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Ce manuel introductif s'adresse à tout étudiant (classe préparatoire, université, école ingénieurs) connaissant les principes de bases en algèbre linéaire, calcul différentiel et intégral. Il aborde notamment les notions de : • fonctions holomorphes, • fonctions analytiques, • équations différentielles ordinaires, • s
Ce recueil d'exercices vise principalement les étudiants qui s'initient à l'analyse complexe, aux équations différentielles, ou aux deux domaines. On y considère notamment les notions de : • fonctions holomorphes, • fonctions analytiques, • équations différentielles ordinaires, • séries de Fourier, • applications aux équations aux dérivées partielles. Au total, le livre propose 400 exercices. Plus de deux cents d'entre eux sont complètement résolus, les autres sont présentés avec leurs solutions. Le contenu et la progression de ces exercices suivent de près le manuel « Analyse Complexe et Équations Différentielles » de Barreira, publié dans la même collection. Luís Barreira et Clàudia Valls, professeurs à l'Instituto Superior Técnico de Lisbonne, sont spécialistes en équations différentielles et systèmes dynamiques, domaines dans lesquels ils ont publié plusieurs livres.
This book follows an advanced course in analysis (vector analysis, complex analysis and Fourier analysis) for engineering students, but can also be useful, as a complement to a more theoretical course, to mathematics and physics students. The first three parts of the book represent the theoretical aspect and are independent of each other. The fourth part gives detailed solutions to all exercises that are proposed in the first three parts. Foreword Foreword (71 KB) Sample Chapter(s) Chapter 1: Differential Operators of Mathematical Physics (272 KB) Chapter 9: Holomorphic functions and Cauchy–Riemann equations (248 KB) Chapter 14: Fourier series (281 KB) Request Inspection Copy Contents: Vector Analysis:Differential Operators of Mathematical PhysicsLine IntegralsGradient Vector FieldsGreen TheoremSurface IntegralsDivergence TheoremStokes TheoremAppendixComplex Analysis:Holomorphic Functions and Cauchy–Riemann EquationsComplex IntegrationLaurent SeriesResidue Theorem and ApplicationsConformal MappingFourier Analysis:Fourier SeriesFourier TransformLaplace TransformApplications to Ordinary Differential EquationsApplications to Partial Differential EquationsSolutions to the Exercises:Differential Operators of Mathematical PhysicsLine IntegralsGradient Vector FieldsGreen TheoremSurface IntegralsDivergence TheoremStokes TheoremHolomorphic Functions and Cauchy–Riemann EquationsComplex IntegrationLaurent SeriesResidue Theorem and ApplicationsConformal MappingFourier SeriesFourier TransformLaplace TransformApplications to Ordinary Differential EquationsApplications to Partial Differential Equations Readership: Undergraduate students in analysis & differential equations, complex analysis, civil, electrical and mechanical engineering.
This first of two bound volumes present the proceedings of the conference, Complex Analysis, Dynamical Systems, Summability of Divergent Series and Galois Theories, held in Toulouse on the occasion of J.-P. Ramis' sixtieth birthday. The first volume opens with two articles composed of recollections and three articles on J.-P. Ramis' works on complex analysis and ODE theory, both linear and non-linear. This introduction is followed by papers concerned with Galois theories, arithmetic or integrability: analogies between differential and arithmetical theories, $q$-difference equations, classical or $p$-adic, the Riemann-Hilbert problem and renormalization, $b$-functions, descent problems, Krichever modules, the set of integrability, Drach theory, and the VI${}^{{th}}$ Painleve equation. The second volume contains papers dealing with analytical or geometrical aspects: Lyapunov stability, asymptotic and dynamical analysis for pencils of trajectories, monodromy in moduli spaces, WKB analysis and Stokes geometry, first and second Painleve equations, normal forms for saddle-node type singularities, and invariant tori for PDEs. The volumes are suitable for graduate students and researchers interested in differential equations, number theory, geometry, and topology.
Singularity theory appears in numerous branches of mathematics, as well as in many emerging areas such as robotics, control theory, imaging, and various evolving areas in physics. The purpose of this proceedings volume is to cover recent developments in singularity theory and to introduce young researchers from developing countries to singularities in geometry and topology.The contributions discuss singularities in both complex and real geometry. As such, they provide a natural continuation of the previous school on singularities held at ICTP (1991), which is recognized as having had a major influence in the field.
Singularity theory appears in numerous branches of mathematics, as well as in many emerging areas such as robotics, control theory, imaging, and various evolving areas in physics. The purpose of this proceedings volume is to cover recent developments in singularity theory and to introduce young researchers from developing countries to singularities in geometry and topology.The contributions discuss singularities in both complex and real geometry. As such, they provide a natural continuation of the previous school on singularities held at ICTP (1991), which is recognized as having had a major influence in the field.