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Perturbation theory, one of the most intriguing and essential topics in mathematics, and its applications to the natural and engineering sciences is the main focus of this workbook. In a systematic introductory manner, this unique book deliniates boundary layer theory for ordinary and partial differential equations, multi-timescale phenomena for nonlinear oscillations, diffusion and nonlinear wave equations. The book provides analysis of simple examples in the context of the general theory, as well as a final discussion of the more advanced problems. Precise estimates and excursions into the theoretical background makes this workbook valuable to both the applied sciences and mathematics fields. As a bonus in its last chapter the book includes a collection of rare and useful pieces of literature, such as the summary of the Perturbation theory of Matrices. Detailed illustrations, stimulating examples and exercises as well as a clear explanation of the underlying theory makes this workbook ideal for senior undergraduate and beginning graduate students in applied mathematics as well as science and engineering fields.

Boundary value problems --- Singular perturbations (Mathematics) --- Numerical solutions. --- Differential equations --- Perturbation (Mathematics) --- Asymptotic theory --- Differential Equations. --- Differential equations, partial. --- Mathematical physics. --- Differentiable dynamical systems. --- Numerical analysis. --- Mathematics. --- Ordinary Differential Equations. --- Partial Differential Equations. --- Mathematical Methods in Physics. --- Dynamical Systems and Ergodic Theory. --- Numerical Analysis. --- Applications of Mathematics. --- 517.91 Differential equations --- Differential dynamical systems --- Dynamical systems, Differentiable --- Dynamics, Differentiable --- Global analysis (Mathematics) --- Topological dynamics --- Physical mathematics --- Physics --- Partial differential equations --- Math --- Science --- Mathematical analysis --- Mathematics --- Differential equations. --- Partial differential equations. --- Physics. --- Dynamics. --- Ergodic theory. --- Applied mathematics. --- Engineering mathematics. --- Engineering --- Engineering analysis --- Ergodic transformations --- Continuous groups --- Mathematical physics --- Measure theory --- Transformations (Mathematics) --- Dynamical systems --- Kinetics --- Mechanics, Analytic --- Force and energy --- Mechanics --- Statics --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- Dynamics

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This book describes the life and work of Henri Poincaré, detailing most of his unique achievements in mathematics and physics. It is divided into two parts—the first on Poincaré’s life, and the second on his contributions to the mathematical sciences. Apart from biographical details, attention is given to Poincaré’s results on automorphic functions; differential equations and dynamical systems; celestial mechanics; mathematical physics, in particular the theory of the electron and relativity; and topology (analysis situs). A chapter on philosophy explains Poincaré’s conventionalism in mathematics and his view of conventionalism in physics. The book shows how Poincaré reached his fundamentally new results in many different fields, how he thought about problems, and how one should read his work. Simultaneously, it is made clear how analysis and geometry are intertwined in Poincaré’s thinking and work. In dynamical systems, this becomes clear in his description of invariant manifolds, his association of differential equation flow with mappings, and his fixed-point theory. There is no comparable book on Poincaré presenting such a relatively complete vision of his life and the working of his very original mind. Scientists and engineers as well as general readers interested in the history of science will find this book of interest. Reviews of this book:"The title of this biography is particularly well chosen : Henri Poincaré was a true genius, and he was impatient. It gives a fair picture of both the man and the scientist, completed by particularly well chosen illustrations. Jean Mawhin, Université Catholique de Louvain, Belgium "Ferdinand Verhulst has written a true scientific biography, introducing Poincaré the man, his cultural milieu, and his mathematics. This book shows why, a century after his death, Poincaré's ideas still shape a substantial part of the mathematical sciences." Philip J Holmes, Princeton University, USA  .

Mathematicians -- Biography -- France. --- Physicists -- Biography -- France. --- Poincare, Henri, -- 1854-1912. --- Mathematicians --- Physicists --- Physics --- Mathematics --- Physical Sciences & Mathematics --- Physics - General --- Mathematics - General --- Poincaré, Henri, --- Puankare, G., --- Poincaré, Jules Henri, --- Poincaré, H. --- Puankare, Anri, --- Puankare, A. --- פואנקרה, הנרי --- פואנקרה, הנרי, --- Mathematics. --- History. --- Astrophysics. --- Engineering. --- History of Mathematical Sciences. --- Mathematics, general. --- Astrophysics and Astroparticles. --- Engineering, general. --- Construction --- Industrial arts --- Technology --- Math --- Science --- Astronomical physics --- Astronomy --- Cosmic physics --- Annals --- Auxiliary sciences of history

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517.95 --- differentiaalvergelijkingen --- dynamica --- niet-lineaire systemen --- Differentiable dynamical systems --- Differential equations, Nonlinear --- Nonlinear differential equations --- Nonlinear theories --- Differential dynamical systems --- Dynamical systems, Differentiable --- Dynamics, Differentiable --- Differential equations --- Global analysis (Mathematics) --- Topological dynamics --- 517.95 Partial differential equations --- Partial differential equations --- Equations différentielles non linéaires --- Equations différentielles non linéaires --- Équations différentielles non linéaires --- Dynamique différentiable --- Differential equations, Nonlinear. --- Differentiable dynamical systems. --- Dynamique différentiable --- Équations différentielles non linéaires. --- Dynamique différentiable. --- Équations différentielles non linéaires. --- Dynamique différentiable.

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This primer on averaging theorems provides a practical toolbox for applied mathematicians, physicists, and engineers seeking to apply the well-known mathematical theory to real-world problems. With a focus on practical applications, the book introduces new approaches to dissipative and Hamiltonian resonances and approximations on timescales longer than 1/ε. Accessible and clearly written, the book includes numerous examples ranging from elementary to complex, making it an excellent basic reference for anyone interested in the subject. The prerequisites have been kept to a minimum, requiring only a working knowledge of calculus and ordinary and partial differential equations (ODEs and PDEs). In addition to serving as a valuable reference for practitioners, the book could also be used as a reading guide for a mathematics seminar on averaging methods. Whether you're an engineer, scientist, or mathematician, this book offers a wealth of practical tools and theoretical insights to help you tackle a range of mathematical problems.

Differential equations. --- Engineering mathematics. --- Differential Equations. --- Engineering Mathematics. --- Engineering --- Engineering analysis --- Mathematical analysis --- 517.91 Differential equations --- Differential equations --- Mathematics --- Equacions diferencials --- Equacions en derivades parcials

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Catalogues de ventes publiques --- 19e siecle