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This book is based on a one semester course for graduate students in physical sciences and applied mathemat- ics. Not detailed mathematical background is needed but the student should be familiar with the theory of analytic functions of a complex variable. Since the course is problem-solving rather than theorem proving, the main requirement is that the student should be willing to work out a large number of specific examples. The course is divided about equally into three parts, where the first part is mostly theoretical and the remaining two parts emphasize on problem solving. ... Read more

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This handbook is presented in chapters, sections and subsections to aid the reader. Within each subsection the equations are arranged in order of increasing complexity. The book pays special attention to equations of the general form, showing their dependence on arbitrary functions. It presents equations and their applications; these include differential geometry, nonlinear mechanics, gas dynamics, heat and mass transfer, wave theory and much more. ... Read more

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Acoustic and electromagnetic waves underlie a vast range of modern technology from sonar, radio, and television to microwave heating and electromagnetic compatibility analysis. Mathematical modeling of these waves has undergone considerable growth in recent years, and this timely book, written by a leading international researcher, presents the research in a careful and complete way. ... Read more

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This work focuses exclusively on the distributional solutions of singular integral equations, progressing from basic concepts of the classical theory to the more difficult two-dimensional problems. Integral equation methods can be used more effectively than differential equation techniques to solve many problems in applied mathematics, engineering, and mathematical physics.

Key features of the work include:

Systematic progression from basic classical concepts to more advanced distribution type solutions Applications to a variety of fields, including potential theory, mechanics, fluid dynamics, wave scattering, statistics, and population dynamics Extensive examples, illustrations, and problem sets Good bibliography and index First modern text to exclusively treat singular integral equations

Kanwal has published two related works, "Linear Integral Equations and Generalized Functions", as well as "Asymptotic Analysis: A Distributional Approach" with Estrada. Like these other volumes, "Singular Integral Equations" is an ideal text for a beginning graduate level course or for self-study in a variety of scientific disciplines. ... Read more

Customer Reviews (1)

IE: the distributional approach
The Estrada & Kanwal deals with the Singular Integral Equations (SIE) and their solution by the distributional approach. It requires good skills in maths and maybe the reading of other books by Estrada about the distributional approach. Chapter 1 starts with Abel, Cauchy, Carleman IE. The reader has to be familiar with the theory of IE (for that purpose, I recommend the reading of Jerry, Introduction to IE with applications). Chapters 2 and 3 present the distributional solutions of SIE. Chapter 4 deals with IE with logarithmic kernels, while Chapter 5 introduces the Wiener-Hopf IE. Finally, dual and triple IE are sketched. This book requires more mathematical knowledge than the Jerry or the Hochstadt. Still it is nice reading it. ... Read more

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An attractive book on the intersection of analysis and numerical analysis, deriving classical boundary integral equations arising from the potential theory and acoustics. This self-contained monograph can be used as a textbook by graduate/postgraduate students. It also contains a lot of carefully chosen exercises.

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This book studies the large-time asymptotic behavior of solutions of the pure initial value problem for linear dispersive equations with constant coefficients and homogeneous symbols in one space dimension. Complete matched and uniformly-valid asymptotic expansions are obtained and sharp error estimates are proved. Using the method of steepest descent much new information on the regularity and spatial asymptotics of the solutions are also obtained. Applications to nonlinear dispersive equations are discussed. This monograph is intended for researchers and graduate students of partial differential equations. Familiarity with basic asymptotic, complex and Fourier analysis is assumed. ... Read more

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The quantitative and qualitative study of the physical world makes use of many mathematical models governed by a great diversity of ordinary, partial differential, integral, and integro-differential equations. An essential step in such investigations is the solution of these types of equations, which sometimes can be performed analytically, while at other times only numerically. This edited, self-contained volume presents a series of state-of-the-art analytic and numerical methods of solution constructed for important problems arising in science and engineering, all based on the powerful operation of (exact or approximate) integration.

The book, consisting of twenty seven selected chapters presented by well-known specialists in the field, is an outgrowth of the Eighth International Conference on Integral Methods in Science and Engineering, held August 2–4, 2004, in Orlando, FL. Contributors cover a wide variety of topics, from the theoretical development of boundary integral methods to the application of integration-based analytic and numerical techniques that include integral equations, finite and boundary elements, conservation laws, hybrid approaches, and other procedures.

