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This book covers all topics in mechanics from elementary Newtonian mechanics, the principles of canonical mechanics and rigid body mechanics to relativistic mechanics and nonlinear dynamics. It was among the first textbooks to include dynamical systems and deterministic chaos in due detail. As compared to the previous editions the present fifth edition is updated and revised with more explanations, additional examples and sections on Noether's theorem. Symmetries and invariance principles, the basic geometric aspects of mechanics as well as elements of continuum mechanics also play an important role. The book will enable the reader to develop general principles from which equations of motion follow, to understand the importance of canonical mechanics and of symmetries as a basis for quantum mechanics, and to get practice in using general theoretical concepts and tools that are essential for all branches of physics. The book contains more than 120 problems with complete solutions, as well as some practical examples which make moderate use of personal computers. This will be appreciated in particular by students using this textbook to accompany lectures on mechanics. The book ends with some historical notes on scientists who made important contributions to the development of mechanics.

Physics. --- Mechanics. --- Theoretical and Applied Mechanics. --- Applications of Mathematics. --- Mathematical Methods in Physics. --- Dynamical Systems and Ergodic Theory. --- Differentiable dynamical systems. --- Mathematics. --- Mathematical physics. --- Mechanics, applied. --- Physique --- Dynamique différentiable --- Mathématiques --- Physique mathématique --- Mécanique --- Mechanics, Applied --- Deterministic chaos.

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À partir de connaissances élémentaires sur les probabilités, cet ouvrage propose un cours approfondi de physique mathématique stochastique. D'une part, il expose l'aspect classique des applications probabilistes aux sciences physiques, et introduit les principales notions dans un langage clair et compréhensible par tous ; d'autre part - et c'est là sans doute sa grande originalité - il traite de l'aspect quantique des probabilités, qui sont à la base de développements plus récents en physique statistique et en théorie des champs. Il ne néglige pas pour autant les techniques de simulation aléatoire qui intéresseront aussi bien les milieux de la recherche que de l'industrie. Ce livre s'appuie sur la longue expérience d'enseignement de l'auteur auprès d'étudiants en master et de futurs ingénieurs. C'est à eux que l'ouvrage s'adresse en priorité, ainsi qu'aux élèves des classes préparatoires intéressés par les méthodes stochastiques. Des exercices corrigés complètent chaque chapitre et permettent une meilleure compréhension de leur contenu. Une importante bibliographie termine l'ouvrage, laissant au lecteur le loisir d'approfondir quelques-uns des plus beaux thèmes de ce vaste territoire aléatoire, qui est au cœur des préoccupations scientifiques d'aujourd'hui. Franck Jedrzejewski est chercheur au Commissariat à l'énergie atomique (CEA). Il est l'auteur chez Springer d'une Introduction aux méthodes numériques (2e éd., 2005). 

Mathematics. --- Probability Theory and Stochastic Processes. --- Mathematical Methods in Physics. --- Statistical Physics, Dynamical Systems and Complexity. --- Quantum Physics. --- Mathematical Modeling and Industrial Mathematics. --- Distribution (Probability theory). --- Quantum theory. --- Mathematical physics. --- Mathématiques --- Distribution (Théorie des probabilités) --- Théorie quantique --- Physique mathématique --- Stochastic processes

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The second in a series of three volumes surveying the theory of theta functions, this volume gives emphasis to the special properties of the theta functions associated with compact Riemann surfaces and how they lead to solutions of the Korteweg-de-Vries equations as well as other non-linear differential equations of mathematical physics. This book presents an explicit elementary construction of hyperelliptic Jacobian varieties and is a self-contained introduction to the theory of the Jacobians. It also ties together nineteenth-century discoveries due to Jacobi, Neumann, and Frobenius with recent discoveries of Gelfand, McKean, Moser, John Fay, and others. A definitive body of information and research on the subject of theta functions, this volume will be a useful addition to individual and mathematics research libraries.

Mathematics. --- Special Functions. --- Algebraic Geometry. --- Mathematical Methods in Physics. --- Functions of a Complex Variable. --- Algebraic Topology. --- Partial Differential Equations. --- Geometry, algebraic. --- Functions of complex variables. --- Differential equations, partial. --- Functions, special. --- Algebraic topology. --- Mathematical physics. --- Mathématiques --- Fonctions d'une variable complexe --- Topologie algébrique --- Physique mathématique --- Mathematics --- Physical Sciences & Mathematics --- Calculus --- Functions, Theta. --- Differential equations. --- 517.91 Differential equations --- Differential equations --- Theta functions --- Algebraic geometry. --- Partial differential equations. --- Special functions. --- Physics.

