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In questo testo si introducono i concetti fondamentali per la modellistica numerica di problemi differenziali alle derivate parziali. Si considerano le classiche equazioni lineari ellittiche, paraboliche ed iperboliche, ma anche altre equazioni, quali quelle di diffusione e trasporto, di Navier-Stokes, e le leggi di conservazione. Si forniscono numerosi esempi fisici che stanno alla base di tali equazioni, se ne studiano le principali proprieta' matematiche, quindi si propongono ed analizzano metodi di risoluzione numerica basati su elementi finiti, differenze finite, volumi finiti e metodi spettrali. In particolare vengono discussi gli aspetti algoritmici e di implementazione al calcolatore e si forniscono alcuni programmi in linguaggio C++ di semplice utilizzo. Il testo non presuppone una avanzata conoscenza matematica delle equazioni alle derivate parziali: i concetti rigorosamente indispensabili al riguardo sono riportati nell'Appendice. Il volume è pertanto adatto agli studenti dei corsi di laurea di indirizzo scientifico (Ingegneria, Matematica, Fisica, Chimica, Scienze dell'Informazione) e consigliabile a ricercatori del mondo accademico ed extra-accademico che vogliano avvicinarsi a questo interessante ramo della matematica applicata.
Differential equations, Partial --- Mathematical analysis. --- 517.1 Mathematical analysis --- Mathematical analysis --- Numerical solutions. --- Numerical analysis --- Computer science. --- Computer science --- Global analysis (Mathematics). --- Mathematics. --- Computational Science and Engineering. --- Computational Mathematics and Numerical Analysis. --- Mathematical Modeling and Industrial Mathematics. --- Analysis. --- Mathematics, general. --- Math --- Science --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic --- Computer mathematics --- Discrete mathematics --- Electronic data processing --- Informatics --- Mathematics --- Computer mathematics. --- Mathematical models. --- Analysis (Mathematics). --- Models, Mathematical --- Simulation methods
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In this text, we introduce the basic concepts for the numerical modelling of partial differential equations. We consider the classical elliptic, parabolic and hyperbolic linear equations, but also the diffusion, transport, and Navier-Stokes equations, as well as equations representing conservation laws, saddle-point problems and optimal control problems. Furthermore, we provide numerous physical examples which underline such equations. We then analyze numerical solution methods based on finite elements, finite differences, finite volumes, spectral methods and domain decomposition methods, and reduced basis methods. In particular, we discuss the algorithmic and computer implementation aspects and provide a number of easy-to-use programs. The text does not require any previous advanced mathematical knowledge of partial differential equations: the absolutely essential concepts are reported in a preliminary chapter. It is therefore suitable for students of bachelor and master courses in scientific disciplines, and recommendable to those researchers in the academic and extra-academic domain who want to approach this interesting branch of applied mathematics.
Mathematics. --- Mathematics, general. --- Analysis. --- Numerical Analysis. --- Mathematical Modeling and Industrial Mathematics. --- Applications of Mathematics. --- Computational Mathematics and Numerical Analysis. --- Global analysis (Mathematics). --- Computer science --- Numerical analysis. --- Mathématiques --- Analyse globale (Mathématiques) --- Informatique --- Analyse numérique --- Differential equations, Partial --- Numerical analysis --- Numerical solutions --- Numerical solutions. --- Differential equations, Partial -- Numerical solutions. --- Electronic books. -- local. --- Mathematics --- Mathematical Theory --- Calculus --- Physical Sciences & Mathematics --- Mathematical analysis. --- Analysis (Mathematics). --- Applied mathematics. --- Engineering mathematics. --- Computer mathematics. --- Mathematical models. --- Mathematical analysis --- Models, Mathematical --- Simulation methods --- Computer mathematics --- Discrete mathematics --- Electronic data processing --- Engineering --- Engineering analysis --- 517.1 Mathematical analysis --- Math --- Science --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic --- Differential equations, Partial - Numerical solutions
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In questo testo si introducono i concetti di base per la modellistica numerica di problemi differenziali alle derivate parziali. Si considerano le classiche equazioni lineari ellittiche, paraboliche ed iperboliche, ma anche altre equazioni, quali quelle di diffusione e trasporto, di Navier-Stokes, e le leggi di conservazione, e si forniscono numerosi esempi fisici che stanno alla base di tali equazioni. Quindi si analizzano metodi di risoluzione numerica basati su elementi finiti, differenze finite, volumi finiti, metodi spettrali e metodi di decomposizione di domini. In particolare vengono discussi gli aspetti algoritmici e di implementazione al calcolatore e si forniscono diversi programmi di semplice utilizzo. Il testo non presuppone una approfondita conoscenza matematica delle equazioni alle derivate parziali: i concetti rigorosamente indispensabili al riguardo sono riportati nell'Appendice. Esso è pertanto adatto agli studenti dei corsi di laurea di indirizzo scientifico (Ingegneria, Matematica, Fisica, Scienze dell'Informazione) e consigliabile a ricercatori del mondo accademico ed extra-accademico che vogliano avvicinarsi a questo interessante ramo della matematica applicata.
