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Differential equations --- Banach spaces. --- Differential equations. --- Functional analysis. --- Hilbert space. --- Functional analysis --- Hilbert space --- Banach spaces

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Analyse --- Mathématiques --- Wiskunde --- Hilbert, Espaces de --- Hilbert space --- Hilbert space. --- Distributions, Théorie des (analyse fonctionnelle) --- Mathematiques --- Analyse mathematique --- Analyse fonctionnelle --- Problemes et exercices --- Problemes --- Espaces particuliers --- Espaces de lebesgue

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Semiclassical approximation addresses the important relationship between quantum and classical mechanics. There has been a very strong development in the mathematical theory, mainly thanks to methods of microlocal analysis. This book develops the basic methods, including the WKB-method, stationary phase and h-pseudodifferential operators. The applications include results on the tunnel effect, the asymptotics of eigenvalues in relation to classical trajectories and normal forms, plus slow perturbations of periodic Schrödinger operators appearing in solid state physics. No previous specialized knowledge in quantum mechanics or microlocal analysis is assumed, and only general facts about spectral theory in Hilbert space, distributions, Fourier transforms and some differential geometry belong to the prerequisites. This book is addressed to researchers and graduate students in mathematical analysis, as well as physicists who are interested in rigorous results. A fairly large fraction can be (and has been) covered in a one semester course.

Microlocal analysis. --- Quantum theory. --- Approximation theory. --- Spectral theory (Mathematics) --- Mathematical physics. --- Physical mathematics --- Physics --- Functional analysis --- Hilbert space --- Measure theory --- Transformations (Mathematics) --- Theory of approximation --- Functions --- Polynomials --- Chebyshev systems --- Quantum dynamics --- Quantum mechanics --- Quantum physics --- Mechanics --- Thermodynamics --- Mathematics

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Traditionally spectral methods in fluid dynamics were used in direct and large eddy simulations of turbulent flow in simply connected computational domains. The methods are now being applied to more complex geometries, and the spectral/hp element method, which incorporates both multi-domain spectral methods and high-order finite element methods, has been particularly successful. This book provides a comprehensive introduction to these methods. Written by leaders in the field, the book begins with a full explanation of fundamental concepts and implementation issues. It then illustrates how thes

Fluid dynamics. --- Spectral theory (Mathematics) --- Finite element method. --- FEA (Numerical analysis) --- FEM (Numerical analysis) --- Finite element analysis --- Numerical analysis --- Isogeometric analysis --- Functional analysis --- Hilbert space --- Measure theory --- Transformations (Mathematics) --- Dynamics --- Fluid mechanics --- Finite element method --- Fluid dynamics --- 519.6 --- 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) --- 519.6 Computational mathematics. Numerical analysis. Computer programming --- Computational mathematics. Numerical analysis. Computer programming --- Spectral theory (Mathematics).