Diffusione -- Equazione di Laplace -- Equazioni del primo ordine -- Onde -- Analisi funzionale -- Formulazioni variazionali.La presente raccolta di problemi ed esercizi nasce dall'esperienza maturata durante il corso di Equazioni a Derivate Parziali (EDP), tenuto nell'ambito delle lauree di primo e secondo livello presso il Politecnico di Milano. Il volume è diviso in due parti; nei primi quat…
Hyperbolicity and Beyond -- One-Dimensional Dynamics -- Homoclinic Tangencies -- Hénon-like Dynamics -- Non-Critical Dynamics and Hyperbolicity -- Heterodimensional Cycles and Blenders -- Robust Transitivity -- Stable Ergodicity -- Robust Singular Dynamics -- Generic Diffeomorphisms -- SRB Measures and Gibbs States -- Lyapunov Exponents.In broad terms, the goal of dynamics is to describe the l…
Abstract Theory of Schwarz Methods -- Two-Level Overlapping Methods -- Substructuring Methods: Introduction -- Primal Iterative Substructuring Methods -- Neumann-Neumann and FETI Methods -- Spectral Element Methods -- Linear Elasticity -- Preconditioners for Saddle Point Problems -- Problems in H (div ; ?) and H (curl ; ?) -- Indefinite and Nonsymmetric Problems -- Elliptic Problems and Sobolev…
Surveys -- Linear Semi-infinite Optimization: Recent Advances -- Some Theoretical Aspects of Newton’s Method for Constrained Best Interpolation -- Optimization Methods in Direct and Inverse Scattering -- On Complexity of Stochastic Programming Problems -- Nonlinear Optimization in Modeling Environments -- Supervised Data Classification via Max-min Separability -- A Review of Applications of t…
Elements of Convex Analysis and Separation -- to Image Space Analysis -- Alternative and Separation -- Optimality Conditions. Preliminary Results.Over the last twenty years, Professor Franco Giannessi, a highly respected researcher, has been working on an approach to optimization theory based on image space analysis. His theory has been elaborated by many other researchers in a wealth of papers…
Question and Method -- Paths Toward Algebraization — Development to the Eighteenth Century. The Number Field -- Paths toward Algebraization — The Field of Limits: The Development of Infinitely Small Quantities -- Culmination of Algebraization and Retour du Refoulé -- Le Retour du Refoulé: From the Perspective of Mathematical Concepts -- Cauchy’s Compromise Concept -- Development of Pure…
The Main Theorem: Cyclic Algebras -- The Paper: Dedication to Hensel -- The Local-Global Principle -- From the Local-Global Principle to the Main Theorem -- The Brauer Group and Class Field Theory -- The Team: Noether, Brauer and Hasse -- The American Connection: Albert -- Epilogue: Käte Hey.The unpublished writings of Helmut Hasse, consisting of letters, manuscripts and other papers, are kept…
Theory of Calculus in One Real Variable -- Metric Spaces -- Theory of Calculus in Several Real Variables -- Theory of Ordinary Differential Equations and Systems -- Lebesgue Measure and Abstract Measure Theory -- Measure Theory for Euclidean Space -- Differentiation of Lebesgue Integrals on the Line -- Fourier Transform in Euclidean Space -- Lp Spaces -- Topological Spaces -- Integration on Loc…
Arnold's Problems contains mathematical problems brought up by Vladimir Arnold in his famous seminar at Moscow State University over several decades. In addition, there are problems published in his numerous papers and books. The invariable peculiarity of these problems was that Arnold did not consider mathematics a game with deductive reasoning and symbols, but a part of natural science (espec…
Foundations -- Convergence -- Continuous Functions -- Differentiation in One Variable -- Sequences of Functions.Logical thinking, the analysis of complex relationships, the recognition of und- lying simple structures which are common to a multitude of problems — these are the skills which are needed to do mathematics, and their development is the main goal of mathematics education. Of course,…