Methodes Mathematique Pour Les Sciences Physiques

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Méthodes mathématiques et numériques pour les équations aux dérivées partielles

Author : CHASKALOVIC Joël
Publisher : Lavoisier
ISBN 13 : 2743064803
Total Pages : 382 pages
Book Rating : 4.7/5 (43 download)

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Book Synopsis Méthodes mathématiques et numériques pour les équations aux dérivées partielles by : CHASKALOVIC Joël

Download or read book Méthodes mathématiques et numériques pour les équations aux dérivées partielles written by CHASKALOVIC Joël and published by Lavoisier. This book was released on 2013-01-21 with total page 382 pages. Available in PDF, EPUB and Kindle. Book excerpt: Qu’il s’agisse d’applications en physique ou en mécanique, en médecine ou en biologie, mais aussi en économie, dans les médias et en marketing, ou encore dans le domaine des finances, la traduction phénoménologique du système étudié conduit très souvent à la résolution d’équations différentielles ou aux dérivées partielles. Incontestablement, ce sont les éléments finis qui ont bouleversé le monde de l’approximation numérique des équations aux dérivées partielles. Cet ouvrage est composé de deux parties : la première est un abrégé de cours portant sur les outils de base de l’analyse mathématique des équations aux dérivées partielles et la seconde contient des problèmes corrigés qui abordent l’approximation par éléments finis des formulations variationnelles des problèmes aux limites elliptiques. Des applications en mécanique des solides déformables, à la résistance des matériaux, en mécanique des fluides et en thermique ainsi que quelques problèmes non linéaires y sont présentés.Cet ouvrage s'adresse aux étudiants en sciences et techniques de l'ingénieur des universités et des grandes écoles.

Mathematical Methods in Aerodynamics

Author : Lazãr Dragos
Publisher : Springer Science & Business Media
ISBN 13 : 9781402016639
Total Pages : 626 pages
Book Rating : 4.0/5 (166 download)

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Book Synopsis Mathematical Methods in Aerodynamics by : Lazãr Dragos

Download or read book Mathematical Methods in Aerodynamics written by Lazãr Dragos and published by Springer Science & Business Media. This book was released on 2003 with total page 626 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book provides a solid and unitary mathematical foundation of the basic and advanced principles of aerodynamics. The densities of the fundamental solutions are determined from singular integral equations. The fundamental solutions method in aerodynamics was considered for the first time and used by the author in over 30 papers published in prestigious journals (e.g. QAM, AIAA, ZAMM, etc) in order to develop a unitary theory. The boundary element method is used for numerical approximations in compressible aerodynamics. The text incorporates several original contributions, among other traditional mathematical methods. The book also represents a comprehensive presentation of research results since the seminal books on aerodynamics of Ashley and Landahl (1965) and Katz & Plotkin (1991). A rigorous mathematical approach is used to present and explain classic and modern results in this field of science. The author has therefore conceived several appendices on the Distribution Theory, the singular Integral Equations Theory, the Finite Part, Gauss Quadrature Formulae, etc. The book is concluded by a relevant bibliographical list which is especially useful for researchers. The book is aimed primarily at applied mathematicians, aeronautical engineers and space science researchers. The text may be used also as a comprehensive introduction to the mathematical foundations fo aerodynamics, by graduate students n engineering and fluid dynamics with a strong mathematical background.

Mathematical and Numerical Methods for Partial Differential Equations

Author : Joël Chaskalovic
Publisher : Springer
ISBN 13 : 3319035630
Total Pages : 362 pages
Book Rating : 4.3/5 (19 download)

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Book Synopsis Mathematical and Numerical Methods for Partial Differential Equations by : Joël Chaskalovic

Download or read book Mathematical and Numerical Methods for Partial Differential Equations written by Joël Chaskalovic and published by Springer. This book was released on 2014-05-16 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: This self-tutorial offers a concise yet thorough introduction into the mathematical analysis of approximation methods for partial differential equation. A particular emphasis is put on finite element methods. The unique approach first summarizes and outlines the finite-element mathematics in general and then in the second and major part, formulates problem examples that clearly demonstrate the techniques of functional analysis via numerous and diverse exercises. The solutions of the problems are given directly afterwards. Using this approach, the author motivates and encourages the reader to actively acquire the knowledge of finite- element methods instead of passively absorbing the material as in most standard textbooks. This English edition is based on the Finite Element Methods for Engineering Sciences by Joel Chaskalovic.

