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Exercices originaux accompagnés par leurs corrigés, cet ouvrage s'adresse principalement aux étudiants de licence de Mathématiques (L3), et principalement du module d'enseignement "Calcul différentiel-Equations différentielles". Ce livre scientifique pourra également être utile aux éléves ingénieurs et aux étudiants préparant des masters ou des concours de recrutements (Capes, Agrégations). Il s'agit d'une recueil de 36 devoirs, au sens premier de vocable, c'est à dire de travaux à effectuer, en temps limité ou chez soi, seul ou à plusieurs. La durée estimée moyenne est de 3 heures pour chaque devoir, lequel comporte généralement deux ou trois exercices indépendants. La plupart des problèmes et exercices proposés sont originaux, ils ont été posés durant les dernières années dans plusieurs universités, sous forme d'examens intermédiaires ou terminaux en temps limité ou à rendre rédigés après y avoir travailler chez soi. Les thèmes traités suivent globalement le déroulement d'un programme standard de module " Calcul différentiel-Equations différentielles", avec au fur et à mesure de l'avancée dans le livre, un retour sur les chapitres passés: une progression en spirale plutôt linéaire.

Calculus --- Differential equations --- 517.91 Differential equations

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The aim of the Sino-Japan Conference of Young Mathematicians was to provide a forum for presenting and discussing recent trends and developments in differential equations and their applications, as well as to promote scientific exchanges and collaborations among young mathematicians both from China and Japan.The topics discussed in this proceedings include mean curvature flows, KAM theory, N-body problems, flows on Riemannian manifolds, hyperbolic systems, vortices, water waves, and reaction diffusion systems.

Differential equations --- 517.91 Differential equations

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Computational Techniques for Differential Equations

Differential equations --- Differential equations, Partial --- Numerical solutions --- 517.91 Differential equations --- 517.91 --- Congresses

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The book contains twenty-two original scientific research articles that address the state-of-the-art in using partial differential equations for image and signal processing. The articles arose from presentations given at the international conference on PDE-Based Image Processing and Related Inverse Problems, held at the Centre of Mathematics for Applications, University of Oslo, Norway, August 8-12, 2005. The purpose of the conference was to bring together international - searchers to present various aspects of new developments in using numerical techniques for partial differential equations to analyse and process digital - ages. Various aspects of new trends and techniques in this field were discussed in the conference, covering the following topics: • Level set methods and applications • Total variation regularization and other nonlinear filters • Noise analysis and removal • Image in painting • Image dejittering • Optical flow estimation • Image segmentation • Image registration • Analysis and processing of MR images and brain mapping • Image construction techniques • Level set methods for inverse problems Inverse problems for partial differential equations have large areas of app- cations. Although image analysis and PDE inverse problems seem to be - related at a first glance, there are many techniques used in one of these two areas that are useful for the other. One goal of the conference was to highlight some of the recent efforts in merging some of the techniques for these two research areas.

Image processing --- Differential equations --- Digital techniques --- 517.91 Differential equations

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The material collected in this volume discusses the present as well as expected future directions of development of the field with particular emphasis on applications. The seven survey articles present different topics in Evolutionary PDE's, written by leading experts.- Review of new results in the area- Continuation of previous volumes in the handbook series covering Evolutionary PDEs- Written by leading experts

Differential equations --- Mathematics. --- Math --- Science --- 517.91 Differential equations