Mathematical analysis --- Calculus --- Analyse mathématique --- Calcul infinitésimal --- Calculus. --- Mathematical analysis. --- Mathematics --- Engineering & Applied Sciences --- Physical Sciences & Mathematics --- Mathematical Theory --- Applied Mathematics --- Mathematical models. --- Differential equations --- Numerical solutions. --- 517.91 Differential equations --- Models, Mathematical --- Mathematics. --- Analysis (Mathematics). --- Applied mathematics. --- Engineering mathematics. --- Computer mathematics. --- Numerical analysis. --- Mathematics, general. --- Analysis. --- Numerical Analysis. --- Mathematical Modeling and Industrial Mathematics. --- Applications of Mathematics. --- Computational Mathematics and Numerical Analysis. --- Simulation methods --- Computer mathematics --- Discrete mathematics --- Electronic data processing --- Engineering --- Engineering analysis --- 517.1 Mathematical analysis --- Math --- Science --- Global analysis (Mathematics). --- Computer science --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic
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In questo testo si introducono i concetti di base per la modellistica numerica di problemi differenziali alle derivate parziali. Si considerano le classiche equazioni lineari ellittiche, paraboliche ed iperboliche, ma anche altre equazioni, quali quelle di diffusione e trasporto, di Navier-Stokes e le leggi di conservazione; si forniscono inoltre numerosi esempi fisici che stanno alla base di tali equazioni. Quindi si analizzano metodi di risoluzione numerica basati su elementi finiti (continui e discontinui), differenze finite, volumi finiti, metodi spettrali (continui e discontinui), nonché strategie di approssimazione più avanzate basate sui metodi di decomposizione di domini o quelli di risoluzione di problemi di controllo ottimale. In particolare vengono discussi gli aspetti algoritmici e di implementazione al calcolatore e si forniscono diversi programmi di semplice utilizzo. Il testo non presuppone una approfondita conoscenza matematica delle equazioni alle derivate parziali: i concetti rigorosamente indispensabili al riguardo sono riportati nell'Appendice. Esso è pertanto adatto agli studenti dei corsi di laurea di indirizzo scientifico (Ingegneria, Matematica, Fisica, Scienze dell'Informazione) e consigliabile a ricercatori del mondo accademico ed extra-accademico che vogliano avvicinarsi a questo interessante ramo della matematica applicata e delle scienze computazionali.
