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This text introduces to undergraduates the more abstract concepts of advanced calculus, smoothing the transition from standard calculus to the more rigorous approach of proof writing and a deeper understanding of mathematical analysis. The first part deals with the basic foundation of analysis on the real line; the second part studies more abstract notions in mathematical analysis. Each topic contains a brief introduction and detailed examples.
Aspects of Integration: Novel Approaches to the Riemann and Lebesgue Integrals is comprised of two parts. The first part is devoted to the Riemann integral, and provides not only a novel approach, but also includes several neat examples that are rarely found in other treatments of Riemann integration. Historical remarks trace the development of integration from the method of exhaustion of Eudoxus and Archimedes, used to evaluate areas related to circles and parabolas, to Riemann’s careful definition of the definite integral, which is a powerful expansion of the method of exhaustion and makes it clear what a definite integral really is. The second part follows the approach of Riesz and Nagy in which the Lebesgue integral is developed without the need for any measure theory. Our approach is novel in part because it uses integrals of continuous functions rather than integrals of step functions as its starting point. This is natural because Riemann integrals of continuous functions occur much more frequently than do integrals of step functions as a precursor to Lebesgue integration. In addition, the approach used here is natural because step functions play no role in the novel development of the Riemann integral in the first part of the book. Our presentation of the Riesz-Nagy approach is significantly more accessible, especially in its discussion of the two key lemmas upon which the approach critically depends, and is more concise than other treatments. Features Presents novel approaches designed to be more accessible than classical presentations A welcome alternative approach to the Riemann integral in undergraduate analysis courses Makes the Lebesgue integral accessible to upper division undergraduate students How completion of the Riemann integral leads to the Lebesgue integral Contains a number of historical insights Gives added perspective to researchers and postgraduates interested in the Riemann and Lebesgue integrals
In the United States, broad study in an array of different disciplines â€"arts, humanities, science, mathematics, engineeringâ€" as well as an in-depth study within a special area of interest, have been defining characteristics of a higher education. But over time, in-depth study in a major discipline has come to dominate the curricula at many institutions. This evolution of the curriculum has been driven, in part, by increasing specialization in the academic disciplines. There is little doubt that disciplinary specialization has helped produce many of the achievement of the past century. Researchers in all academic disciplines have been able to delve more deeply into their areas of expertise, grappling with ever more specialized and fundamental problems. Yet today, many leaders, scholars, parents, and students are asking whether higher education has moved too far from its integrative tradition towards an approach heavily rooted in disciplinary "silos". These "silos" represent what many see as an artificial separation of academic disciplines. This study reflects a growing concern that the approach to higher education that favors disciplinary specialization is poorly calibrated to the challenges and opportunities of our time. The Integration of the Humanities and Arts with Sciences, Engineering, and Medicine in Higher Education examines the evidence behind the assertion that educational programs that mutually integrate learning experiences in the humanities and arts with science, technology, engineering, mathematics, and medicine (STEMM) lead to improved educational and career outcomes for undergraduate and graduate students. It explores evidence regarding the value of integrating more STEMM curricula and labs into the academic programs of students majoring in the humanities and arts and evidence regarding the value of integrating curricula and experiences in the arts and humanities into college and university STEMM education programs.
Principles of Data Integration is the first comprehensive textbook of data integration, covering theoretical principles and implementation issues as well as current challenges raised by the semantic web and cloud computing. The book offers a range of data integration solutions enabling you to focus on what is most relevant to the problem at hand. Readers will also learn how to build their own algorithms and implement their own data integration application. Written by three of the most respected experts in the field, this book provides an extensive introduction to the theory and concepts underlying today's data integration techniques, with detailed, instruction for their application using concrete examples throughout to explain the concepts. This text is an ideal resource for database practitioners in industry, including data warehouse engineers, database system designers, data architects/enterprise architects, database researchers, statisticians, and data analysts; students in data analytics and knowledge discovery; and other data professionals working at the R&D and implementation levels. Offers a range of data integration solutions enabling you to focus on what is most relevant to the problem at hand Enables you to build your own algorithms and implement your own data integration applications
The European Union might be the most prominent example of regional integration but it is by far not the only one. The importance of regional integration in Africa, Asia, Latin America, the Caribbean and even in the Pacific Islands region is constantly growing. All these regions aspire for more than pure economic cooperation. In addition to intensified economic cooperation, political, legal and cultural aspects are important factors as well that form a Mixtum Compositum of regional integration elements. The present volume discusses these different components of regional integration in theoretical perspective and in a policy-oriented approach. It contributes to comparative regional integration studies through theoretical analysis and case studies from different regions. Elements of Regional Integration presents the main features of regional integration in an interdisciplinary manner. It addresses scholars of political sciences, economics and law as well as students and is suited as accompanying material for courses.
Over the past decade or so, systems integration has become a key factor in the operations, strategy and competitive advantage of major corporations in a wide variety of sectors (e.g. computing, automotive, telecommunications, military systems and aerospace). Systems integration is a strategic task that pervades business management not only at the technical level but also at the management and strategic levels. This book shows how and why this new kind of systems integration has evolved into an emerging model of industrial organization whereby firms, and groups of firms, join together different types of knowledge, skill and activity, as well as hardware, software, and human resources to produce new products for the marketplace. This book is the first to systematically explore systems integration from a business and innovation perspective. Contributors delve deeply into the nature, dimensions and dynamics of the new systems integration, deploying research and analytical techniques from a wide variety of disciplines including, the theory of the firm, the history of technology, industrial organization, regional studies, strategic management, and innovation studies. This wealth of research capability provides deep insights into the new model of systems integration and supports this with an abundance of empirical evidence. The book is organized in three main parts. The first part focuses on the history of systems integration. Contributors trace the early history of systems integration using different industrial examples. The second part presents theoretical and analytical aspects of systems integration. Contributions concentrate on the regulatory and cognitive features of systems integration, the relationships between systems integration and regional competitive advantage, and the way in which systems integration supports the competitive advantage of firms. The third part takes industry and firm-level approaches. Contributions focus on different sectors and highlight the specificity of systems integration in various industrial domains, stressing its importance for systems integration in the case of complex capital goods, such as aircraft and telecommunications equipment, as well as consumer goods, such as personal computers and automobiles.
In this open access book, experts on integration processes, integration policies, transnationalism, and the migration and development framework provide an academic assessment of the 2011 European Agenda for the Integration of Third-Country Nationals, which calls for integration policies in the EU to involve not only immigrants and their society of settlement, but also actors in their country of origin. Moreover, a heuristic model is developed for the non-normative, analytical study of integration processes and policies based on conceptual, demographic, and historical accounts. The volume addresses three interconnected issues: What does research have to say on (the study of) integration processes in general and on the relevance of actors in origin countries in particular? What is the state of the art of the study of integration policies in Europe and the use of the concept of integration in policy formulation and practice? Does the proposal to include actors in origin countries as important players in integration policies find legitimation in empirical research? A few general conclusions are drawn. First, integration policies have developed at many levels of government: nationally, locally, regionally, and at the supra-national level of the EU. Second, a multitude of stakeholders has become involved in integration as policy designers and implementers. Finally, a logic of policymaking—and not an evidence-based scientific argument—can be said to underlie the European Commission’s redefinition of integration as a three-way process. This book will appeal to academics and policymakers at international, European, national, regional, and local levels. It will also be of interest to graduate and master-level students of political science, sociology, social anthropology, international relations, criminology, geography, and history.