Geometric, Algebraic and Topological Methods for Quantum Field Theory

Author : Sylvie Payche
Publisher : World Scientific
ISBN 13 : 9814460052
Total Pages : 378 pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Geometric, Algebraic and Topological Methods for Quantum Field Theory by : Sylvie Payche

Download or read book Geometric, Algebraic and Topological Methods for Quantum Field Theory written by Sylvie Payche and published by World Scientific. This book was released on 2014 with total page 378 pages. Available in PDF, EPUB and Kindle. Book excerpt: Based on lectures held at the 7th Villa de Leyva summer school, this book presents an introduction to topics of current interest in the interface of geometry, topology and physics. It is aimed at graduate students in physics or mathematics with interests in geometric, algebraic as well as topological methods and their applications to quantum field theory. This volume contains the written notes corresponding to lectures given by experts in the field. They cover current topics of research in a way that is suitable for graduate students of mathematics or physics interested in the recent developments and interactions between geometry, topology and physics. The book also contains contributions by younger participants, displaying the ample range of topics treated in the school. A key feature of the present volume is the provision of a pedagogical presentation of rather advanced topics, in a way which is suitable for both mathematicians and physicists.

Finite Element Methods for Engineering Sciences

Author : Joel Chaskalovic
Publisher : Springer Science & Business Media
ISBN 13 : 3540763430
Total Pages : 261 pages
Book Rating : 4.5/5 (47 download)

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Book Synopsis Finite Element Methods for Engineering Sciences by : Joel Chaskalovic

Download or read book Finite Element Methods for Engineering Sciences written by Joel Chaskalovic and published by Springer Science & Business Media. This book was released on 2008-09-16 with total page 261 pages. Available in PDF, EPUB and Kindle. Book excerpt: This self-tutorial offers a concise yet thorough grounding in the mathematics necessary for successfully applying FEMs to practical problems in science and engineering. The unique approach first summarizes and outlines the finite-element mathematics in general and then, in the second and major part, formulates problem examples that clearly demonstrate the techniques of functional analysis via numerous and diverse exercises. The solutions of the problems are given directly afterwards. Using this approach, the author motivates and encourages the reader to actively acquire the knowledge of finite-element methods instead of passively absorbing the material, as in most standard textbooks. The enlarged English-language edition, based on the original French, also contains a chapter on the approximation steps derived from the description of nature with differential equations and then applied to the specific model to be used. Furthermore, an introduction to tensor calculus using distribution theory offers further insight for readers with different mathematical backgrounds.

A Collection of Problems on the Equations of Mathematical Physics

Author : Vasilij S. Vladimirov
Publisher : Springer Science & Business Media
ISBN 13 : 3662055589
Total Pages : 288 pages
Book Rating : 4.6/5 (62 download)

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Book Synopsis A Collection of Problems on the Equations of Mathematical Physics by : Vasilij S. Vladimirov