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This monograph is devoted to a completely new approach to geometric problems arising in the study of random fields. The groundbreaking material in Part III, for which the background is carefully prepared in Parts I and II, is of both theoretical and practical importance, and striking in the way in which problems arising in geometry and probability are beautifully intertwined. The three parts to the monograph are quite distinct. Part I presents a user-friendly yet comprehensive background to the general theory of Gaussian random fields, treating classical topics such as continuity and boundedness, entropy and majorizing measures, Borell and Slepian inequalities. Part II gives a quick review of geometry, both integral and Riemannian, to provide the reader with the material needed for Part III, and to give some new results and new proofs of known results along the way. Topics such as Crofton formulae, curvature measures for stratified manifolds, critical point theory, and tube formulae are covered. In fact, this is the only concise, self-contained treatment of all of the above topics, which are necessary for the study of random fields. The new approach in Part III is devoted to the geometry of excursion sets of random fields and the related Euler characteristic approach to extremal probabilities. "Random Fields and Geometry" will be useful for probabilists and statisticians, and for theoretical and applied mathematicians who wish to learn about new relationships between geometry and probability. It will be helpful for graduate students in a classroom setting, or for self-study. Finally, this text will serve as a basic reference for all those interested in the companion volume of the applications of the theory. These applications, to appear in a forthcoming volume, will cover areas as widespread as brain imaging, physical oceanography, and astrophysics.

Mathematics. --- Probability Theory and Stochastic Processes. --- Statistics, general. --- Geometry. --- Mathematical Methods in Physics. --- Distribution (Probability theory). --- Mathematical physics. --- Statistics. --- Mathématiques --- Géométrie --- Distribution (Théorie des probabilités) --- Physique mathématique --- Statistique --- Global differential geometry. --- Random fields. --- Stochastic geometry. --- Random fields --- Global differential geometry --- Mathematical Statistics --- Mathematics --- Physical Sciences & Mathematics --- Fields, Random --- Probabilities. --- Physics. --- Statistical analysis --- Statistical data --- Statistical methods --- Statistical science --- Econometrics --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- Dynamics --- Probability --- Statistical inference --- Combinations --- Chance --- Least squares --- Mathematical statistics --- Risk --- Euclid's Elements --- Math --- Science --- Geometry, Differential --- Stochastic processes --- Distribution (Probability theory. --- Physical mathematics --- Physics --- Distribution functions --- Frequency distribution --- Characteristic functions --- Probabilities --- Statistics .

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This volume presents the Proceedings of the 8th International Conference on Vibration Problems, held from 30 January 2007 to 3 February 2007, in Howrah, Kolkata, West Bengal, India. As with the earlier conferences in the ICOVP series, the purpose of ICOVP-2007 was to bring together scientists with different backgrounds, actively working on vibration-related problems of engineering both in theoretical and applied fields. The main objective did not lie, however, in reporting specific results as such, but rather in joining and exchanging different languages, questions and methods developed in the respective disciplines, and to thus stimulate a broad interdisciplinary research. The topics, indeed, cover a wide variety of vibration-related subjects. Audience: Scientists, researchers and graduate students in Physics and Engineering.

Physics. --- Mechanics. --- Continuum Mechanics and Mechanics of Materials. --- Vibration, Dynamical Systems, Control. --- Mechanics, Fluids, Thermodynamics. --- Mathematical and Computational Physics. --- Mathematical physics. --- Thermodynamics. --- Materials. --- Vibration. --- Physique --- Physique mathématique --- Thermodynamique --- Mécanique --- Matériaux --- Vibration --- Applied Physics --- Applied Mathematics --- Engineering & Applied Sciences --- Continuum physics. --- Continuum mechanics. --- Dynamical systems. --- Dynamics. --- Mechanical engineering. --- Mechanical Engineering. --- Classical Continuum Physics. --- Theoretical, Mathematical and Computational Physics. --- Mechanics, Applied. --- Classical Mechanics. --- Solid Mechanics. --- Classical and Continuum Physics. --- Applied mechanics --- Engineering, Mechanical --- Engineering mathematics --- Cycles --- Mechanics --- Sound --- Engineering --- Machinery --- Steam engineering --- Classical mechanics --- Newtonian mechanics --- Physics --- Dynamics --- Quantum theory --- Physical mathematics --- Classical field theory --- Continuum physics --- Continuum mechanics --- Dynamical systems --- Kinetics --- Mathematics --- Mechanics, Analytic --- Force and energy --- Statics