This textbook is devoted to second order linear partial differential equations. The focus is on variational formulations in Hilbert spaces. It contains elliptic equations, including some basic results on Fredholm alternative and spectral theory, some useful notes on functional analysis, a brief presentation of Sobolev spaces and their properties, saddle point problems, parabolic equations and hyperbolic equations. Many exercises are added, and the complete solution of all of them is included. The work is mainly addressed to students in Mathematics, but also students in Engineering with a good mathematical background should be able to follow the theory presented here.
Everything is more simple than one thinks but at the same time more complex than one can understand Johann Wolfgang von Goethe To reach the point that is unknown to you, you must take the road that is unknown to you St. John of the Cross This is a book on the numerical approximation ofpartial differential equations (PDEs). Its scope is to provide a thorough illustration of numerical methods (especially those stemming from the variational formulation of PDEs), carry out their stability and convergence analysis, derive error bounds, and discuss the algorithmic aspects relative to their implementation. A sound balancing of theoretical analysis, description of algorithms and discussion of applications is our primary concern. Many kinds of problems are addressed: linear and nonlinear, steady and time-dependent, having either smooth or non-smooth solutions. Besides model equations, we consider a number of (initial-) boundary value problems of interest in several fields of applications. Part I is devoted to the description and analysis of general numerical methods for the discretization of partial differential equations. A comprehensive theory of Galerkin methods and its variants (Petrov Galerkin and generalized Galerkin), as wellas ofcollocationmethods, is devel oped for the spatial discretization. This theory is then specified to two numer ical subspace realizations of remarkable interest: the finite element method (conforming, non-conforming, mixed, hybrid) and the spectral method (Leg endre and Chebyshev expansion).
This book deals with the mathematical analysis and the numerical approximation of eddy current problems in the time-harmonic case. It takes into account all the most used formulations, placing the problem in a rigorous functional framework.
This textbook is devoted to second order linear partial differential equations. The focus is on variational formulations in Hilbert spaces. It contains elliptic equations, including the biharmonic problem, some useful notes on functional analysis, a brief presentation of Sobolev spaces and their properties, some basic results on Fredholm alternative and spectral theory, saddle point problems, parabolic and linear Navier-Stokes equations, and hyperbolic and Maxwell equations. Almost 80 exercises are added, and the complete solution of all of them is included. The work is mainly addressed to students in Mathematics, but also students in Engineering with a good mathematical background should be able to follow the theory presented here. This second edition has been enriched by some new sections and new exercises; in particular, three important equations are now included: the biharmonic equation, the linear Navier-Stokes equations and the Maxwell equations.
Everything is more simple than one thinks but at the same time more complex than one can understand Johann Wolfgang von Goethe To reach the point that is unknown to you, you must take the road that is unknown to you St. John of the Cross This is a book on the numerical approximation ofpartial differential equations (PDEs). Its scope is to provide a thorough illustration of numerical methods (especially those stemming from the variational formulation of PDEs), carry out their stability and convergence analysis, derive error bounds, and discuss the algorithmic aspects relative to their implementation. A sound balancing of theoretical analysis, description of algorithms and discussion of applications is our primary concern. Many kinds of problems are addressed: linear and nonlinear, steady and time-dependent, having either smooth or non-smooth solutions. Besides model equations, we consider a number of (initial-) boundary value problems of interest in several fields of applications. Part I is devoted to the description and analysis of general numerical methods for the discretization of partial differential equations. A comprehensive theory of Galerkin methods and its variants (Petrov Galerkin and generalized Galerkin), as wellas ofcollocationmethods, is devel oped for the spatial discretization. This theory is then specified to two numer ical subspace realizations of remarkable interest: the finite element method (conforming, non-conforming, mixed, hybrid) and the spectral method (Leg endre and Chebyshev expansion).
This book deals with the mathematical analysis and the numerical approximation of eddy current problems in the time-harmonic case. It takes into account all the most used formulations, placing the problem in a rigorous functional framework.