Download or read book A Collection of Problems on the Equations of Mathematical Physics written by Vasilij S. Vladimirov and published by Springer Science & Business Media. This book was released on 2013-11-09 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: The extensive application of modern mathematical teehniques to theoretical and mathematical physics requires a fresh approach to the course of equations of mathematical physics. This is especially true with regards to such a fundamental concept as the 80lution of a boundary value problem. The concept of a generalized solution considerably broadens the field of problems and enables solving from a unified position the most interesting problems that cannot be solved by applying elassical methods. To this end two new courses have been written at the Department of Higher Mathematics at the Moscow Physics anrl Technology Institute, namely, "Equations of Mathematical Physics" by V. S. Vladimirov and "Partial Differential Equations" by V. P. Mikhailov (both books have been translated into English by Mir Publishers, the first in 1984 and the second in 1978). The present collection of problems is based on these courses and amplifies them considerably. Besides the classical boundary value problems, we have ineluded a large number of boundary value problems that have only generalized solutions. Solution of these requires using the methods and results of various branches of modern analysis. For this reason we have ineluded problems in Lebesgue in tegration, problems involving function spaces (especially spaces of generalized differentiable functions) and generalized functions (with Fourier and Laplace transforms), and integral equations.

Methods of the Theory of Generalized Functions

Author : V. S. Vladimirov
Publisher : CRC Press
ISBN 13 : 9780415273565
Total Pages : 332 pages
Book Rating : 4.2/5 (735 download)

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Book Synopsis Methods of the Theory of Generalized Functions by : V. S. Vladimirov

Download or read book Methods of the Theory of Generalized Functions written by V. S. Vladimirov and published by CRC Press. This book was released on 2002-08-15 with total page 332 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents the general theory of generalized functions, including the Fourier, Laplace, Mellin, Hilbert, Cauchy-Bochner and Poisson integral transforms and operational calculus, with the traditional material augmented by the theory of Fourier series, abelian theorems, and boundary values of helomorphic functions for one and several variables. The author addresses several facets in depth, including convolution theory, convolution algebras and convolution equations in them, homogenous generalized functions, and multiplication of generalized functions. This book will meet the needs of researchers, engineers, and students of applied mathematics, control theory, and the engineering sciences.

Boundary Value Problems of Mathematical Physics

Author : Olʹga A. Ladyženskaja
Publisher : American Mathematical Soc.
ISBN 13 : 9780821830680
Total Pages : 224 pages
Book Rating : 4.8/5 (36 download)

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Book Synopsis Boundary Value Problems of Mathematical Physics by : Olʹga A. Ladyženskaja

Download or read book Boundary Value Problems of Mathematical Physics written by Olʹga A. Ladyženskaja and published by American Mathematical Soc.. This book was released on 1981 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Functional Analysis Tools for Practical Use in Sciences and Engineering

Author : Carlos A. de Moura
Publisher : Springer Nature
ISBN 13 : 3031105982
Total Pages : 223 pages
Book Rating : 4.0/5 (311 download)

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Book Synopsis Functional Analysis Tools for Practical Use in Sciences and Engineering by : Carlos A. de Moura

Download or read book Functional Analysis Tools for Practical Use in Sciences and Engineering written by Carlos A. de Moura and published by Springer Nature. This book was released on 2022-10-13 with total page 223 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook describes selected topics in functional analysis as powerful tools of immediate use in many fields within applied mathematics, physics and engineering. It follows a very reader-friendly structure, with the presentation and the level of exposition especially tailored to those who need functional analysis but don’t have a strong background in this branch of mathematics. For every tool, this work emphasizes the motivation, the justification for the choices made, and the right way to employ the techniques. Proofs appear only when necessary for the safe use of the results. The book gently starts with a road map to guide reading. A subsequent chapter recalls definitions and notation for abstract spaces and some function spaces, while Chapter 3 enters dual spaces. Tools from Chapters 2 and 3 find use in Chapter 4, which introduces distributions. The Linear Functional Analysis basic triplet makes up Chapter 5, followed by Chapter 6, which introduces the concept of compactness. Chapter 7 brings a generalization of the concept of derivative for functions defined in normed spaces, while Chapter 8 discusses basic results about Hilbert spaces that are paramount to numerical approximations. The last chapter brings remarks to recent bibliographical items. Elementary examples included throughout the chapters foster understanding and self-study. By making key, complex topics more accessible, this book serves as a valuable resource for researchers, students, and practitioners alike that need to rely on solid functional analysis but don’t need to delve deep into the underlying theory.

