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This book resulted from the author's fascination with the mathematical beauty of integral equations. It is an attempt to combine theory, applications, and numerical methods, and cover each of these fields with the same weight. In order to make the book accessible to mathematicians, physicists, and engineers, the author has made the work as self-contained as possible, by requiring only a solid foundation in differential and integral calculus. The functional analysis which is necessary for an adequate treatment of the theory and the numerical solution of integral equations is developed within the book. Problems are included at the end of each chapter. For the second edition, in addition to corrections and adjustments throughout the text, as well as an updated reference section, new topics have been added.

Integral equations --- Equations intégrales --- Integral equations. --- Equations intégrales --- Mathematical analysis. --- Analysis (Mathematics). --- Analysis. --- 517.1 Mathematical analysis --- Mathematical analysis --- Equations, Integral --- Functional equations --- Functional analysis

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517.9 --- Engineering design --- -Nonlinear systems --- -#KVIV:BB --- Systems, Nonlinear --- System theory --- Design, Engineering --- Engineering --- Industrial design --- Strains and stresses --- Differential equations. Integral equations. Other functional equations. Finite differences. Calculus of variations. Functional analysis --- Mathematical models --- Design --- Nonlinear systems --- Mathematical models. --- 517.9 Differential equations. Integral equations. Other functional equations. Finite differences. Calculus of variations. Functional analysis --- #KVIV:BB --- Engineering design. --- Modeling. --- Mathematics. --- MODELLING --- Nonlinear systems. --- Math --- Science --- Models, Mathematical --- Simulation methods --- Clay modeling --- Modelling --- Molding (Clay, plaster, etc.) --- Clay --- Sculpture --- Technique --- Monograph

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Numerical analysis --- Mathematical optimization --- Programming (Mathematics) --- Optimisation mathématique --- Programmation (Mathématiques) --- Théorie des jeux --- Mathematical optimization. --- 519.8 --- 519.8 Operational research --- Operational research --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Maxima and minima --- Operations research --- Simulation methods --- System analysis --- Mathematical programming --- Goal programming --- Algorithms --- Functional equations --- Programmation (mathématiques) --- Numerical methods of optimisation

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[Infotext]((Kurztext))These are the proceedings of the 7th International Conference on Hyperbolic Problems, held in Zürich in February 1998. The speakers and contributors have been rigorously selected and present the state of the art in this field. The articles, both theoretical and numerical, encompass a wide range of applications, such as nonlinear waves in solids, various computational fluid dynamics from small-scale combustion to relativistic astrophysical problems, multiphase phenomena and geometrical optics. ((Volltext))These proceedings contain, in two volumes, approximately one hundred papers presented at the conference on hyperbolic problems, which has focused to a large extent on the laws of nonlinear hyperbolic conservation. Two-fifths of the papers are devoted to mathematical aspects such as global existence, uniqueness, asymptotic behavior such as large time stability, stability and instabilities of waves and structures, various limits of the solution, the Riemann problem and so on. Roughly the same number of articles are devoted to numerical analysis, for example stability and convergence of numerical schemes, as well as schemes with special desired properties such as shock capturing, interface fitting and high-order approximations to multidimensional systems. The results in these contributions, both theoretical and numerical, encompass a wide range of applications such as nonlinear waves in solids, various computational fluid dynamics from small-scale combustion to relativistic astrophysical problems, multiphase phenomena and geometrical optics.

Differential equations, Hyperbolic --- Differential equations, Nonlinear --- 519.6 --- 517.9 --- 681.3*G18 --- 681.3 *G18 Partial differential equations: difference methods; elliptic equations; finite element methods; hyperbolic equations; method of lines; parabolic equations (Numerical analysis) --- Partial differential equations: difference methods; elliptic equations; finite element methods; hyperbolic equations; method of lines; parabolic equations (Numerical analysis) --- 517.9 Differential equations. Integral equations. Other functional equations. Finite differences. Calculus of variations. Functional analysis --- Differential equations. Integral equations. Other functional equations. Finite differences. Calculus of variations. Functional analysis --- 519.6 Computational mathematics. Numerical analysis. Computer programming --- Computational mathematics. Numerical analysis. Computer programming --- Conferences - Meetings --- 681.3 *G18 --- Mathematical analysis. --- Analysis (Mathematics). --- Numerical analysis. --- Applied mathematics. --- Engineering mathematics. --- Analysis. --- Numerical Analysis. --- Mathematical and Computational Engineering. --- Engineering --- Engineering analysis --- Mathematical analysis --- 517.1 Mathematical analysis --- Mathematics --- Differential equations, Hyperbolic - Congresses.

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Harmonic analysis. Fourier analysis --- Fourier analysis --- Analyse de Fourier --- 517.518.5 --- 517.518.4 --- Analysis, Fourier --- Mathematical analysis --- Theory of the Fourier integral --- Trigonometric series --- Fourier analysis. --- 517.518.4 Trigonometric series --- 517.518.5 Theory of the Fourier integral --- Functional analysis. --- Applied mathematics. --- Engineering mathematics. --- Mathematical analysis. --- Analysis (Mathematics). --- Computational intelligence. --- Chemometrics. --- Functional Analysis. --- Applications of Mathematics. --- Analysis. --- Computational Intelligence. --- Math. Applications in Chemistry. --- Chemistry, Analytic --- Analytical chemistry --- Chemistry --- Intelligence, Computational --- Artificial intelligence --- Soft computing --- 517.1 Mathematical analysis --- Engineering --- Engineering analysis --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations --- Mathematics --- Measurement --- Statistical methods