Ce livre présente les bases théoriques et méthodologiques de l'analyse numérique, en se concentrant sur la stabilité, la précision et la complexité des algorithmes. Il couvre des thèmes variés tels que la résolution de systèmes, l'optimisation et l'intégration numérique, avec de nombreux exemples et des programmes MATLAB pour une application concrète.
"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.
Focusing on the numerical approximation of Partial Differential Equations (PDEs), this volume draws on extensive teaching experience to guide students through essential concepts in numerical analysis. It includes a variety of examples and exercises, emphasizing practical applications and problem-solving skills to enhance understanding and mastery of the subject.
Questo testo offre una raccolta di esercizi su metodi analitici e numerici, adatta a corsi di Ingegneria e Matematica. Tratta equazioni alle derivate parziali, diffusione, convezione e fluidodinamica, con focus sul metodo degli elementi finiti e tecniche numeriche. Include esercizi pratici con la libreria MLife in MATLAB.