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Lectures: J. Chazarain, A. Piriou: Problèmes mixtes hyperboliques: Première partie: Les problèmes mixtes hyperboliques vérifiant 1a condition de Lopatinski uniforme; Deuxième partie: Propagation et réflexion des singularités.- L. Gårding: Introduction to hyperbolicity.- T. Kato: Linear and quasi-linear equations of evolution of hyperbolic type.- K.W. Morton: Numerical methods for non-linear hyperbolic equations of mathematical physics.- Seminars: H. Brezis: First-order quasilinear equation on a torus.
Dynamics. --- Geometry, Hyperbolic. --- Geometry. --- Mathematics --- Physical Sciences & Mathematics --- Calculus --- Differential equations, Hyperbolic --- Differential equations --- 517.91 Differential equations --- Mathematics. --- Ergodic theory. --- Dynamical Systems and Ergodic Theory. --- Differentiable dynamical systems. --- Differential dynamical systems --- Dynamical systems, Differentiable --- Dynamics, Differentiable --- Global analysis (Mathematics) --- Topological dynamics --- Ergodic transformations --- Continuous groups --- Mathematical physics --- Measure theory --- Transformations (Mathematics) --- Dynamical systems --- Kinetics --- Mechanics, Analytic --- Force and energy --- Mechanics --- Physics --- Statics
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This textbook collects the notes for an introductory course in measure theory and integration. The course was taught by the authors to undergraduate students of the Scuola Normale Superiore, in the years 2000-2011. The goal of the course was to present, in a quick but rigorous way, the modern point of view on measure theory and integration, putting Lebesgue's Euclidean space theory into a more general context and presenting the basic applications to Fourier series, calculus and real analysis. The text can also pave the way to more advanced courses in probability, stochastic processes or geometric measure theory. Prerequisites for the book are a basic knowledge of calculus in one and several variables, metric spaces and linear algebra. All results presented here, as well as their proofs, are classical. The authors claim some originality only in the presentation and in the choice of the exercises. Detailed solutions to the exercises are provided in the final part of the book.
Integrals, Generalized -- Textbooks. --- Mathematics -- Textbooks. --- Measure theory -- Textbooks. --- Mathematics --- Physical Sciences & Mathematics --- Calculus --- Mathematics. --- Measure theory. --- Measure and Integration. --- Math --- Science --- Matheorie. --- Integrationstheorie. --- Lebesgue measure --- Measurable sets --- Measure of a set --- Algebraic topology --- Integrals, Generalized --- Measure algebras --- Rings (Algebra)
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