Alfio Quarteroni Boeken

This book delves into the numerical approximation of partial differential equations (PDEs), aiming to illustrate various numerical methods, particularly those derived from the variational formulation of PDEs. It covers stability and convergence analysis, error bounds, and algorithmic implementation aspects, balancing theoretical analysis with practical applications. The text addresses a variety of problems, including linear and nonlinear, steady and time-dependent scenarios, with both smooth and non-smooth solutions. It also explores model equations and several (initial-) boundary value problems relevant to multiple application fields. Part I focuses on general numerical methods for discretizing PDEs, developing a comprehensive theory around Galerkin methods and their variants (such as Petrov Galerkin and generalized Galerkin), alongside collocation methods for spatial discretization. This theoretical framework is then applied to two significant numerical subspace realizations: the finite element method (including conforming, non-conforming, mixed, and hybrid types) and the spectral method (utilizing Legendre and Chebyshev expansions).

"One of the purposes of this book is to provide the mathematical foundations of numerical methods, to analyze their basic theoretical properties (stability, accuracy, and computational complexity), and to demonstrate their performances on examples and counterexamples, which outline their pros and cons. This is done using the MATLAB software environment, which is user-friendly and widely adopted. Within any specific class of problems, the most appropriate scientific computing algorithms are reviewed, their theoretical analyses are carried out, and the expected results are verified on a MATLAB computer implementation. Every chapter is supplied with examples, exercises, and applications of the discussed theory to the solution of real-life problems.". "This book is addressed to senior undergraduate and graduate students with particular focus on degree courses in engineering, mathematics, physics, and computer science. The attention paid to the applications and the related development of software makes it valuable also to researchers and users of scientific computing in a large variety of professional fields."--BOOK JACKET.

This introduction to Scientific Computing illustrates several numerical methods for the computer solution of certain classes of mathematical problems. The authors show how to compute the zeros or the integrals of continuous functions, solve linear systems, approximate functions by polynomials and construct accurate approximations for the solution of differential equations. To make the presentation concrete, the programming environment Matlab is adopted as a faithful companion.

Focusing on the numerical modeling of partial differential equations, this book covers essential concepts and emphasizes algorithmic and computer implementation. It includes straightforward programs designed for practical use, making it accessible for readers interested in applying these techniques in computational settings.

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.

Covid-19 has shown us the importance of mathematical and statistical models to interpret reality, provide forecasts, and explore future scenarios. Algorithms, artificial neural networks, and machine learning help us discover the opportunities and pitfalls of a world governed by mathematics and artificial intelligence.

Numerische Mathematik ist ein zentrales Gebiet der Mathematik, das für vielfältige Anwendungen die Grundlage bildet und das alle Studierenden der Mathematik, Ingenieurwissenschaften, Informatik und Physik kennenlernen. Das vorliegende Lehrbuch ist eine didaktisch exzellente, besonders sorgfältig ausgearbeitete Einführung für Anfänger. Eines der Ziele dieses Buches ist es, die mathematischen Grundlagen der numerischen Methoden zu liefern, ihre grundlegenden theoretischen Eigenschaften (Stabilität, Genauigkeit, Komplexität)zu analysieren, und ihre Leistungsfähigkeit an Beispielen und Gegenbeispielen mittels MATLAB zu demonstrieren. Die besondere Sorgfalt, die den Anwendungen und betreffenden Softwareentwicklungen gewidmet wurde, macht das vorliegende Werk auch für Studenten mit abgeschlossenem Studium, Wissenschaftler und Anwender des wissenschaftlichen Rechnens in vielen Berufsfeldern zu einem unverzichtbaren Arbeitsmittel.

In questo testo si introducono i concetti elementari di 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 e metodi spettrali. Il volume h adatto agli studenti dei corsi di laurea di indirizzo scientifico (Ingegneria, Fisica, Matematica, Chimica, Scienza dell'Informazione) e consigliato ai ricercatori del mondo accademico ed extra-accademico che vogliano avvicinarsi a questo interessante ramo della matematica applicata.

La Matematica Numerica è elemento fondante del calcolo scientifico. Punto di contatto di diverse discipline nella matematica e nelle moderne scienze applicate, ne diventa strumento di indagine qualitativa e quantitativa. Scopo di questo testo è fornire i fondamenti metodologici della matematica numerica, richiamandone le principali proprietà, quali la stabilità, l'accuratezza e la complessità algoritmica. Nel contesto di ogni specifica classe di problemi vengono illustrati gli algoritmi più idonei, ne viene fatta l'analisi teorica e se ne verificano i risultati previsti implementandoli con ausilio di programmi in linguaggio MATLAB. Il volume è indirizzato principalmente agli studenti delle facoltà scientifiche, con particolare attenzione ai corsi di laurea in Ingegneria, Matematica e Scienze dell'Informazione. L'enfasi posta sullo sviluppo di software lo rende interessante auche per ricercatori e utilizzatori delle tecniche del calcolo scientifico nei campi professionali piú disparati.

Mathematik spielt eine entscheidende Rolle bei der Lösung vielfältiger Herausforderungen, von der Herzsimulation über Wettervorhersagen bis hin zur Optimierung von Sportgeräten. Das Buch eröffnet eine faszinierende Welt, in der Gleichungen nicht nur abstrakte Konzepte sind, sondern praktische Werkzeuge zur Bewältigung alltäglicher Probleme bieten. Leser werden eingeladen, die vielseitigen Anwendungen der Mathematik zu entdecken und deren Bedeutung für verschiedene Fachgebiete zu erkennen.