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Integral Equations and Integral Transforms
by Sudeshna Banerjea Birendra Nath MandalThis comprehensive textbook on linear integral equations and integral transforms is aimed at senior undergraduate and graduate students of mathematics and physics. The book covers a range of topics including Volterra and Fredholm integral equations, the second kind of integral equations with symmetric kernels, eigenvalues and eigen functions, the Hilbert–Schmidt theorem, and the solution of Abel integral equations by using an elementary method. In addition, the book covers various integral transforms including Fourier, Laplace, Mellin, Hankel, and Z-transforms. One of the unique features of the book is a general method for the construction of various integral transforms and their inverses, which is based on the properties of delta function representation in terms of Green’s function of a Sturm–Liouville type ordinary differential equation and its applications to physical problems. The book is divided into two parts: integral equations and integral transforms. Each chapter is supplemented with numerous illustrative examples to aid in understanding. The clear and concise presentation of the topics covered makes this book an ideal resource for students, researchers, and professionals interested in the theory and application of linear integral equations and integral transforms.
Integral Expansions Related to Mehler-Fock Type Transforms
by B N Mandal Nanigopal MandalAn important class of integral expansions generated by Sturm-Liouville theory involving spherical harmonics is commonly known as Mehler-Fock integral transforms. In this book, a number of integral expansions of such type have been established rigorously. As applications, integral expansions of some simple function are also obtained.
Integral Inequalities and Generalized Convexity
by Shashi Kant Mishra Nidhi Sharma Jaya BishtThe book covers several new research findings in the area of generalized convexity and integral inequalities. Integral inequalities using various type of generalized convex functions are applicable in many branches of mathematics such as mathematical analysis, fractional calculus, and discrete fractional calculus. The book contains integral inequalities of Hermite-Hadamard type, Hermite- Hadamard-Fejer type and majorization type for the generalized strongly convex functions. It presents Hermite-Hadamard type inequalities for functions defined on Time scales. Further, it provides the generalization and extensions of the concept of preinvexity for interval-valued functions and stochastic processes, and give Hermite-Hadamard type and Ostrowski type inequalities for these functions. These integral inequalities are utilized in numerous areas for the boundedness of generalized convex functions. Features: Covers Interval-valued calculus, Time scale calculus, Stochastic processes – all in one single book. Numerous examples to validate results Provides an overview of the current state of integral inequalities and convexity for a much wider audience, including practitioners. Applications of some special means of real numbers are also discussed. The book is ideal for anyone teaching or attending courses in integral inequalities along with researchers in this area.
Integral, Measure and Derivative: A Unified Approach
by G. E. Shilov B. L. GurevichThis graduate-level textbook and monograph defines the functions of a real variable through consistent use of the Daniell scheme, offering a rare and useful alternative to customary approaches. The treatment can be understood by any reader with a solid background in advanced calculus, and it features many problems with hints and answers. "The exposition is fresh and sophisticated," declared Sci-Tech Book News, "and will engage the interest of accomplished mathematicians." Part one is devoted to the integral, moving from the Reimann integral and step functions to a general theory, and obtaining the "classical" Lebesgue integral in n space. Part two constructs the Lebesgue-Stieltjes integral through the Daniell scheme using the Reimann-Stieltjes integral as the elementary integral. Part three develops theory of measure with the general Daniell scheme, and the final part is devoted to the theory of the derivative.