Calculus. --- Mathematical analysis. --- Mathematics. --- Mathematics --- Physical Sciences & Mathematics --- Mathematical Theory --- Analysis (Mathematics). --- Applied mathematics. --- Engineering mathematics. --- Computer mathematics. --- Numerical analysis. --- Mathematical models. --- Mathematics, general. --- Analysis. --- Numerical Analysis. --- Mathematical Modeling and Industrial Mathematics. --- Applications of Mathematics. --- Computational Mathematics and Numerical Analysis. --- Global analysis (Mathematics). --- Computer science --- Computer mathematics --- Discrete mathematics --- Electronic data processing --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic --- Mathematical analysis --- Math --- Science --- Engineering --- Engineering analysis --- Models, Mathematical --- Simulation methods --- 517.1 Mathematical analysis
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In questo testo si introducono i concetti di base per la modellistica numerica di problemi differenziali alle derivate parziali. Si considerano le classiche equazioni lineari ellittiche, paraboliche ed iperboliche, ma anche altre equazioni, quali quelle di diffusione e trasporto, di Navier-Stokes e le leggi di conservazione. Si forniscono inoltre numerosi esempi fisici che stanno alla base di tali equazioni. Quindi si analizzano metodi di risoluzione numerica basati su elementi finiti (continui e discontinui), differenze finite, volumi finiti, metodi spettrali (continui e discontinui), nonché strategie di approssimazione più avanzate basate sui metodi di decomposizione di domini, i metodi a basi ridotte o quelli di risoluzione di problemi di controllo ottimale. In particolare vengono discussi gli aspetti algoritmici e di implementazione al calcolatore e si forniscono diversi programmi di semplice utilizzo. Il testo non presuppone una approfondita conoscenza matematica delle equazioni alle derivate parziali: i concetti rigorosamente indispensabili al riguardo sono riportati nell’Appendice. Esso è pertanto adatto agli studenti dei corsi di laurea di indirizzo scientifico (Ingegneria, Matematica, Fisica, Scienze dell’Informazione) e consigliabile a ricercatori del mondo accademico ed extra-accademico che vogliano avvicinarsi a questo interessante ramo della matematica applicata e delle scienze computazionali. Nel corso delle diverse edizioni i contenuti sono aumentati significativamente, aprendo a temi di crescente attualità nel contesto del calcolo scientifico per problemi differenziali. In particolare la sesta edizione contiene rispetto alla precedente un capitolo nuovo sulle basi ridotte, una moderna strategia di riduzione di modello per la risoluzione efficiente di problemi differenziali parametrizzati.
Mathematics. --- Mathematical analysis. --- Analysis (Mathematics). --- Applied mathematics. --- Engineering mathematics. --- Computer mathematics. --- Numerical analysis. --- Mathematical models. --- Mathematics, general. --- Analysis. --- Numerical Analysis. --- Mathematical Modeling and Industrial Mathematics. --- Applications of Mathematics. --- Computational Mathematics and Numerical Analysis. --- Models, Mathematical --- Computer mathematics --- Discrete mathematics --- Electronic data processing --- Engineering --- Engineering analysis --- 517.1 Mathematical analysis --- Mathematical analysis --- Math --- Mathematics --- Global analysis (Mathematics). --- Computer science --- Science --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic --- Simulation methods
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Mathematics forms bridges between knowledge, tradition, and contemporary life. The continuous development and growth of its many branches, both classical and modern, permeates and fertilizes all aspects of applied science and technology, and so has a vital impact on our modern society. The book will focus on these aspects and will benefit from the contribution of several world-famous scientists from mathematics and related sciences.
Mathematics. --- Science. --- Mathematics --- Engineering & Applied Sciences --- Applied Mathematics --- Mathematical Theory --- Physical Sciences & Mathematics --- Measurement. --- Measuring --- Mensuration --- Math --- Architecture. --- Applied mathematics. --- Engineering mathematics. --- Computer mathematics. --- Mathematical models. --- Applications of Mathematics. --- Mathematics, general. --- Mathematical Modeling and Industrial Mathematics. --- Computational Mathematics and Numerical Analysis. --- Computational Science and Engineering. --- Architecture, general. --- Science --- Technology --- Metrology --- Physical measurements --- Computer science --- Computer science. --- Architecture, Western (Western countries) --- Building design --- Buildings --- Construction --- Western architecture (Western countries) --- Art --- Building --- Informatics --- Computer mathematics --- Discrete mathematics --- Electronic data processing --- Design and construction --- Models, Mathematical --- Simulation methods --- Engineering --- Engineering analysis --- Mathematical analysis --- Architecture, Primitive
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La Matematica Numerica una disciplina che si sviluppa in simbiosi con il calcolatore; essa fa uso di linguaggi di programmazione che consentono di tradurre gli algoritmi in programmi eseguibili. Questo testo si propone di aiutare lo studente nella transizione fra i concetti teorici e metodologici della Matematica Numerica e la loro implementazione al computer. A questo scopo vengono proposti Esercizi teorici da risolvere con carta e penna atti a far comprendere meglio al lettore la teoria, e Laboratori, in cui per un dato problema si debbono scegliere gli algoritmi pi adatti, realizzare un programma in linguaggio MATLAB per la loro implementazione, rappresentare graficamente in maniera idonea i risultati ottenuti dal calcolatore, infine interpretarli ed analizzarli alla luce della teoria. Per ogni Esercizio ed ogni Laboratorio si presenta una risoluzione dettagliata,completata da una ampia discussione critica. Per una migliore fruizione degli argomenti sviluppati, il testo si apre con una introduzione allambiente di programmazione MATLAB. Il testo contiene infine alcuni Progetti. Il primo concerne gli algoritmi di page ranking dei moderni motori di ricerca, il secondo la determinazione del campo elettrico fra due conduttori e il calcolo della capacit di un condensatore, il terzo lo studio di sistemi dinamici oscillanti di grande rilevanza in applicazioni elettroniche e biologiche. Il testo rivolto a studenti dei corsi di laurea in Matematica, Ingegneria, Fisica e Informatica. La seconda edizione stata arricchita con numerosi nuovi Esercizi e Progetti.
