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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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Volterra equations. --- Inverse problems (Differential equations) --- Differential equations --- Equations, Volterra --- Integral equations

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517.9 --- Differential equations. Integral equations. Other functional equations. Finite differences. Calculus of variations. Functional analysis --- Mathematical models. --- Science --- Engineering --- 517.9 Differential equations. Integral equations. Other functional equations. Finite differences. Calculus of variations. Functional analysis

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There has in recent years been a remarkable growth of interest in the area of discrete integrable systems. Much progress has been made by applying symmetry groups to the study of differential equations, and connections have been made to other topics such as numerical methods, cellular automata and mathematical physics. This volume comprises state of the art articles from almost all the leading workers in this important and rapidly developing area, making it a necessary resource for all researchers interested in discrete integrable systems or related subjects.

Difference equations --- Hypergeometric functions --- Symmetry (Physics) --- Functions, Hypergeometric --- Transcendental functions --- Hypergeometric series --- Calculus of differences --- Differences, Calculus of --- Equations, Difference --- 517.96 --- 517.96 Finite differences. Functional and integral equations --- Finite differences. Functional and integral equations --- Congresses --- Congresses. --- Difference equations - Congresses --- Hypergeometric functions - Congresses --- Symmetry (Physics) - Congresses

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Differential equations --- Numerical solutions. --- 517.9 --- -Lie groups --- 519.6 --- 681.3*G17 --- Groups, Lie --- Lie algebras --- Symmetric spaces --- Topological groups --- Equations, Differential --- Bessel functions --- Calculus --- Differential equations. Integral equations. Other functional equations. Finite differences. Calculus of variations. Functional analysis --- Numerical solutions --- Computational mathematics. Numerical analysis. Computer programming --- Ordinary differential equations: boundary value problems; convergence and stability; error analysis; initial value problems; multistep methods; single step methods; stiff equations (Numerical analysis) --- Lie groups. --- 681.3*G17 Ordinary differential equations: boundary value problems; convergence and stability; error analysis; initial value problems; multistep methods; single step methods; stiff equations (Numerical analysis) --- 519.6 Computational mathematics. Numerical analysis. Computer programming --- 517.91 Differential equations --- 517.9 Differential equations. Integral equations. Other functional equations. Finite differences. Calculus of variations. Functional analysis --- Lie groups --- 517.91 --- Numerical solutions&delete& --- Differential equations - Numerical solutions.