Integral Methods in Science and Engineering: Progress in Numerical and Analytic Techniques
by Bardo E.J. Bodmann Christian Constanda Haroldo F. VelhoAdvances in science and technology are driven by the development of rigorous mathematical foundations for the study of both theoretical and experimental models. With certain methodological variations, this type of study always comes down to the application of analytic or computational integration procedures, making such tools indispensible. With a wealth of cutting-edge research in the field, Integral Methods in Science and Engineering: Progress in Numerical and Analytic Techniques provides a detailed portrait of both the construction of theoretical integral techniques and their application to specific problems in science and engineering. The chapters in this volume are based on talks given by well-known researchers at the Twelfth International Conference on Integral Methods in Science and Engineering, July 23-27, 2012, in Porto Alegre, Brazil. They address a broad range of topics, from problems of existence and uniqueness for singular integral equations on domain boundaries to numerical integration via finite and boundary elements, conservation laws, hybrid methods, and other quadrature-related approaches. The contributing authors bring their expertise to bear on a number of topical problems that have to date resisted solution, thereby offering help and guidance to fellow professionals worldwide. Integral Methods in Science and Engineering: Progress in Numerical and Analytic Techniques will be a valuable resource for researchers in applied mathematics, physics, and mechanical and electrical engineering, for graduate students in these disciplines, and for various other professionals who use integration as an essential tool in their work.
Integral Methods in Science and Engineering: Computational Methods (Chapman And Hall/crc Research Notes In Mathematics Ser.)
by B Bertram C Constanda A StruthersBased on proceedings of the International Conference on Integral Methods in Science and Engineering, this collection of papers addresses the solution of mathematical problems by integral methods in conjunction with approximation schemes from various physical domains. Topics and applications include: wavelet expansions, reaction-diffusion systems, variational methods , fracture theory, boundary value problems at resonance, micromechanics, fluid mechanics, combustion problems, nonlinear problems, elasticity theory, and plates and shells.
Integral Methods in Science and Engineering: Analytic and Computational Procedures
by Christian Constanda Bardo E. J. Bodmann Paul J. HarrisThis volume contains a collection of articles on state-of-the-art developments in the construction of theoretical integral techniques and their application to specific problems in science and engineering. Chapters in this book are based on talks given at the Seventeenth International Conference on Integral Methods in Science and Engineering, held virtually in July 2022, and are written by internationally recognized researchers. This collection will be of interest to researchers in applied mathematics, physics, and mechanical, electrical, and petroleum engineering, as well as graduate students in these disciplines and other professionals for whom integration is an essential working tool.
Integral Methods in Science and Engineering: Analytic Treatment and Numerical Approximations
by Christian Constanda Paul HarrisThis contributed volume contains a collection of articles on state-of-the-art developments on the construction of theoretical integral techniques and their application to specific problems in science and engineering. The chapters in this book are based on talks given at the Fifteenth International Conference on Integral Methods in Science and Engineering, held July 16-20, 2018 at the University of Brighton, UK, and are written by internationally recognized researchers. The topics addressed are wide ranging, and include:Asymptotic analysisBoundary-domain integral equationsViscoplastic fluid flowStationary wavesInterior Neumann shape optimizationSelf-configuring neural networksThis 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 other professionals for whom integration is an essential tool.
Integral Methods in Science and Engineering
by Christian Constanda Andreas KirschThis contributed volume contains a collection of articles on state-of-the-art developments on the construction of theoretical integral techniques and their application to specific problems in science and engineering. Written by internationally recognized researchers, the chapters in this book are based on talks given at the Thirteenth International Conference on Integral Methods in Science and Engineering, held July 21-25, 2014, in Karlsruhe, Germany. A broad range of topics is addressed, from problems of existence and uniqueness for singular integral equations on domain boundaries to numerical integration via finite and boundary elements, conservation laws, hybrid methods, and other quadrature-related approaches. 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 other professionals for whom integration is an essential tool.
Integral Methods in Science and Engineering (Chapman And Hall/crc Research Notes In Mathematics Ser.)
by Christian Constanda Jukka Saranen S SeikkalaBased on proceedings of the International Conference on Integral Methods in Science and Engineering, this collection of papers addresses the solution of mathematical problems by integral methods in conjunction with approximation schemes from various physical domains. Topics and applications include: wavelet expansions, reaction-diffusion systems, variational methods , fracture theory, boundary value problems at resonance, micromechanics, fluid mechanics, combustion problems, nonlinear problems, elasticity theory, and plates and shells. Volume 1 covers Analytic Methods.
