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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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Stochastic differential equations : an introduction with applications / par k̲sendal,, Bernt. Publication : [S.l.] : Springer, 2003 . 374 p. ; , This book gives an introduction to the basic theory of stochastic calculus and its applications. Examples are given throughout the text, in order to motivate and illustrate the theory and show its importance for many applications in e.g. economics, biology and physics. The basic idea of the presentation is to start from some basic results (without proofs) of the easier cases and develop the theory from there, and to concentrate on the proofs of the easier case (which nevertheless are often sufficiently general for many purposes) in order to be able to reach quickly the parts of the theory which is most important for the applications. For the 6th edition the author has added further exercises and, for the first time, solutions to many of the exercises are provided. 24 cm. Date : 2003 Disponibilité : Exemplaires disponibles: La bibliothèque des Sciences Exactes et Naturelles (1),

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The Monge-ampere equation / par Gutierrez,, Cristian E. Publication : [S.l.] : BirkhƲuser Boston, 2001 . 127 p. ; , A self-contained exposition of the theory of weak solutions, including the regularity results of L.A. Caffarelli, featuring examples, illustrations, bibliographical references and comprehensive index. Topics covered include non-divergence equations, generalized solutions, and regularity theory. DLC: Monge-ampere equations. 25 cm. Date : 2001 Disponibilité : Exemplaires disponibles: La bibliothèque des Sciences Exactes et Naturelles (1),

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Tutorials in mathematical biosciences I : mathematical neuroscience / par Borisyuk, Alla. Publication : [S.l.] : Springer, 2005 . 170 p. ; , This volume introduces some basic theories on computational neuroscience. Chapter 1 is a brief introduction to neurons, tailored to the subsequent chapters. Chapter 2 is a self-contained introduction to dynamical systems and the bifurcation theory, oriented toward neuronal dynamics. The theory is illustrated with a model of Parkinson's disease. Chapter 3 reviews the theory of coupled neural oscillators observed ghroughout the nervous systems at all levels; it describes how oscillations arise, what pattern they take, and how they depend on excitory of inhibitory synaptic connections. Chapter 4 specializes to one particular neuronal system, namely, the auditory system. It includes a self-contained introduction, from the anatomy and physiology of the inner ear to the neuronal network which connects the hair cells to the cortex, and describes various models of subsystems. 24 cm. Date : 2005 Disponibilité : Exemplaires disponibles: La bibliothèque des Sciences Exactes et Naturelles (1),

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Wave propagation and time reversal in randomly layered media / par Fouque, Jean-Pierre. Publication : [S.l.] : Springer, 2007 . 612 p. ; , Wave propagation in random media is an interdisciplinary field that has emerged from the need in physics and engineering to model and analyze wave energy transport in complex environments. This book gives a systematic and self-contained presentation of wave propagation in randomly layered media using the asymptotic theory of ordinary differential equations with random coefficients. The first half of the book gives a detailed treatment of wave reflection and transmission in one-dimensional random media, after introducing gradually the tools from partial differential equations and probability theory that are needed for the analysis. The second half of the book presents wave propagation in three-dimensional randomly layered media along with several applications, primarily involving time reversal. Many new results are presented here for the first time. 24 cm. Date : 2007 Disponibilité : Exemplaires disponibles: La bibliothèque des Sciences Exactes et Naturelles (1),

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The ADI Model Problem par Wachspress, Eugene. Publication : . X, 167 p. Disponibilité :  http://dx.doi.org/10.1007/978-1-4614-5122-8,

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Numerical Approximation of Exact Controls for Waves par Ervedoza, Sylvain. Publication : . XVII, 122 p. 17 illus., 3 illus. in color. Disponibilité :  http://dx.doi.org/10.1007/978-1-4614-5808-1,

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Symmetric Discontinuous Galerkin Methods for 1-D Waves Fourier Analysis, Propagation, Observability and Applications / par Marica, Aurora. Publication : . XVI, 104 p. 18 illus. in color. Disponibilité :  http://dx.doi.org/10.1007/978-1-4614-5811-1,

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Linear Integral Equations Theory & Technique / par Kanwal, Ram P. Publication : . XIII, 318 p. 13 illus. Disponibilité :  http://dx.doi.org/10.1007/978-1-4614-6012-1,

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The Mathematical Structure of Classical and Relativistic Physics A General Classification Diagram / par Tonti, Enzo. Publication : . XXXVI, 514 p. 164 illus. Disponibilité :  http://dx.doi.org/10.1007/978-1-4614-7422-7,

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Advanced H∞ Control Towards Nonsmooth Theory and Applications / par Orlov, Yury V. Publication : . XI, 218 p. 43 illus., 12 illus. in color. Disponibilité :  http://dx.doi.org/10.1007/978-1-4939-0292-7,

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Mathematical and Numerical Foundations of Turbulence Models and Applications par Chacón Rebollo, Tomás. Publication : . XVII, 517 p. 18 illus., 9 illus. in color. Disponibilité :  http://dx.doi.org/10.1007/978-1-4939-0455-6,

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Stability of Vector Differential Delay Equations par Gil’, Michael I. Publication : . X, 259 p. Disponibilité :  http://dx.doi.org/10.1007/978-3-0348-0577-3,

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Numerical Simulation of Distributed Parameter Processes par Colosi, Tiberiu. Publication : . XX, 343 p. Disponibilité :  http://dx.doi.org/10.1007/978-3-319-00014-5,

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A Textbook on Ordinary Differential Equations par Ahmad, Shair. Publication : . XIV, 312 p. Disponibilité :  http://dx.doi.org/10.1007/978-3-319-02129-4,

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