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The book is intended as an advanced undergraduate or first-year graduate course for students from various disciplines, including applied mathematics, physics and engineering. It has evolved from courses offered on partial differential equations (PDEs) over the last several years at the Politecnico di Milano. These courses had a twofold purpose: on the one hand, to teach students to appreciate the interplay between theory and modeling in problems arising in the applied sciences, and on the other to provide them with a solid theoretical background in numerical methods, such as finite elements. Accordingly, this textbook is divided into two parts. The first part, chapters 2 to 5, is more elementary in nature and focuses on developing and studying basic problems from the macro-areas of diffusion, propagation and transport, waves and vibrations. In turn the second part, chapters 6 to 11, concentrates on the development of Hilbert spaces methods for the variational formulation and the analysis of (mainly) linear boundary and initial-boundary value problems.

Mathematics. --- Mathematical Modeling and Industrial Mathematics. --- Partial Differential Equations. --- Mathematical Applications in the Physical Sciences. --- Appl.Mathematics/Computational Methods of Engineering. --- Differential equations, partial. --- Engineering mathematics. --- Mathématiques --- Mathématiques de l'ingénieur --- Mathematics --- Differential equations, Partial --- Differential equations, Elliptic --- Boundary value problems --- Geometry, Differential --- Functions --- Diffusion --- Engineering & Applied Sciences --- Applied Mathematics --- 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 --- Math --- Partial differential equations. --- Mathematical physics. --- Mathematical models. --- Applied mathematics. --- Mathematical and Computational Engineering. --- Engineering --- Engineering analysis --- Mathematical analysis --- Physical mathematics --- Physics --- Models, Mathematical --- Simulation methods --- Geometry, Differential. --- Functions. --- Diffusion. --- Differential equations, Partial. --- Differential equations, Elliptic. --- Boundary value problems. --- Numerical solutions.

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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.

Mathematics. --- Partial differential equations. --- Partial Differential Equations. --- Partial differential equations --- Math --- Differential equations, partial.

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The book is intended as an advanced undergraduate or first-year graduate course for students from various disciplines, including applied mathematics, physics and engineering. It has evolved from courses offered on partial differential equations (PDEs) over the last several years at the Politecnico di Milano. These courses had a twofold purpose: on the one hand, to teach students to appreciate the interplay between theory and modeling in problems arising in the applied sciences, and on the other to provide them with a solid theoretical background in numerical methods, such as finite elements. Accordingly, this textbook is divided into two parts. The first part, chapters 2 to 5, is more elementary in nature and focuses on developing and studying basic problems from the macro-areas of diffusion, propagation and transport, waves and vibrations. In turn the second part, chapters 6 to 11, concentrates on the development of Hilbert spaces methods for the variational formulation and the analysis of (mainly) linear boundary and initial-boundary value problems.

Mathematics. --- Partial differential equations. --- Mathematical physics. --- Mathematical models. --- Applied mathematics. --- Engineering mathematics. --- Mathematical Modeling and Industrial Mathematics. --- Partial Differential Equations. --- Mathematical Applications in the Physical Sciences. --- Appl.Mathematics/Computational Methods of Engineering. --- Engineering --- Engineering analysis --- Models, Mathematical --- Physical mathematics --- Physics --- Partial differential equations --- Math --- Mathematics --- Mathematical analysis --- Simulation methods --- Science --- Differential equations, partial. --- Mathematical and Computational Engineering. --- Differential equations, Partial.

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Partial differential equations --- differentiaalvergelijkingen