular and nonlinear integral equations, orthogonal systems of functions, Green's function as a symmetric kernel of the integral equations.

Author : Hemen Dutta,Ljubiša D. R. Kočinac,Hari M. Srivastava
Publisher : Springer Nature
Page : 912 pages
File Size : 42,5 Mb
Release : 2019-08-23
Category : Mathematics
ISBN : 9783030152420

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Current Trends in Mathematical Analysis and Its Interdisciplinary Applications by Hemen Dutta,Ljubiša D. R. Kočinac,Hari M. Srivastava Pdf

This book explores several important aspects of recent developments in the interdisciplinary applications of mathematical analysis (MA), and highlights how MA is now being employed in many areas of scientific research. Each of the 23 carefully reviewed chapters was written by experienced expert(s) in respective field, and will enrich readers’ understanding of the respective research problems, providing them with sufficient background to understand the theories, methods and applications discussed. The book’s main goal is to highlight the latest trends and advances, equipping interested readers to pursue further research of their own. Given its scope, the book will especially benefit graduate and PhD students, researchers in the applied sciences, educators, and engineers with an interest in recent developments in the interdisciplinary applications of mathematical analysis.

Author : Michael A. Golberg
Publisher : Springer Science & Business Media
Page : 428 pages
File Size : 51,6 Mb
Release : 2013-11-11
Category : Mathematics
ISBN : 9781489925930

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Numerical Solution of Integral Equations by Michael A. Golberg Pdf

In 1979, I edited Volume 18 in this series: Solution Methods for Integral Equations: Theory and Applications. Since that time, there has been an explosive growth in all aspects of the numerical solution of integral equations. By my estimate over 2000 papers on this subject have been published in the last decade, and more than 60 books on theory and applications have appeared. In particular, as can be seen in many of the chapters in this book, integral equation techniques are playing an increas ingly important role in the solution of many scientific and engineering problems. For instance, the boundary element method discussed by Atkinson in Chapter 1 is becoming an equal partner with finite element and finite difference techniques for solving many types of partial differential equations. Obviously, in one volume it would be impossible to present a complete picture of what has taken place in this area during the past ten years. Consequently, we have chosen a number of subjects in which significant advances have been made that we feel have not been covered in depth in other books. For instance, ten years ago the theory of the numerical solution of Cauchy singular equations was in its infancy. Today, as shown by Golberg and Elliott in Chapters 5 and 6, the theory of polynomial approximations is essentially complete, although many details of practical implementation remain to be worked out.