Engineering & Applied Sciences --- Applied Mathematics --- Mathematics. --- Applied mathematics. --- Engineering mathematics. --- Computer mathematics. --- Numerical analysis. --- Numerical Analysis. --- Computational Mathematics and Numerical Analysis. --- Computational Science and Engineering. --- Applications of Mathematics. --- Computer science --- Computer science. --- Mathematical analysis --- Math --- Science --- Informatics --- Computer mathematics --- Discrete mathematics --- Electronic data processing --- Mathematics --- Engineering --- Engineering analysis
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In this text, we introduce the basic concepts for the numerical modelling of partial differential equations. We consider the classical elliptic, parabolic and hyperbolic linear equations, but also the diffusion, transport, and Navier-Stokes equations, as well as equations representing conservation laws, saddle-point problems and optimal control problems. Furthermore, we provide numerous physical examples which underline such equations. We then analyze numerical solution methods based on finite elements, finite differences, finite volumes, spectral methods and domain decomposition methods, and reduced basis methods. In particular, we discuss the algorithmic and computer implementation aspects and provide a number of easy-to-use programs. The text does not require any previous advanced mathematical knowledge of partial differential equations: the absolutely essential concepts are reported in a preliminary chapter. It is therefore suitable for students of bachelor and master courses in scientific disciplines, and recommendable to those researchers in the academic and extra-academic domain who want to approach this interesting branch of applied mathematics.
Mathematics. --- Mathematical analysis. --- Analysis (Mathematics). --- Applied mathematics. --- Engineering mathematics. --- Numerical analysis. --- Mathematical models. --- Analysis. --- Numerical Analysis. --- Mathematical Modeling and Industrial Mathematics. --- Applications of Mathematics. --- Global analysis (Mathematics). --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic --- Mathematical analysis --- Math --- Science --- Models, Mathematical --- Simulation methods --- Engineering --- Engineering analysis --- 517.1 Mathematical analysis --- Mathematics --- Differential equations, Partial --- Numerical solutions.
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In this text, we introduce the basic concepts for the numerical modelling of partial differential equations. We consider the classical elliptic, parabolic and hyperbolic linear equations, but also the diffusion, transport, and Navier-Stokes equations, as well as equations representing conservation laws, saddle-point problems and optimal control problems. Furthermore, we provide numerous physical examples which underline such equations. We then analyze numerical solution methods based on finite elements, finite differences, finite volumes, spectral methods and domain decomposition methods, and reduced basis methods. In particular, we discuss the algorithmic and computer implementation aspects and provide a number of easy-to-use programs. The text does not require any previous advanced mathematical knowledge of partial differential equations: the absolutely essential concepts are reported in a preliminary chapter. It is therefore suitable for students of bachelor and master courses in scientific disciplines, and recommendable to those researchers in the academic and extra-academic domain who want to approach this interesting branch of applied mathematics.
Mathematics. --- Mathematical analysis. --- Analysis (Mathematics). --- Applied mathematics. --- Engineering mathematics. --- Computer mathematics. --- Numerical analysis. --- Mathematical models. --- Mathematics, general. --- Analysis. --- Numerical Analysis. --- Mathematical Modeling and Industrial Mathematics. --- Applications of Mathematics. --- Computational Mathematics and Numerical Analysis. --- Global analysis (Mathematics). --- Computer science --- Computer mathematics --- Discrete mathematics --- Electronic data processing --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic --- Mathematical analysis --- Math --- Science --- Mathematics --- Differential equations, Partial --- Numerical solutions. --- Numerical analysis --- Engineering --- Engineering analysis --- Models, Mathematical --- Simulation methods --- 517.1 Mathematical analysis
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