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A Primer on PDEs
This book is designed as an advanced undergraduate or a first-year graduate course for students from various disciplines like applied mathematics, physics, engineering. It has evolved while teaching courses on partial differential equations during the last decade at the Politecnico of Milan. The main purpose of these courses was twofold: on the one hand, to train the students to appreciate the interplay between theory and modelling in problems arising in the applied sciences and on the other hand to give them a solid background for numerical methods, such as finite differences and finite elements.
Invito alle equazioni a derivate parziali
Il testo è rivolto a studenti di ingegneria, matematica applicata e fisica ed è disegnato per corsi alle fine del triennio o all'inizio del biennio magistrale. obiettivo didattico è duplice: da un lato presentare ed analizzare alcuni classici modelli differenziali della Meccanica dei Continui, completati da esercizi svolti e da simulazioni numeriche, illustrate usando il metodo delle differenze finite; dall'altro introdurre la formulazione variazionale dei più importanti problemi iniziali/al bordo, accompagnate da simulazioni numeriche effettuate utilizzando il metodo degli elementi finiti. In ultima analisi, il percorso didattico è caratterizzato da una costante sinergia tra modello-teoria-simulazione numerica.
The Heart of the City
The Heart of the City concept, which was introduced at CIAM 8 in 1951, has played an important role in architectural and urban debates. The Heart became the most important of the organic references used in the 1950s for defining a theory of urban form. This book focuses on both the historical and theoretical reinterpretation of this seminal concept. Divided into two main sections, both looking at differing ways in which the Heart has influenced more recent urban thinking, it illustrates the continuity and the complexities of the Heart of the City. In doing so, this book offers a new perspective on the significance of public space and shows how The Heart of the City still resonates closely with contemporary debates about centrality, identity and the design of public space. It would be of interest to architects, academics and students of urban design and planning.
Trends in the Theory and Practice of Non-Linear Analysis
Trends in the Theory and Practice of Non-Linear Analysis
Variational Methods for Discontinuous Structures
In recent years many researchers in material science have focused their attention on the study of composite materials, equilibrium of crystals and crack distribution in continua subject to loads. At the same time several new issues in computer vision and image processing have been studied in depth. The understanding of many of these problems has made significant progress thanks to new methods developed in calculus of variations, geometric measure theory and partial differential equations. In particular, new technical tools have been introduced and successfully applied. For example, in order to describe the geometrical complexity of unknown patterns, a new class of problems in calculus of variations has been introduced together with a suitable functional setting: the free-discontinuity problems and the special BV and BH functions. The conference held at Villa Olmo on Lake Como in September 1994 spawned successful discussion of these topics among mathematicians, experts in computer science and material scientists.
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