This textbook introduces the study of partial differential equations using both analytical and numerical methods. By intertwining the two complementary approaches, the authors create an ideal foundation for further study. Motivating examples from the physical sciences, engineering, and economics complete this integrated approach. A showcase of models begins the book, demonstrating how PDEs arise in practical problems that involve heat, vibration, fluid flow, and financial markets. Several important characterizing properties are used to classify mathematical similarities, then elementary methods are used to solve examples of hyperbolic, elliptic, and parabolic equations. From here, an accessible introduction to Hilbert spaces and the spectral theorem lay the foundation for advanced methods. Sobolev spaces are presented first in dimension one, before being extended to arbitrary dimension for the study of elliptic equations. An extensive chapter on numerical methods focuses on finite difference and finite element methods. Computer-aided calculation with MapleTM completes the book. Throughout, three fundamental examples are studied with different tools: Poisson’s equation, the heat equation, and the wave equation on Euclidean domains. The Black–Scholes equation from mathematical finance is one of several opportunities for extension. Partial Differential Equations offers an innovative introduction for students new to the area. Analytical and numerical tools combine with modeling to form a versatile toolbox for further study in pure or applied mathematics. Illuminating illustrations and engaging exercises accompany the text throughout. Courses in real analysis and linear algebra at the upper-undergraduate level are assumed.
Optimal feedback control arises in different areas such as aerospace engineering, chemical processing, resource economics, etc. In this context, the application of dynamic programming techniques leads to the solution of fully nonlinear Hamilton-Jacobi-Bellman equations. This book presents the state of the art in the numerical approximation of Hamilton-Jacobi-Bellman equations, including post-processing of Galerkin methods, high-order methods, boundary treatment in semi-Lagrangian schemes, reduced basis methods, comparison principles for viscosity solutions, max-plus methods, and the numerical approximation of Monge-Ampère equations. This book also features applications in the simulation of adaptive controllers and the control of nonlinear delay differential equations. Contents From a monotone probabilistic scheme to a probabilistic max-plus algorithm for solving Hamilton–Jacobi–Bellman equations Improving policies for Hamilton–Jacobi–Bellman equations by postprocessing Viability approach to simulation of an adaptive controller Galerkin approximations for the optimal control of nonlinear delay differential equations Efficient higher order time discretization schemes for Hamilton–Jacobi–Bellman equations based on diagonally implicit symplectic Runge–Kutta methods Numerical solution of the simple Monge–Ampere equation with nonconvex Dirichlet data on nonconvex domains On the notion of boundary conditions in comparison principles for viscosity solutions Boundary mesh refinement for semi-Lagrangian schemes A reduced basis method for the Hamilton–Jacobi–Bellman equation within the European Union Emission Trading Scheme
This book addresses the state of the art of reduced order methods for modelling and computational reduction of complex parametrised systems, governed by ordinary and/or partial differential equations, with a special emphasis on real time computing techniques and applications in various fields. Consisting of four contributions presented at the CIME summer school, the book presents several points of view and techniques to solve demanding problems of increasing complexity. The focus is on theoretical investigation and applicative algorithm development for reduction in the complexity – the dimension, the degrees of freedom, the data – arising in these models. The book is addressed to graduate students, young researchers and people interested in the field. It is a good companion for graduate/doctoral classes.
Wavelet methods are by now a well-known tool in image processing (jpeg2000). These functions have been used successfully in other areas, however. Elliptic Partial Differential Equations which model several processes in, for example, science and engineering, is one such field. This book, based on the author's course, gives an introduction to wavelet methods in general and then describes their application for the numerical solution of elliptic partial differential equations. Recently developed adaptive methods are also covered and each scheme is complemented with numerical results , exercises, and corresponding software.
Sapere aude! Immanuel Kant (1724-1804) Numerical simulations playa key role in many areas of modern science and technology. They are necessary in particular when experiments for the underlying problem are too dangerous, too expensive or not even possible. The latter situation appears for example when relevant length scales are below the observation level. Moreover, numerical simulations are needed to control complex processes and systems. In all these cases the relevant problems may become highly complex. Hence the following issues are of vital importance for a numerical simulation: - Efficiency of the numerical solvers: Efficient and fast numerical schemes are the basis for a simulation of 'real world' problems. This becomes even more important for realtime problems where the runtime of the numerical simulation has to be of the order of the time span required by the simulated process. Without efficient solution methods the simulation of many problems is not feasible. 'Efficient' means here that the overall cost of the numerical scheme remains proportional to the degrees of freedom, i. e. , the numerical approximation is determined in linear time when the problem size grows e. g. to upgrade accuracy. Of course, as soon as the solution of large systems of equations is involved this requirement is very demanding.
