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Fourier analysis --- Analysis, Fourier --- Fourier analysis. --- Mathematical analysis

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Harmonic analysis. Fourier analysis --- FT (Fourier transformatie) --- Fourieranalyse --- Fourier analysis --- Fourier transformations --- 517 --- algoritmen --- analyse --- Transformations, Fourier --- Transforms, Fourier --- Transformations (Mathematics) --- Analysis, Fourier --- Mathematical analysis

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Fourier Analysis and Boundary Value Problems provides a thorough examination of both the theory and applications of partial differential equations and the Fourier and Laplace methods for their solutions. Boundary value problems, including the heat and wave equations, are integrated throughout the book. Written from a historical perspective with extensive biographical coverage of pioneers in the field, the book emphasizes the important role played by partial differential equations in engineering and physics. In addition, the author demonstrates how efforts to deal with these problems hav

Fourier analysis. --- Boundary value problems --- Numerical solutions. --- Analysis, Fourier --- Mathematical analysis

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Fondée sur la théorie métaxiale de G. Bonnet et sur l’emploi de la transformation de Fourier fractionnaire, la présentation de l'optique de Fourier adoptée dans cet ouvrage est originale et renouvelle en grande partie le sujet. Outre les thèmes traités habituellement dans ce domaine – diffraction scalaire, formation des images, transfert de la cohérence, holographie, filtrage et corrélation optiques –, le livre inclut une théorie fractionnaire des résonateurs optiques et des faisceaux gaussiens, ou développe encore l’analogie entre diffraction et dispersion de groupe dans les fibres optiques, élargissant de la sorte le champ de la discipline. Issu de l’enseignement dispensé par l’auteur à l’Université et en écoles d’ingénieurs, étayé par ses propres recherches, le livre s’adresse autant à des étudiants en mastère de physique ou des élèves-ingénieurs qu’à des chercheurs ou ingénieurs souhaitant s’initier à l’optique de Fourier fractionnaire. Pierre Pellat-Finet est professeur à l’université de Bretagne-Sud, où il enseigne la physique. Il est également chercheur associé à Télécom Bretagne et professeur associé à l’université nationale de Colombie à Medellin. Ses travaux de recherche portent sur le traitement du signal optique, les télécommunications optiques, la représentation mathématique de la lumière polarisée et l’optique de Fourier fractionnaire.

Fourier analysis. --- Physics. --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- Dynamics --- Analysis, Fourier --- Mathematical analysis

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Nonlinear resonance analysis is a unique mathematical tool that can be used to study resonances in relation to, but independently of, any single area of application. This is the first book to present the theory of nonlinear resonances as a new scientific field, with its own theory, computational methods, applications and open questions. The book includes several worked examples, mostly taken from fluid dynamics, to explain the concepts discussed. Each chapter demonstrates how nonlinear resonance analysis can be applied to real systems, including large-scale phenomena in the Earth's atmosphere and novel wave turbulent regimes, and explains a range of laboratory experiments. The book also contains a detailed description of the latest computer software in the field. It is suitable for graduate students and researchers in nonlinear science and wave turbulence, along with fluid mechanics and number theory. Colour versions of a selection of the figures are available at www.cambridge.org/9780521763608.

Differential equations, Nonlinear --- Fourier analysis. --- Resonance. --- Mathematical analysis. --- 517.1 Mathematical analysis --- Mathematical analysis --- Analysis, Fourier --- Numerical analysis --- Numerical solutions.