Integral Representations For Spatial Models of Mathematical Physics (Chapman And Hall/crc Research Notes In Mathematics Ser. #351)
by Vladislav V Kravchenko Michael ShapiroThis book provides a new mathematical theory for the treatment of an ample series of spatial problems of electrodynamics, particle physics, quantum mechanics and elasticity theory. This technique proves to be as powerful for solving the spatial problems of mathematical physics as complex analysis is for solving planar problems.The main analytic tool of the book, a non-harmonic version of hypercomplex analysis recently developed by the authors, is presented in detail. There are given applications of this theory to the boundary value problems of electrodynamics and elasticity theory as well as to the problem of quark confinement. A new approach to the linearization of special classes of the self-duality equation is also considered. Detailed proofs are given throughout. The book contains an extensive bibliography on closely related topics.This book will be of particular interest to academic and professional specialists and students in mathematics and physics who are interested in integral representations for partial differential equations. The book is self-contained and could be used as a main reference for special course seminars on the subject.
Integral Transform Techniques for Green's Function
by Kazumi WatanabeIn this book mathematical techniques for integral transforms are described in detail but concisely. The techniques are applied to the standard partial differential equations, such as the Laplace equation, the wave equation and elasticity equations. The Green's functions for beams, plates and acoustic media are also shown along with their mathematical derivations. Lists of Green's functions are presented for the future use. The Cagniard's-de Hoop method for the double inversion is described in detail, and 2D and 3D elasto-dynamics problems are fully treated.
Integral Transforms and Engineering: Theory, Methods, and Applications (Mathematics and its Applications)
by Abdon Atangana Ali AkgülWith the aim to better understand nature, mathematical tools are being used nowadays in many different fields. The concept of integral transforms, in particular, has been found to be a useful mathematical tool for solving a variety of problems not only in mathematics, but also in various other branches of science, engineering, and technology. Integral Transforms and Engineering: Theory, Methods, and Applications presents a mathematical analysis of integral transforms and their applications. The book illustrates the possibility of obtaining transfer functions using different integral transforms, especially when mapping any function into the frequency domain. Various differential operators, models, and applications are included such as classical derivative, Caputo derivative, Caputo-Fabrizio derivative, and Atangana-Baleanu derivative. This book is a useful reference for practitioners, engineers, researchers, and graduate students in mathematics, applied sciences, engineering, and technology fields.
Integral Transforms, Reproducing Kernels and Their Applications
by Saburou SaitohThe general theories contained in the text will give rise to new ideas and methods for the natural inversion formulas for general linear mappings in the framework of Hilbert spaces containing the natural solutions for Fredholm integral equations of the first kind.
Integralrechnung für Höhlenmenschen und andere Anfänger: Die Berechnung von Flächen und Lösung von Differentialgleichungen (essentials)
by Jürgen BeetzJürgen Beetz führt zuerst in den Ursprung der erdachten Geschichten der Mathematik aus der Steinzeit ein. Im Anschluss daran stellt er die zentrale Fragestellung der ,,Infinitesimalrechnung" anhand eines einfachen Beispiels dar. Dann erläutert der Autor die Grundproblematik des Integrierens: die Fläche zwischen einer beliebigen Stelle einer Funktion y=f(x) und der x-Achse festzustellen. Es gibt einige bekannte Sätze, z. B. den Mittelwertsatz und den Hauptsatz der Integralrechnung. Hauptanwendungsgebiet der Integralrechnung ist das Lösen von Differentialgleichungen: Gleichungen, die Funktionen und ihre Ableitungen nebeneinander enthalten.
Integrals and Series: Direct Laplace Transforms
by A.B PrudnikovVolumes 4 and 5 of the extensive series Integrals and Series are devoted to tables of LaplaceTransforms. In these companion volumes the authors have collected data scatteredthroughout the literature, and have augmented this material with many unpublished resultsobtained in their own research.Volume 4 contains tables of direct Laplace transforms, a number of which are expressed interms of the Meijer G-function. When combined with the table of special cases, theseformulas can be used to obtain Laplace transforms of numerous elementary and specialfunctions of mathematical physics.Volume 5 offers tables of inversion formulas for the Laplace transformation and includestables of factorization and inversion of various integral transforms.