This pathbreaking ethnography of population movements between rural and urban places in Peru addresses the conceptual and methodological problems of studying ‘deterritorialized' populations and the implications of this for anthropology's notions of culture and identity. Based on extensive fieldwork, this book explores the economic, social and ritual bonds which link migrants in Peru's major cities to their Andean native village. Many urban migrants establish networks based on kinship and marriage ties to exploit resources in the city as well as the village. These networks ensure they maintain strong links to their native village. Fiestas, soccer tournaments and folklore festivals also play a crucial role in the formation of migrant communities in Peru's cities. The author analyses these performance practices and shows how they give rise to the creation of new social identities. The participation of second generation migrants, returning migrants, and migrant spouses in village life is also discussed.
In the face of great challenges, utopian thinking is currently in vogue. The fact that utopias, with their ideas of an idealized target society, are not compatible with the basic features of an Open Society was already pointed out by Karl Popper in his book 'Die Offene Gesellschaft und ihre Feinde' (The Open Society and its Enemies) under the impression of National Socialism and Stalinism. In the present book, further forms of Closed Societies and the principal similarities (and differences) of their construction are examined. This is done by drawing on Ralf Dahrendorf's concept of life chances, in which he deals with the interaction of options and ligatures. The ambivalence of Dahrendorf's understanding of ligatures, since they restrict options on the one hand, but also give them meaning on the other, is resolved by a threefold differentiation: into ethical and moral, internally and externally directed, and explicit and implicit ligatures. While the former are capable of enabling life chances, the latter tend to limit them. Based on this, the authors elaborate on the landscape (side) consequences of various closed societies and how ill-suited they are for dealing with current challenges.
City-regions are areas where the daily journeys for work, shopping and leisure frequently cross administrative boundaries. They are seen as engines of the national economy, but are also facing congestion and disparities. Thus, all over the world, governments attempt to increase problem-solving capacities in city-regions by institutional reform and a shift of functions. This book analyses the recent reforms and changes in the governance of city-regions in France, Germany and Italy. It covers themes such as the impact of austerity measures, territorial development, planning and state modernisation. The authors provide a systematic cross-country perspective on two levels, between six city-regions and between the national policy frameworks in these three countries. They use a solid comparative framework, which refers to the four dimensions functions, institutions and governance, ideas and space. They describe the course of the reforms, the motivations and the results, and consequently, they question the widespread metropolitan fever or resurgence of city-regions and provide a better understanding of recent changes in city-regional governance in Europe. The primary readership will be researchers and master students in planning, urban studies, urban geography, political science and governance studies, especially those interested in metropolitan regions and / or decentralisation. Due to the uniqueness of the work, the book will be of particular interest to scholars working on the comparative European dimension of territorial governance and planning. The Open Access version of this book, available at www.taylorfrancis.com, has been made available under a Creative Commons Attribution-Non Commercial-No Derivatives 4.0 license.
The understanding of landscape in the German-speaking area has some similarities with the discussions of the topic in other European languages and scientific communities, but there are some specifics. These specifics can be found both in the common sense understanding of landscape and in the history of scientific conceptualization. Special features of the common sense understanding lie on the one hand in the medieval roots, a strong romantic charge and the strong connection between home and landscape. With regard to the scientific examination of landscape, there are specific fractions and discontinuities in the German-speaking world. Contents• Theoretical Framing: the Creation of Landscape• The Genesis of the Landscape Concept in the German Language Regions – the Common Sense Understanding• The Concept of Landscape in Landscape-Related Sciences• Landscape Research in its Interdisciplinary and Transdisciplinary Challenge About the AuthorsDr. Karsten Berr works as a research assistant at the Department for Urban and Regional Development at the Eberhard Karls University Tübingen.Dr. Dr. Olaf Kühne is professor for Urban and Regional Development at the Eberhard Karls University Tübingen.
The urban morphology investigates settlement and urban forms. These do not change overnight, but in a process that follows certain principles. There is hardly anything more complex and contradictory than a city. Precisely because of this complexity, there is little agreement on definitions and procedural methods. This applies in particular to urban planning, which is not only concerned with analysis, but also with the design and transformation of cities. A variety of different urban morphological approaches exist today. The authors from the areas of research and practice investigate the relevance of the morphological perspective in the field of contemporary urban landscapes. They link historical roots and current approaches and explain the relationship between analysis and design.
Diploma Thesis from the year 2003 in the subject Social Work, grade: 1,0 (A), University of Applied Sciences Frankfurt am Main (Social Work and Health), language: English, abstract: Migration to urban areas is seen as a big contributor to the infrastructural problems in the cities. But, people do not migrate to the cities just because of the bright city lights; they also face problems in the rural areas which drive them to migrate. Social work is active in working with people and it shall be found out how the situation of rural out- migration and urbanisation is and what the impacts of social work can be in the rural areas as cause oriented intervention.
This volume provides a basic introduction to the philosophy of science and its central concepts, theories, and philosophical, scientific, and spatial positions and approaches.
