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This is the first book that presents the theory of stochastic integral using the generalized Riemann approach. Readers who are familiar with undergraduate calculus and want to have an easy access to the theory of stochastic integral will find most of this book pleasantly readable, especially the first four chapters. The references to the theory of classical stochastic integral and stochastic processes are also included for the convenience of readers who are familiar with the measure theoretic approach.
Every good mathematical book stands like a tree with its roots in the past and its branches stretching out towards the future. Whether the fruits of this tree are desirable and whether the branches will be quarried for mathematical wood to build further edifices, I will leave to the judgment of history. The roots of this book take nourishment from the concept of definite integration of continuous functions, where Riemann's method is the high water mark of the simpler theory.
The story of West Indian immigrants to the United States is generally considered to be a great success. Mary Waters, however, tells a very different story. She finds that the values that gain first-generation immigrants initial success--a willingness to work hard, a lack of attention to racism, a desire for education, an incentive to save--are undermined by the realities of life and race relations in the United States. Contrary to long-held beliefs, Waters finds, those who resist Americanization are most likely to succeed economically, especially in the second generation.
Methods of Numerical Integration, Second Edition describes the theoretical and practical aspects of major methods of numerical integration. Numerical integration is the study of how the numerical value of an integral can be found. This book contains six chapters and begins with a discussion of the basic principles and limitations of numerical integration. The succeeding chapters present the approximate integration rules and formulas over finite and infinite intervals. These topics are followed by a review of error analysis and estimation, as well as the application of functional analysis to numerical integration. A chapter describes the approximate integration in two or more dimensions. The final chapter looks into the goals and processes of automatic integration, with particular attention to the application of Tschebyscheff polynomials. This book will be of great value to theoreticians and computer programmers.
This first volume in the series "Algorithms and Computation in Mathematics", is destined to become the standard reference work in the field. Manuel Bronstein is the number-one expert on this topic and his book is the first to treat the subject both comprehensively and in sufficient detail - incorporating new results along the way. The book addresses mathematicians and computer scientists interested in symbolic computation, developers and programmers of computer algebra systems as well as users of symbolic integration methods. Many algorithms are given in pseudocode ready for immediate implementation, making the book equally suitable as a textbook for lecture courses on symbolic integration.
This book is intended to be self-contained, giving the theory of absolute (equivalent to Lebesgue) and non-absolute (equivalent to Denjoy-Perron) integration by using a simple extension of the Riemann integral. A useful tool for mathematicians and scientists needing advanced integration theory would be a method combining the ideas of the calculus of indefinite integral and Riemann definite integral in such a way that Lebesgue properties can be proved easily.Three important results that have not appeared in any other book distinguish this book from the rest. First a result on limits of sequences under the integral sign, secondly the necessary and sufficient conditions for the various limits under the integral sign and thirdly the application of these results to ordinary differential equations. The present book will give non-absolute integration theory just as easily as the absolute theory, and Stieltjes-type integration too.
Calculus is designed for the typical two- or three-semester general calculus course, incorporating innovative features to enhance student learning. The book guides students through the core concepts of calculus and helps them understand how those concepts apply to their lives and the world around them. Due to the comprehensive nature of the material, we are offering the book in three volumes for flexibility and efficiency. Volume 3 covers parametric equations and polar coordinates, vectors, functions of several variables, multiple integration, and second-order differential equations.
Integrating Social Care into the Delivery of Health Care: Moving Upstream to Improve the Nation's Health was released in September 2019, before the World Health Organization declared COVID-19 a global pandemic in March 2020. Improving social conditions remains critical to improving health outcomes, and integrating social care into health care delivery is more relevant than ever in the context of the pandemic and increased strains placed on the U.S. health care system. The report and its related products ultimately aim to help improve health and health equity, during COVID-19 and beyond. The consistent and compelling evidence on how social determinants shape health has led to a growing recognition throughout the health care sector that improving health and health equity is likely to depend â€" at least in part â€" on mitigating adverse social determinants. This recognition has been bolstered by a shift in the health care sector towards value-based payment, which incentivizes improved health outcomes for persons and populations rather than service delivery alone. The combined result of these changes has been a growing emphasis on health care systems addressing patients' social risk factors and social needs with the aim of improving health outcomes. This may involve health care systems linking individual patients with government and community social services, but important questions need to be answered about when and how health care systems should integrate social care into their practices and what kinds of infrastructure are required to facilitate such activities. Integrating Social Care into the Delivery of Health Care: Moving Upstream to Improve the Nation's Health examines the potential for integrating services addressing social needs and the social determinants of health into the delivery of health care to achieve better health outcomes. This report assesses approaches to social care integration currently being taken by health care providers and systems, and new or emerging approaches and opportunities; current roles in such integration by different disciplines and organizations, and new or emerging roles and types of providers; and current and emerging efforts to design health care systems to improve the nation's health and reduce health inequities.