Fleeing a Hollywood that spurned him, Orson Welles arrived in Italy in 1947 to begin his career anew. Far from being welcomed as the celebrity who directed and starred in Citizen Kane, his six-year exile in Italy was riddled with controversy, financial struggles, disastrous love affairs, and failed projects. Alberto Anile's book depicts the artist's life and work in Italy, including his reception by the Italian press, his contentious interactions with key political figures, and his artistic output, which culminated in the filming of Othello. Drawing on revelatory new material on the artist's personal and professional life abroad, Orson Welles in Italy also chronicles Italian cinema's transition from the social concerns of neorealism to the alienated characters in films such as Federico Fellini's La Dolce Vita, amid the cultural politics of postwar Europe and the beginnings of the cold war.
ENGLISH - ITALIAN TEXT Amalia is a heroin, a mother and a wife: she retraces the events of her family through three generations. She welcomes their inheritance in a hard struggle to survive between a Country's rural age at its sunset and a working-class Milan in which the war is perceived by apocalyptic aerial bombardments and alarm sirens. Of the war she talks about the anxiety and the horror: she faces losses and mourning with an aching and courageous heart, with the determination to build a future for her and her little daughter and with the certainty of the return of her never forgotten hero, Commander Guido. He, in the meanwhile, is engaged with his patrol in an epic crossing of the Sahara desert through Libya, Tunisia and Algeria, trying to bring his men to safety.
Megalithism, or the art of using huge boulders to create sacred, pagan monuments and sites, still fascinates us today. How did Prehistoric man cut, transport, and place such enormous stones, some weighing up to 200 metric tons, without bulldozers, drills, and cranes? Yet primitive man, without the written word or wheel, created structures which still stupefy us in the 21st century, both due to their components and the precision used in positioning them. This book takes us back in time to the 5th-2nd millennia B.C. and helps us visualise the Stone Age world and its constructions - menhirs, dolmens, rows and circles of standing stones. Undoubtedly they were sacred places, used for pagan rituals and funerary purposes, but the author also gives us details of their astronomic and physical alignment, which clearly demonstrates the knowledge of the heavens these ancestors had and how they applied it without slide-rules, set squares, and theodolites. The high priests of ancient times could calculate when the solstices and equinoxes would occur and thus regulate the seasons for sowing and reaping. The author's careful and updated identification of all such structures leads us through 'Ancient European Megalithism' complete with the religious and social aspects of it and its pagan legacies. He does not neglect forms of 'sub-actual' megalithism either - the use of massive stones by peoples described as primitive but with a relatively advanced culture who lived in times closer to our own in Africa, Asia, and South America. The myths and legends arising from the megalithic structures are recounted here in detail; the author also describes megalithic art in the form of statue-stele and menhir statues, as well as the often intricate decoration carved on single stones and in construction such as dolmens, funerary mounds, astronomic observatories, and temples. He also describes studies and experiments on the methods of transport and construction used by Prehistoric peoples, together with conflicting opinions and theories. Amply illustrated with photographs and drawings, Megalithism guides the reader through every part of the megalithic world with smooth-flowing text that will be accessible to specialists and interested general public alike.
Alberto Cossu's ethnographic research on the MACAO centre in Italy radiates out to questions about what it means to be a modern artist, and how much autonomy is left to the artist in a globalized and politicised world. "Autonomous Art Institutions" provides a unique perspective on the political engagement of artists in order to investigate the reconfiguration of contemporary art practices as they dissolve in social and economic processes. The book provides insight into the making of a radical art institution across seven years of activity, showing how social, cultural and economic elements are appropriated and repurposed by artists in the process. Based on years of sociological research as well as direct involvement of the author in the artistic practices, the book illuminates the spark of society-to-come by examining the doings of artists as they attempt to disrupt the ‘creative city’.
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