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Mathematical analysis and numerical methods for science and technology : physical origins and classical methods / Volume 1 : par Dautray, Robert. Publication : [S.l.] : Springer, 2000 . 722 p. ; , These 6 volumes - the result of a 10 year collaboration between the authors, two of France's leading scientists and both distinguished international figures - compile the mathematical knowledge required by researchers in mechanics, physics, engineering, chemistry and other branches of application of mathematics for the theoretical and numerical resolution of physical models on computers. Since the publication in 1924 of the "Methoden der mathematischen Physik" by Courant and Hilbert, there has been no other comprehensive and up-to-date publication presenting the mathematical tools needed in applications of mathematics in directly implementable form. The advent of large computers has in the meantime revolutionised methods of computation and made this gap in the literature intolerable: the objective of the present work is to fill just this gap. Many phenomena in physical mathematics may be modeled by a system of partial differential equations in distributed systems:! a model here means a set of equations, which together with given boundary data and, if the phenomenon is evolving in time, initial data, defines the system. The advent of high-speed computers has made it possible for the first time to calculate values from models accurately and rapidly. Researchers and engineers thus have a crucial means of using numerical results to modify and adapt arguments and experiments along the way. Every facet of technical and industrial activity has been affected by these developments. Modeling by distributed systems now also supports work in many areas of physics (plasmas, new materials, astrophysics, geophysics), chemistry and mechanics and is finding increasing use in the life sciences. The main physical examples examined in the 6 volumes are presented in Chapter I: Classical Fluids and the Navier-Stokes System; Linear Elasticity, Linear Viscoelasticity, Electromagnetism and Maxwell's Equation, Neutronics, and Quantum Physics. Then a first examin! ation of the mathematical model. 24 cm. Date : 2000 Disponibilité : Exemplaires disponibles: La bibliothèque des Sciences Exactes et Naturelles (1),

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Methods of nonlinear analysis applications to differential equations par Dràbek, Pavel Publication : Basel | Boston | Berlin Birkhäuser 2007 . 568 p. , In this book, the basic methods of nonlinear analysis are emphasized and illustrated in simple examples. Every considered method is motivated, explained in a general form but in the simplest possible abstract framework. Its applications are shown, particularly to boundary value problems for elementary ordinary or partial differential equations. The text is organized in two levels: a self-contained basic and, organized in appendices, an advanced level for the more experienced reader. Exercises are an organic part of the exposition and accompany the reader throughout the book. 24 cm. Date : 2007 Disponibilité : Exemplaires disponibles: La bibliothèque des Sciences Exactes et Naturelles (1),

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Operator approach in linear problems of hydrodynamics par Kopachevsky,, Nikolay D. Publication : [S.l.] Birkhäuser Basel 2001 . 384 p. , This is the first volume of a set of two devoted to the operator approach to linear problems in hydrodynamics. It presents functional analytical methods applied to the study of small movements and normal oscillations of hydromechanical systems having cavities filled with either ideal or viscous fluids. The work is a sequel to and at the same time substantially extends the volume "Operator Methods in Linear Hydrodynamics: Evolution and Spectral Problems" by N.D. Kopachevsky, S.G. Krein and Ngo Zuy Kan, published in 1989 by Nauka in Moscow. It includes several new problems on the oscillations of partially dissipative hydrosystems and the oscillations of visco-elastic or relaxing fluids. The work relies on the authors' and their students' works of the last 30-40 years. The readers are not supposed to be familiar with the methods of functional analysis. In the first part of the present volume, the main facts of linear operator theory relevant to linearized problems of hydrodynamics are summarized, including elements of the theories of distributions, self-adjoint operators in Hilbert spaces and in spaces with an indefinite metric, evolution equations and asymptotic methods for their solutions, the spectral theory of operator pencils. The book is particularly useful for researchers, engineers and students in fluid mechanics and mathematics interested in operator theoretical methods for the analysis of hydrodynamical problems. 24 cm. Date : 2001 Disponibilité : Exemplaires disponibles: La bibliothèque des Sciences Exactes et Naturelles (1), La bibliothèque des Sciences Exactes et Naturelles (1),