The volume may be used as a reference guide and a practical resource. It is suitable for researchers and practitioners in applied mathematics, physics, and mechanical and electrical engineering, as well as graduate students in these disciplines.

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In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation;
methods for low-rank matrix approximations; hybrid methods based on a combination of iterative procedures and best operator approximation; and
methods for information compression and filtering under condition that a filter model should satisfy restrictions associated with causality and different types of memory.

As a result, the book represents a blend of new methods in general computational analysis,
and specific, but also generic, techniques for study of systems theory ant its particular
branches, such as optimal filtering and information compression.

- Best operator approximation,
- Non-Lagrange interpolation,
- Generic Karhunen-Loevetransform
- Generalised low-rank matrix approximation
- Optimal data compression
- Optimal nonlinear filtering ... Read more

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Fractional calculus was first developed by pure mathematicians in the middle of the 19th century. Some 100 years later, engineers and physicists have found applications for these concepts in their areas. However there has traditionally been little interaction between these two communities. In particular, typical mathematical works provide extensive findings on aspects with comparatively little significance in applications, and the engineering literature often lacks mathematical detail and precision. This book bridges the gap between the two communities. It concentrates on the class of fractional derivatives most important in applications, the Caputo operators, and provides a self-contained, thorough and mathematically rigorous study of their properties and of the corresponding differential equations. The text is a useful tool for mathematicians and researchers from the applied sciences alike. It can also be used as a basis for teaching graduate courses on fractional differential equations. ... Read more

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The method-of-moments solution of the electric field and magnetic field integral equations (EFIE and MFIE) is extended to conducting objects modeled with curved cells. These techniques are important for electromagnetic scattering, antenna, radar signature, and wireless communication applications. Vector basis functions of the divergence-conforming and curl-conforming types are explained, and specific interpolatory and hierarchical basis functions are reviewed. Procedures for mapping these basis functions from a reference domain to a curved cell, while preserving the desired continuity properties on curved cells, are discussed in detail. For illustration, results are presented for examples that employ divergence-conforming basis functions with the EFIE and curl-conforming basis functions with the MFIE. The intended audience includes electromagnetic engineers with some previous familiarity with numerical techniques. ... Read more

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Transient electromagnetic phenomena can be treated in two ways, either using direct time domain modeling or frequency domain analysis applying the inverse Fourier transform.Both approaches are important since each has distinct advantages depending on the situation or the application.

Offering a unique opportunity for academic researchers and engineers from industry to follow both the indirect and direct approach in parallel, this book starts by reviewing fundamental aspects of transient electromagnetics followed by the governing differential and integral equations.A special feature is the detailed treatment given to both the frequency and time domain integral equation techniques originally developed by the authors.The time independent Method of Moments and the time domain Finite Element Integral Equation Method are both fully presented.

Various applications of practical interest such as modeling of wire antenna arrays, analysis of aboveground and underground cables, lightning effects analysis, analysis of transients on printed circuit boards (PCBs), and the study of the effects on the human body of exposure to transient electromagnetic radiation are also covered. ... Read more

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This tract is devoted to the theory of linear equations, mainly of the second kind, associated with the names of Volterra, Fredholm, Hilbert and Schmidt. The treatment has been modernised by the systematic use of the Lebesgue integral, which considerably widens the range of applicability of the theory. Special attention is paid to the singular functions of non-symmetric kernels and to obtaining as strong results as possible for the convergence of the expansions in infinite series. References are given to work on numerical methods of solution. Individual chapters deal with the resolvent kernel and the Neumann series, the Fredholm theorems, orthonormal systems of functions, the classical Fredholm theory, the Fred-holm formulae for ß2 kernels, Hermitian kernels, singular functions and singular values. ... Read more

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Volterra and Fredholm integral equations form the domain of this book. Special chapters are devoted to Abel's integral equations and the singular integral equation with the Cauchy kernel; others focus on the integral equation method and the boundary element method (BEM). While a small section affords some theoretical grounding in integral equations (covering existence, regularity, etc.), the larger part of the book is devoted to a description and analysis of the discretisation methods (Galerkin / collocation / Nyström). Also the multigrid method for the solution of discrete equations is analysed. The most prominent application of integral equations occurs in the use of the boundary element method, which here is discussed from the numerical point of view in particular. New results about numerical integration and the panel clustering technique are included. Many chapters have an introductory character, while special subsections give more advanced information. Intended readers are students of mathematics as well as postgraduates. ... Read more

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