Taking examples from major European cities, 'Public Spaces and Urbanity' is a practical guide demonstrating what urban development with a human face might look like. This involves renewing and enhancing humane cities using architecture on a human scale while taking their history into account. Thus the book follows the tradition established by Jan Gehl that regards urban space as a framework for people to live in and socialise. The European tradition of the dense classical city marks the point of departure for this book. Special emphasis is placed on physical and spatial parameters, on development patterns and building types, on the guiding principles governing access, and on interconnections with public roads and pathways --all of which form the foundations of urban life as well as cities that provide safety and security. The book is divided into ten thematic chapters, each providing a definition and general outline of core challenges together with proposals for meeting them. An historical outline of urban development and the practically organised thematic structure underlying concepts discussed allow the examples given to greatly broaden the field of understanding around this topic.
City-regions are areas where the daily journeys for work, shopping and leisure frequently cross administrative boundaries. They are seen as engines of the national economy, but are also facing congestion and disparities. Thus, all over the world, governments attempt to increase problem-solving capacities in city-regions by institutional reform and a shift of functions. This book analyses the recent reforms and changes in the governance of city-regions in France, Germany and Italy. It covers themes such as the impact of austerity measures, territorial development, planning and state modernisation. The authors provide a systematic cross-country perspective on two levels, between six city-regions and between the national policy frameworks in these three countries. They use a solid comparative framework, which refers to the four dimensions functions, institutions and governance, ideas and space. They describe the course of the reforms, the motivations and the results, and consequently, they question the widespread metropolitan fever or resurgence of city-regions and provide a better understanding of recent changes in city-regional governance in Europe. The primary readership will be researchers and master students in planning, urban studies, urban geography, political science and governance studies, especially those interested in metropolitan regions and / or decentralisation. Due to the uniqueness of the work, the book will be of particular interest to scholars working on the comparative European dimension of territorial governance and planning. The Open Access version of this book, available at www.taylorfrancis.com, has been made available under a Creative Commons Attribution-Non Commercial-No Derivatives 4.0 license.
People often associate postwar Germany with technology and with its products of mass consumption, such as luxury cars. Even pop music, most notably Kraftwerk (literally 'power station') with songs such as Autobahn, Radioactivity or We are the Robots, disseminates the stereotype of a close link between German culture and technology. Technology in Modern German History explores various forms of technology in 200 years of German history and explains how technology has been fundamental to the shaping of modern Germany. The book investigates the role technology played in transforming Germany's culture, society and politics during the 19th and 20th centuries. Key topics covered include the different stages of industrialization, the growth of networked cities, and the triumph of a teleological narrative of technology as progress. Moreover, it provides a critical revision of the history of high technology which reveals how high-tech euphoria determined certain paths in history regardless of whether the respective technology proved to be successful. In its second part, the volume introduces new avenues in scholarship. Karsten Uhl examines neglected areas, such as rural technologies or the often-overlooked importance of everyday technologies: How did consumers or workers use new technologies? How did they appropriate and modify them? Lastly, the book considers the final decades of the 20th century and asks if they provided a significant new quality of technological change: To what degree and effects did computerization transform professional and private life in Germany? In culture and politics, reinforced by the German variety of environmentalism, the idea of progress was challenged, as the once prevailing vision of progress gave way to new apprehensions of uncertainty evident to this day. Technology in Modern German History brings fascinating insight into a much neglected area of German history for students and scholars alike.
Return to Sender is an anthropological account of how Peruvian emigrants raise and remit money and what that activity means for themselves and for their home communities. The book draws on first-hand ethnographic data from North and South America, Europe, and Japan to describe how Peruvians remit to relatives at home, collectively raise money to organize development projects in their regions of origin, and invest savings in business and other activities. Karsten Paerregaard challenges unqualified approval of remittances as beneficial resources of development for home communities and important income for home countries. He finds a more complex situation in which remittances can also create dependency and deprivation.
Historicizing both emotions and politics, this open access book argues that the historical work of emotion is most clearly understood in terms of the dynamics of institutionalization. This is shown in twelve case studies that focus on decisive moments in European and US history from 1800 until today. Each case study clarifies how emotions were central to people’s political engagement and its effects. The sources range from parliamentary buildings and social movements, to images and speeches of presidents, from fascist cemeteries to the International Criminal Court. Both the timeframe and the geographical focus have been chosen to highlight the increasingly participatory character of nineteenth- and twentieth-century politics, which is inconceivable without the work of emotions.
This pathbreaking ethnography of population movements between rural and urban places in Peru addresses the conceptual and methodological problems of studying ‘deterritorialized' populations and the implications of this for anthropology's notions of culture and identity. Based on extensive fieldwork, this book explores the economic, social and ritual bonds which link migrants in Peru's major cities to their Andean native village. Many urban migrants establish networks based on kinship and marriage ties to exploit resources in the city as well as the village. These networks ensure they maintain strong links to their native village. Fiestas, soccer tournaments and folklore festivals also play a crucial role in the formation of migrant communities in Peru's cities. The author analyses these performance practices and shows how they give rise to the creation of new social identities. The participation of second generation migrants, returning migrants, and migrant spouses in village life is also discussed.
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