Numerical Simulation in Physics and Engineering

Author : Inmaculada Higueras
Publisher : Springer
ISBN 13 : 3319321463
Total Pages : 256 pages
Book Rating : 4.3/5 (193 download)

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Book Synopsis Numerical Simulation in Physics and Engineering by : Inmaculada Higueras

Download or read book Numerical Simulation in Physics and Engineering written by Inmaculada Higueras and published by Springer. This book was released on 2016-07-01 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents lecture notes from the XVI ‘Jacques-Louis Lions’ Spanish-French School on Numerical Simulation in Physics and Engineering, held in Pamplona (Navarra, Spain) in September 2014. The subjects covered include: numerical analysis of isogeometric methods, convolution quadrature for wave simulations, mathematical methods in image processing and computer vision, modeling and optimization techniques in food processes, bio-processes and bio-systems, and GPU computing for numerical simulation. The book is highly recommended to graduate students in Engineering or Science who want to focus on numerical simulation, either as a research topic or in the field of industrial applications. It can also benefit senior researchers and technicians working in industry who are interested in the use of state-of-the-art numerical techniques in the fields addressed here. Moreover, the book can be used as a textbook for master courses in Mathematics, Physics, or Engineering.

Quantum Field Theory I: Basics in Mathematics and Physics

Author : Eberhard Zeidler
Publisher : Springer Science & Business Media
ISBN 13 : 354034764X
Total Pages : 1060 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis Quantum Field Theory I: Basics in Mathematics and Physics by : Eberhard Zeidler

Download or read book Quantum Field Theory I: Basics in Mathematics and Physics written by Eberhard Zeidler and published by Springer Science & Business Media. This book was released on 2007-04-18 with total page 1060 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first volume of a modern introduction to quantum field theory which addresses both mathematicians and physicists, at levels ranging from advanced undergraduate students to professional scientists. The book bridges the acknowledged gap between the different languages used by mathematicians and physicists. For students of mathematics the author shows that detailed knowledge of the physical background helps to motivate the mathematical subjects and to discover interesting interrelationships between quite different mathematical topics. For students of physics, fairly advanced mathematics is presented, which goes beyond the usual curriculum in physics.

Geometric Methods in Physics XXXVI

Author : Piotr Kielanowski
Publisher : Springer
ISBN 13 : 3030011569
Total Pages : 409 pages
Book Rating : 4.0/5 (3 download)

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Book Synopsis Geometric Methods in Physics XXXVI by : Piotr Kielanowski

Download or read book Geometric Methods in Physics XXXVI written by Piotr Kielanowski and published by Springer. This book was released on 2019-03-11 with total page 409 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book collects papers based on the XXXVI Białowieża Workshop on Geometric Methods in Physics, 2017. The Workshop, which attracts a community of experts active at the crossroads of mathematics and physics, represents a major annual event in the field. Based on presentations given at the Workshop, the papers gathered here are previously unpublished, at the cutting edge of current research, and primarily grounded in geometry and analysis, with applications to classical and quantum physics. In addition, a Special Session was dedicated to S. Twareque Ali, a distinguished mathematical physicist at Concordia University, Montreal, who passed away in January 2016. For the past six years, the Białowieża Workshops have been complemented by a School on Geometry and Physics, comprising a series of advanced lectures for graduate students and early-career researchers. The extended abstracts of this year’s lecture series are also included here. The unique character of the Workshop-and-School series is due in part to the venue: a famous historical, cultural and environmental site in the Białowieża forest, a UNESCO World Heritage Centre in eastern Poland. Lectures are given in the Nature and Forest Museum, and local traditions are interwoven with the scientific activities.

