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Il testo costituisce una introduzione alla teoria delle equazioni a derivate parziali, strutturata in modo da abituare il lettore ad una sinergia tra modellistica e aspetti teorici. La prima parte riguarda le più note equazioni della fisica-matematica, idealmente raggruppate nelle tre macro-aree diffusione, propagazione e trasporto, onde e vibrazioni. Nella seconda parte si presenta la formulazione variazionale dei principali problemi iniziali e/o al bordo e la loro analisi con i metodi dell'Analisi Funzionale negli spazi di Hilbert.

Difference equations. --- Differential equations. --- Stability. --- Differential equations, Partial. --- Mathematics. --- Math --- Partial differential equations --- Partial differential equations. --- Partial Differential Equations. --- Science --- Differential equations, partial.

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This book is designed as an advanced undergraduate or a first-year graduate course for students from various disciplines like applied mathematics, physics, engineering. The main purpose is on the one hand to train the students to appreciate the interplay between theory and modelling in problems arising in the applied sciences; on the other hand to give them a solid theoretical background for numerical methods, such as finite elements. Accordingly, this textbook is divided into two parts. The first one has a rather elementary character with the goal of developing and studying basic problems from the macro-areas of diffusion, propagation and transport, waves and vibrations. Ideas and connections with concrete aspects are emphasized whenever possible, in order to provide intuition and feeling for the subject. For this part, a knowledge of advanced calculus and ordinary differential equations is required. Also, the repeated use of the method of separation of variables assumes some basic results from the theory of Fourier series, which are summarized in an appendix. The main topic of the second part is the development of Hilbert space methods for the variational formulation and analysis of linear boundary and initial-boundary value problemsemph{. }% Given the abstract nature of these chapters, an effort has been made to provide intuition and motivation for the various concepts and results. The understanding of these topics requires some basic knowledge of Lebesgue measure and integration, summarized in another appendix. At the end of each chapter, a number of exercises at different level of complexity is included. The most demanding problems are supplied with answers or hints. The exposition if flexible enough to allow substantial changes without compromising the comprehension and to facilitate a selection of topics for a one or two semester course.

Differential equations, Partial. --- Electronic books. -- local. --- Laplacian operator. --- Calculus --- Mathematics --- Physical Sciences & Mathematics --- Operator, Laplacian --- Mathematics. --- Partial differential equations. --- Partial Differential Equations. --- Partial differential equations --- Math --- Science --- Differential equations, Partial --- Differential equations, partial.

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This textbook presents problems and exercises at various levels of difficulty in the following areas: Classical Methods in PDEs (diffusion, waves, transport, potential equations); Basic Functional Analysis and Distribution Theory; Variational Formulation of Elliptic Problems; and Weak Formulation for Parabolic Problems and for the Wave Equation. Thanks to the broad variety of exercises with complete solutions, it can be used in all basic and advanced PDE courses.

Mathematics. --- Functional Analysis. --- Partial Differential Equations. --- Mathematical Applications in the Physical Sciences. --- Mathematical Physics. --- Functional analysis. --- Differential equations, partial. --- Mathématiques --- Analyse fonctionnelle --- Differential equations, Partial --- Differential equations, Elliptic --- Boundary value problems --- Geometry, Differential --- Functions --- Diffusion --- Mathematics --- Physical Sciences & Mathematics --- Calculus --- Numerical solutions --- Gases --- Liquids --- Analysis (Mathematics) --- Differential geometry --- Boundary conditions (Differential equations) --- Elliptic differential equations --- Elliptic partial differential equations --- Linear elliptic differential equations --- Partial differential equations --- Partial differential equations. --- Mathematical physics. --- Physical mathematics --- Physics --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations --- Math --- Science --- Boundary value problems. --- Differential equations, Elliptic. --- Differential equations, Partial. --- Diffusion. --- Geometry, Differential. --- Functions. --- Numerical solutions. --- Numerical analysis --- Differential equations --- Mathematical analysis --- Numbers, Complex --- Set theory --- Separation (Technology) --- Solution (Chemistry) --- Solutions, Solid --- Matter --- Packed towers --- Semiconductor doping --- Differential equations, Linear --- Functions of complex variables --- Mathematical physics --- Initial value problems --- Properties

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This book is designed as an advanced undergraduate or a first-year graduate course for students from various disciplines like applied mathematics, physics, engineering. It has evolved while teaching courses on partial differential equations during the last decade at the Politecnico of Milan. The main purpose of these courses was twofold: on the one hand, to train the students to appreciate the interplay between theory and modelling in problems arising in the applied sciences and on the other hand to give them a solid background for numerical methods, such as finite differences and finite elements.

Mathematics --- Physical Sciences & Mathematics --- Mathematical Theory --- Mathematics. --- Mathematical analysis. --- Analysis (Mathematics). --- Partial differential equations. --- Mathematics, general. --- Partial Differential Equations. --- Analysis. --- Differential equations, partial. --- Global analysis (Mathematics). --- Math --- Science --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic --- Partial differential equations --- Global analysis (Mathematics) --- Differential equations, Partial. --- 517.1 Mathematical analysis --- Mathematical analysis