Integrals Related to the Error Function
by Nikolai E. Korotkov Alexander N. KorotkovIntegrals Related to the Error Function presents a table of integrals related to the error function, including indefinite and improper definite integrals. Most of the formulas in this book have not been presented in other tables of integrals or have been presented only for some special cases of parameters or for integration only along the real axis of the complex plane. Many of the integrals presented here cannot be obtained using a computer (except via an approximate numerical integration). Additionally, for improper integrals, this book emphasizes the necessary and sufficient conditions for the validity of the presented formulas, including trajectory for going to infinity on the complex plane; such conditions are usually not given in computer-assisted analytical integration and often not presented in the previously published tables of integrals. Features The first book in English language to present a comprehensive collection of integrals related to the error function Useful for researchers whose work involves the error function (e.g., via probability integrals in communication theory). Additionally, it can also be used by broader audience.
Integrated Approaches to STEM Education: An International Perspective (Advances in STEM Education)
by Judy Anderson Yeping LiThis book provides a platform for international scholars to share evidence for effective practices in integrated STEM education and contributes to the theoretical and practical knowledge gained from the diversity of approaches. Many publications on STEM education focus on one or two of the separate STEM disciplines without considering the potential for delivering STEM curriculum as an integrated approach.This publication analyzes the efficacy of an integrated STEM curriculum and instruction, providing evidence to examine and support various integrations. The volume focuses on the problems seen by academics working in the fields of science, technology, engineering and mathematics (STEM) and provides valuable, high quality research outcomes and a set of valued practices which have demonstrated their use and viability to improve the quality of integrated STEM education.
Integrated Arithmetic and Basic Algebra (5th Edition)
by Bill E. Jordan William P. PalowIntegrated Arithmetic and Basic Algebra, Fifth Edition, integrates arithmetic and algebra to allow students to see the big picture of math. Rather than separating these two subjects, this text helps students recognize algebra as a natural extension of arithmetic. As a result, students see how concepts are interrelated and are better prepared for future courses.
Integrated Catastrophe Risk Modeling: Supporting Policy Processes (Advances in Natural and Technological Hazards Research #32)
by Aniello Amendola Tatiana Ermolieva Joanne Linnerooth-Bayer Reinhard MechlerEfficient and equitable policies for managing disaster risks and adapting to global environmental change are critically dependent on development of robust options supported by integrated modeling. The book is based on research and state-of-the art models developed at IIASA (International Institute for Applied Systems Analysis) and within its cooperation network. It addresses the methodological complexities of assessing disaster risks, which call for stochastic simulation, optimization methods and economic modeling. Furthermore, it describes policy frameworks for integrated disaster risk management, including stakeholder participation facilitated by user-interactive decision-support tools. Applications and results are presented for a number of case studies at different problem scales and in different socio-economic contexts, and their implications for loss sharing policies and economic development are discussed. Among others, the book presents studies for insurance policies for earthquakes in the Tuscany region in Italy and flood risk in the Tisza river basin in Hungary. Further, it investigates the economic impact of natural disasters on development and possible financial coping strategies; and applications are shown for selected South Asian countries. The book is addressed both to researchers and to organizations involved with catastrophe risk management and risk mitigation policies.
Integrated Catastrophe Risk Modeling: Supporting Policy Processes
by Tatiana Ermolieva Aniello Amendola Reinhard Mechler Joanne Linnerooth-BayerEfficient and equitable policies for managing disaster risks and adapting to global environmental change are critically dependent on development of robust options supported by integrated modeling. The book is based on research and state-of-the art models developed at IIASA (International Institute for Applied Systems Analysis) and within its cooperation network. It addresses the methodological complexities of assessing disaster risks, which call for stochastic simulation, optimization methods and economic modeling. Furthermore, it describes policy frameworks for integrated disaster risk management, including stakeholder participation facilitated by user-interactive decision-support tools. Applications and results are presented for a number of case studies at different problem scales and in different socio-economic contexts, and their implications for loss sharing policies and economic development are discussed. Among others, the book presents studies for insurance policies for earthquakes in the Tuscany region in Italy and flood risk in the Tisza river basin in Hungary. Further, it investigates the economic impact of natural disasters on development and possible financial coping strategies; and applications are shown for selected South Asian countries. The book is addressed both to researchers and to organizations involved with catastrophe risk management and risk mitigation policies.