Electromagnetic Optics of Thin-Film Coatings

Author : Claude Amra
Publisher : Cambridge University Press
ISBN 13 : 1108488870
Total Pages : 395 pages
Book Rating : 4.1/5 (84 download)

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Book Synopsis Electromagnetic Optics of Thin-Film Coatings by : Claude Amra

Download or read book Electromagnetic Optics of Thin-Film Coatings written by Claude Amra and published by Cambridge University Press. This book was released on 2021-01-14 with total page 395 pages. Available in PDF, EPUB and Kindle. Book excerpt: A theoretical, self-contained study of periodic multilayers and how they can be effectively exploited in both traditional and modern applications.

Second-Order Equations With Nonnegative Characteristic Form

Author : O. Oleinik
Publisher : Springer Science & Business Media
ISBN 13 : 1468489658
Total Pages : 265 pages
Book Rating : 4.4/5 (684 download)

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Book Synopsis Second-Order Equations With Nonnegative Characteristic Form by : O. Oleinik

Download or read book Second-Order Equations With Nonnegative Characteristic Form written by O. Oleinik and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 265 pages. Available in PDF, EPUB and Kindle. Book excerpt: Second order equations with nonnegative characteristic form constitute a new branch of the theory of partial differential equations, having arisen within the last 20 years, and having undergone a particularly intensive development in recent years. An equation of the form (1) is termed an equation of second order with nonnegative characteristic form on a set G, kj if at each point x belonging to G we have a (xHk~j ~ 0 for any vector ~ = (~l' ... '~m)' In equation (1) it is assumed that repeated indices are summed from 1 to m, and x = (x l' ••• , x ). Such equations are sometimes also called degenerating m elliptic equations or elliptic-parabolic equations. This class of equations includes those of elliptic and parabolic types, first order equations, ultraparabolic equations, the equations of Brownian motion, and others. The foundation of a general theory of second order equations with nonnegative characteristic form has now been established, and the purpose of this book is to pre sent this foundation. Special classes of equations of the form (1), not coinciding with the well-studied equations of elliptic or parabolic type, were investigated long ago, particularly in the paper of Picone [105], published some 60 years ago.

Fractional Calculus with Applications in Mechanics

Author : Teodor M. Atanackovic
Publisher : John Wiley & Sons
ISBN 13 : 1848216793
Total Pages : 437 pages
Book Rating : 4.8/5 (482 download)

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Book Synopsis Fractional Calculus with Applications in Mechanics by : Teodor M. Atanackovic

Download or read book Fractional Calculus with Applications in Mechanics written by Teodor M. Atanackovic and published by John Wiley & Sons. This book was released on 2014-03-17 with total page 437 pages. Available in PDF, EPUB and Kindle. Book excerpt: The books Fractional Calculus with Applications in Mechanics: Vibrations and Diffusion Processes and Fractional Calculus with Applications in Mechanics: Wave Propagation, Impact and Variational Principles contain various applications of fractional calculus to the fields of classical mechanics. Namely, the books study problems in fields such as viscoelasticity of fractional order, lateral vibrations of a rod of fractional order type, lateral vibrations of a rod positioned on fractional order viscoelastic foundations, diffusion-wave phenomena, heat conduction, wave propagation, forced oscillations of a body attached to a rod, impact and variational principles of a Hamiltonian type. The books will be useful for graduate students in mechanics and applied mathematics, as well as for researchers in these fields. Part 1 of this book presents an introduction to fractional calculus. Chapter 1 briefly gives definitions and notions that are needed later in the book and Chapter 2 presents definitions and some of the properties of fractional integrals and derivatives. Part 2 is the central part of the book. Chapter 3 presents the analysis of waves in fractional viscoelastic materials in infinite and finite spatial domains. In Chapter 4, the problem of oscillations of a translatory moving rigid body, attached to a heavy, or light viscoelastic rod of fractional order type, is studied in detail. In Chapter 5, the authors analyze a specific engineering problem of the impact of a viscoelastic rod against a rigid wall. Finally, in Chapter 6, some results for the optimization of a functional containing fractional derivatives of constant and variable order are presented.

