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Mathematical analysis --- Mathematics --- Planning (firm) --- Computer science --- Computer. Automation --- analyse (wiskunde) --- informatica --- mathematische modellen --- wiskunde --- informaticaonderzoek
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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 --- Differential geometry. Global analysis --- Mathematical analysis --- Numerical analysis --- Mathematics --- Planning (firm) --- Computer. Automation --- analyse (wiskunde) --- toegepaste wiskunde --- informatica --- mathematische modellen --- statistiek --- externe fixatie (geneeskunde --- wiskunde --- wiskunde --- numerieke analyse
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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.
Mathematics --- Numerical analysis --- Mathematics --- Computer science --- Computer. Automation --- Matlab (informatica) --- toegepaste wiskunde --- computers --- informatica --- externe fixatie (geneeskunde --- wiskunde --- wiskunde --- algoritmen --- informaticaonderzoek --- computerkunde --- numerieke analyse
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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.
Mathematical analysis --- Numerical analysis --- Mathematics --- Applied physical engineering --- Planning (firm) --- Computer. Automation --- analyse (wiskunde) --- toegepaste wiskunde --- computers --- economie --- informatica --- mathematische modellen --- wiskunde --- algoritmen --- numerieke analyse
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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.
Differential geometry. Global analysis --- Mathematical analysis --- Numerical analysis --- Mathematics --- Planning (firm) --- analyse (wiskunde) --- toegepaste wiskunde --- mathematische modellen --- statistiek --- wiskunde --- numerieke analyse
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The book comprises contributions by some of the most respected scientists in the field of mathematical modeling and numerical simulation of the human cardiocirculatory system. The contributions cover a wide range of topics, from the preprocessing of clinical data to the development of mathematical equations, their numerical solution, and both in-vivo and in-vitro validation. They discuss the flow in the systemic arterial tree and the complex electro-fluid-mechanical coupling in the human heart. Many examples of patient-specific simulations are presented. This book is addressed to all scientists interested in the mathematical modeling and numerical simulation of the human cardiocirculatory system.
Mathematics --- Biomathematics. Biometry. Biostatistics --- Biology --- Human biochemistry --- Human physiology --- Applied physical engineering --- Engineering sciences. Technology --- Biotechnology --- Computer. Automation --- ICT (informatie- en communicatietechnieken) --- medische biochemie --- toegepaste wiskunde --- biomathematica --- biologie --- economie --- fysiologie --- wiskunde --- ingenieurswetenschappen
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Simulating the behavior of a human heart, predicting tomorrow's weather, optimizing the aerodynamics of a sailboat, finding the ideal cooking time for a hamburger: to solve these problems, cardiologists, meteorologists, sportsmen, and engineers can count on math help. This book will lead you to the discovery of a magical world, made up of equations, in which a huge variety of important problems for our life can find useful answers.
Numerical analysis --- Mathematics --- Epidemiology --- Planning (firm) --- Computer science --- Computer. Automation --- informatica --- mathematische modellen --- epidemiologie --- wiskunde --- algoritmen --- informaticaonderzoek --- numerieke analyse
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Numerical analysis --- Chemistry --- Computer science --- Computer architecture. Operating systems --- Computer. Automation --- Matlab (informatica) --- visualisatie --- chemie --- informatica --- algoritmen --- informaticaonderzoek --- numerieke analyse
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Mathematical analysis --- Numerical analysis --- Mathematics --- Computer science --- Computer. Automation --- Matlab (informatica) --- analyse (wiskunde) --- toegepaste wiskunde --- informatica --- wiskunde --- informaticaonderzoek --- numerieke analyse
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Mathematical analysis --- Numerical analysis --- Mathematics --- Computer science --- Computer. Automation --- Matlab (informatica) --- analyse (wiskunde) --- toegepaste wiskunde --- informatica --- wiskunde --- informaticaonderzoek --- numerieke analyse
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