Integrated Computer Technologies in Mechanical Engineering - 2023: Synergetic Engineering, Volume 2 (Lecture Notes in Networks and Systems #996)
by Mykola Nechyporuk Dmytro Krytskyi Volodymir PavlikovThe International Scientific and Technical Conference “Integrated Computer Technologies in Mechanical Engineering” – Synergetic Engineering (ICTM) was established by National Aerospace University “Kharkiv Aviation Institute”. The Conference ICTM’2023 was held in Kharkiv, Ukraine, during December, 2023. During this conference, technical exchanges between the research community were carried out in the forms of keynote speeches, panel discussions, as well as special session. In addition, participants were treated to a series of receptions, which forge collaborations among fellow researchers. ICTM’2023 received 202 papers submissions from different countries. All of these offer us plenty of valuable information and would be of great benefit to the experience exchange among scientists in modeling and simulation. The organizers of ICTM’2023 made great efforts to ensure the success of this conference. We hereby would like to thank all the members of ICTM’2023 Advisory Committee for their guidance and advice, the members of program committee and organizing committee, and the referees for their effort in reviewing and soliciting the papers, and all authors for their contribution to the formation of a common intellectual environment for solving relevant scientific problems. Also, we grateful to Springer - Janusz Kacprzyk and Thomas Ditzinger as the editor responsible for the series “Lecture Notes in Networks and Systems” for their great support in publishing these selected papers.
Integrated Computer Technologies in Mechanical Engineering - 2023: Synergetic Engineering, Volume 1 (Lecture Notes in Networks and Systems #1008)
by Mykola Nechyporuk Dmytro Krytskyi Volodymir PavlikovThe International Scientific and Technical Conference “Integrated Computer Technologies in Mechanical Engineering” – Synergetic Engineering (ICTM) was established by National Aerospace University “Kharkiv Aviation Institute”. The Conference ICTM’2023 was held in Kharkiv, Ukraine, during December, 2023. During this conference, technical exchanges between the research community were carried out in the forms of keynote speeches, panel discussions, as well as special session. In addition, participants were treated to a series of receptions, which forge collaborations among fellow researchers. ICTM’2023 received 202 papers submissions from different countries. All of these offer us plenty of valuable information and would be of great benefit to the experience exchange among scientists in modeling and simulation. The organizers of ICTM’2023 made great efforts to ensure the success of this conference. We hereby would like to thank all the members of ICTM’2023 Advisory Committee for their guidance and advice, the members of program committee and organizing committee, and the referees for their effort in reviewing and soliciting the papers, and all authors for their contribution to the formation of a common intellectual environment for solving relevant scientific problems. Also, we grateful to Springer - Janusz Kacprzyk and Thomas Ditzinger as the editor responsible for the series “Lecture Notes in Networks and Systems” for their great support in publishing these selected papers.
Integrated Formal Methods: 14th International Conference, IFM 2018, Maynooth, Ireland, September 5-7, 2018, Proceedings (Lecture Notes in Computer Science #11023)
by Carlo A. Furia Kirsten WinterThis book constitutes the refereed proceedings of the 14th International Conference on Integrated Formal Methods, IFM 2018, held in Maynooth, Ireland, in September 2018.The 17 full papers and 5 short papers presented together with 3 invited talks were carefully reviewed and selected from 60 submissions. The conference covers a broad spectrum of topics: from language design, to verification and analysis techniques, to supporting tools and their integration into software engineering practice.