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Partial differential equations par Sauvigny,, Friedrich. Publication : Berlin Springer 2006 . 2 volumes , Expanded version of the German original edition. 24 cm. Date : 2006 Disponibilité : Exemplaires disponibles: La bibliothèque des Sciences Exactes et Naturelles (1),

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Variational methods in some shape optimization problems par Bucur,, Dorin. Publication : [S.l.] Edizioni della Normale 2002 . 217 p. , The study of shape optimization problems is a very wide field, both classical, as the isoperimetric problem and Newton problem of the best aerodynamical shape show, and modern, for all the recent results obtained in the last two, three decades. The fascinating feature is that the competing objects are shapes, i.e. domains of Rn, instead of functions, as usually occurs in problems of calculus of variations. This constraint often produces additional difficulties that lead to a lack of existence of a solution and the introduction of suitable relaxed formulations of the problem. However, in a few cases an optimal solution exists, due to the special form of the cost functional and to the geometrical restriction on the class of competing domains. This volume collects the lecture notes of two courses given in the academic year 2000/01 by the authors at the University of Pisa and at the Scuola Normale Superiore respectively. The courses were mainly addressed to Ph. D. students and required a background in the topics in functional analysis that are usually taught in undergraduate courses. 24 cm. Date : 2002 Disponibilité : Exemplaires disponibles: La bibliothèque des Sciences Exactes et Naturelles (1),

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Bornologies and functional analysis : introductory course on the theory of duality topology-bornology and its use in functional analysis / par Hogbe-Nlend, H. Publication : . 1 online resource (xii, 144 pages) : Disponibilité :  http://www.sciencedirect.com/science/book/9780720407129,  http://www.sciencedirect.com/science/publication?issn=03040208&volume=26,

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Linear differential equations and function spaces / par Massera, José Luis, Publication : . 1 online resource (xx, 404 pages) Disponibilité :  http://www.sciencedirect.com/science/book/9780123745682,  http://www.sciencedirect.com/science/publication?issn=00798169&volume=21,

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Problems in distributions and partial differential equations / par Zuily, Claude, Publication : . 1 online resource (245 pages) , Translation of: Problèmes de distributions. Disponibilité :  http://www.sciencedirect.com/science/book/9780444702487,  http://www.sciencedirect.com/science/publication?issn=03040208&volume=143,

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Functional Analysis in Mechanics par Lebedev, Leonid P. Publication : . X, 310 p. Disponibilité :  http://dx.doi.org/10.1007/978-1-4614-5868-5,

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Functional Analysis Fundamentals and Applications / par Willem, Michel. Publication : . XIII, 213 p. 18 illus. Disponibilité :  http://dx.doi.org/10.1007/978-1-4614-7004-5,

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Geometric Analysis of the Bergman Kernel and Metric par Krantz, Steven G. Publication : . XIII, 292 p. 7 illus. Disponibilité :  http://dx.doi.org/10.1007/978-1-4614-7924-6,

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Distributions, Partial Differential Equations, and Harmonic Analysis par Mitrea, Dorina. Publication : . XXI, 460 p. Disponibilité :  http://dx.doi.org/10.1007/978-1-4614-8208-6,

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Stability of Functional Equations in Random Normed Spaces par Cho, Yeol Je. Publication : . XIX, 246 p. Disponibilité :  http://dx.doi.org/10.1007/978-1-4614-8477-6,

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Methods of Nonlinear Analysis Applications to Differential Equations / par Drábek, Pavel. Publication : . X, 649 p. Disponibilité :  http://dx.doi.org/10.1007/978-3-0348-0387-8,

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The Localization Problem in Index Theory of Elliptic Operators par Nazaikinskii, Vladimir. Publication : . VIII, 117 p. 38 illus., 1 illus. in color. Disponibilité :  http://dx.doi.org/10.1007/978-3-0348-0510-0,

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