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This volume forms a record of the lectures given at this International Conference. Under the general heading of the equations of mathematical physics, contributions are included on a broad range of topics in the theory and applications of ordinary and partial differential equations, including both linear and non-linear equations. The topics cover a wide variety of methods (spectral, theoretical, variational, topological, semi-group), and a equally wide variety of equations including the Laplace equation, Navier-Stokes equations, Boltzmann's equation, reaction-diffusion equations, Schroedinger

Differential equations --- Equations différentielles --- Congresses. --- Congrès --- Congresses --- Mathematical analysis --- 517.1 Mathematical analysis --- 517.91 Differential equations --- Differential equations - Congresses

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This comprehensive history traces the development of mathematical ideas and the careers of the men responsible for them. Volume 1 looks at the discipline's origins in Babylon and Egypt, the creation of geometry and trigonometry by the Greeks, and the role of mathematics in the medieval and early modern periods. Volume 2 focuses on calculus, the rise of analysis in the nineteenth century, and the number theories of Dedekind and Dirichlet. The concluding volume covers the revival of projective geometry, the emergence of abstract algebra, the beginnings of topology, and the influence of Gdel on recent mathematical study.

Mathematics --- Mathematical analysis --- 517.1 Mathematical analysis --- Math --- Science --- History. --- Mathématiques --- History --- Histoire. --- Mathématiques --- Histoire --- Mathematics - History

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Number theory --- Mathematical analysis --- Congresses. --- 51 --- -Number theory --- -Number study --- Numbers, Theory of --- Algebra --- Advanced calculus --- Analysis (Mathematics) --- Mathematics --- Congresses --- 517.1 Mathematical analysis --- 51 Mathematics --- -Mathematics --- -51 Mathematics --- Number study --- 517.1 --- Mathematical analysis - Congresses. --- Number theory - Congresses.

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This book lays the algebraic foundations of a Galois theory of linear difference equations and shows its relationship to the analytic problem of finding meromorphic functions asymptotic to formal solutions of difference equations. Classically, this latter question was attacked by Birkhoff and Tritzinsky and the present work corrects and greatly generalizes their contributions. In addition results are presented concerning the inverse problem in Galois theory, effective computation of Galois groups, algebraic properties of sequences, phenomena in positive characteristics, and q-difference equations. The book is aimed at advanced graduate researchers and researchers.

Group theory --- Functional analysis --- Difference equations --- Galois theory --- Mathematical Theory --- Operations Research --- Mathematics --- Civil & Environmental Engineering --- Physical Sciences & Mathematics --- Engineering & Applied Sciences --- Equations aux differences --- Galois [Theorie de ] --- Galois [Theorie van ] --- Vergelijkingen met differenties --- Mathematical analysis. --- Analysis (Mathematics). --- Algebra. --- Analysis. --- Mathematical analysis --- 517.1 Mathematical analysis --- Difference equations. --- Galois theory. --- Equations, Theory of --- Number theory --- Calculus of differences --- Differences, Calculus of --- Equations, Difference

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Scattering theory is, roughly speaking, perturbation theory of self-adjoint operators on the (absolutely) continuous spectrum. It has its origin in mathematical problems of quantum mechanics and is intimately related to the theory of partial differential equations. Some recently solved problems, such as asymptotic completeness for the Schrödinger operator with long-range and multiparticle potentials, as well as open problems, are discussed. Potentials for which asymptotic completeness is violated are also constructed. This corresponds to a new class of asymptotic solutions of the time-dependent Schrödinger equation. Special attention is paid to the properties of the scattering matrix, which is the main observable of the theory. The book is addressed to readers interested in a deeper study of the subject.

Operator theory --- Scattering (Mathematics) --- Mathematical Theory --- Calculus --- Mathematics --- Physical Sciences & Mathematics --- Mathematical analysis. --- Analysis (Mathematics). --- Functional analysis. --- Integral equations. --- Partial differential equations. --- Mathematical physics. --- Analysis. --- Functional Analysis. --- Integral Equations. --- Partial Differential Equations. --- Theoretical, Mathematical and Computational Physics. --- Physical mathematics --- Physics --- Partial differential equations --- Equations, Integral --- Functional equations --- Functional analysis --- Functional calculus --- Calculus of variations --- Integral equations --- 517.1 Mathematical analysis --- Mathematical analysis