Analytic Number Theory

Author : Carl Pomerance
Publisher : Springer
ISBN 13 : 3319222406
Total Pages : 378 pages
Book Rating : 4.3/5 (192 download)

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Book Synopsis Analytic Number Theory by : Carl Pomerance

Download or read book Analytic Number Theory written by Carl Pomerance and published by Springer. This book was released on 2015-11-18 with total page 378 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains a collection of research and survey papers written by some of the most eminent mathematicians in the international community and is dedicated to Helmut Maier, whose own research has been groundbreaking and deeply influential to the field. Specific emphasis is given to topics regarding exponential and trigonometric sums and their behavior in short intervals, anatomy of integers and cyclotomic polynomials, small gaps in sequences of sifted prime numbers, oscillation theorems for primes in arithmetic progressions, inequalities related to the distribution of primes in short intervals, the Möbius function, Euler’s totient function, the Riemann zeta function and the Riemann Hypothesis. Graduate students, research mathematicians, as well as computer scientists and engineers who are interested in pure and interdisciplinary research, will find this volume a useful resource. Contributors to this volume: Bill Allombert, Levent Alpoge, Nadine Amersi, Yuri Bilu, Régis de la Bretèche, Christian Elsholtz, John B. Friedlander, Kevin Ford, Daniel A. Goldston, Steven M. Gonek, Andrew Granville, Adam J. Harper, Glyn Harman, D. R. Heath-Brown, Aleksandar Ivić, Geoffrey Iyer, Jerzy Kaczorowski, Daniel M. Kane, Sergei Konyagin, Dimitris Koukoulopoulos, Michel L. Lapidus, Oleg Lazarev, Andrew H. Ledoan, Robert J. Lemke Oliver, Florian Luca, James Maynard, Steven J. Miller, Hugh L. Montgomery, Melvyn B. Nathanson, Ashkan Nikeghbali, Alberto Perelli, Amalia Pizarro-Madariaga, János Pintz, Paul Pollack, Carl Pomerance, Michael Th. Rassias, Maksym Radziwiłł, Joël Rivat, András Sárközy, Jeffrey Shallit, Terence Tao, Gérald Tenenbaum, László Tóth, Tamar Ziegler, Liyang Zhang.

Integral Equation Methods for Evolutionary PDE

Author : Lehel Banjai
Publisher : Springer Nature
ISBN 13 : 3031132203
Total Pages : 283 pages
Book Rating : 4.0/5 (311 download)

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Book Synopsis Integral Equation Methods for Evolutionary PDE by : Lehel Banjai

Download or read book Integral Equation Methods for Evolutionary PDE written by Lehel Banjai and published by Springer Nature. This book was released on 2022-11-08 with total page 283 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a comprehensive analysis of time domain boundary integral equations and their discretisation by convolution quadrature and the boundary element method. Properties of convolution quadrature, based on both linear multistep and Runge–Kutta methods, are explained in detail, always with wave propagation problems in mind. Main algorithms for implementing the discrete schemes are described and illustrated by short Matlab codes; translation to other languages can be found on the accompanying GitHub page. The codes are used to present numerous numerical examples to give the reader a feeling for the qualitative behaviour of the discrete schemes in practice. Applications to acoustic and electromagnetic scattering are described with an emphasis on the acoustic case where the fully discrete schemes for sound-soft and sound-hard scattering are developed and analysed in detail. A strength of the book is that more advanced applications such as linear and non-linear impedance boundary conditions and FEM/BEM coupling are also covered. While the focus is on wave scattering, a chapter on parabolic problems is included which also covers the relevant fast and oblivious algorithms. Finally, a brief description of data sparse techniques and modified convolution quadrature methods completes the book. Suitable for graduate students and above, this book is essentially self-contained, with background in mathematical analysis listed in the appendix along with other useful facts. Although not strictly necessary, some familiarity with boundary integral equations for steady state problems is desirable.