Suitable for advanced undergraduate and graduate students of mathematics, physics, or engineering, this introduction to the calculus of variations focuses on variational problems involving one independent variable. It also discusses more advanced topics such as the inverse problem, eigenvalue problems, and Noether’s theorem. The text includes numerous examples along with problems to help students consolidate the material.
Although students of analysis are familiar with real and complex numbers, few treatments of analysis deal with the development of such numbers in any depth. An understanding of number systems at a fundamental level is necessary for a deeper grasp of analysis. Beginning with elementary concepts from logic and set theory, this book develops in turn the natural numbers, the integers and the rational, real and complex numbers. The development is motivated by the need to solve polynomial equations, and the book concludes by proving that such equations have solutions in the complex number system.
This text gives a rigorous treatment of the foundations of calculus. In contrast to more traditional approaches, infinite sequences and series are placed at the forefront. The approach taken has not only the merit of simplicity, but students are well placed to understand and appreciate more sophisticated concepts in advanced mathematics. The authors mitigate potential difficulties in mastering the material by motivating definitions, results and proofs. Simple examples are provided to illustrate new material and exercises are included at the end of most sections. Noteworthy topics include: an extensive discussion of convergence tests for infinite series, Wallis’s formula and Stirling’s formula, proofs of the irrationality of π and e and a treatment of Newton’s method as a special instance of finding fixed points of iterated functions.
Bruce Edward Hall may have an English name and a Connecticut upbringing, but for him a trip to Chinatown, New York, is a visit to the ghosts of his Chinese ancestors - ancestors who helped create the neighborhood that is really as much a transplanted Cantonese village as it is a part of a great American city. Among these Ancestors are missionaries and reprobates, businessmen and scholars. In Tea That Burns, Bruce Edward Hall uses the stories of these and others to tell the history of Chinatown, starting with the tumultuous journey from an ancient empire ruled by the nine dragons of the universe to a bewildering land of elevated trains, solitary labor, and violent discrimination. The world they constructed was built of backbreaking labor and poetry contests; gambling dens and Cantonese opera; Tong Wars, festivals, firecrackers, incense, and food - always food, to celebrate every conceivable occasion and to confound the ever-meddlesome "White Devils" as they attempt to master the mysteries of chop sticks and stir-fry.
The processes of discovery, testing and distribution of new medicines have undergone radical change in recent decades, from a focus on small molecule drugs to biomedicine and related technologies. Bruce Rasmussen very effectively draws upon modern theories of the firm, data analysis, and case studies to provide important insights into the consequences of this change. He offers convincing evidence that contradicts the widely-held view that the biopharmaceutical sector has not generated considerable economic value. Frank R. Lichtenberg, Columbia University, US Bio- and pharmaceutical industry discovery is a distressed asset today. Why? Bruce Rasmussen s book is a timely and very informative work, building on rich data sources and extensive economic research, on a subject of concern to us all. Is medicine discovery in permanent decline? Are the biotechnology and traditional pharma groups on a collision course, will the traditional group absorb the new, will integration take place, will a new discovery model emerge? I commend Bruce s book to all who wish to understand what is happening. David W. Anstice, Merck & Co., Inc. This path-breaking book addresses the ongoing implications for traditional pharmaceutical companies and biopharmaceutical start-ups of the realignment of the industry knowledge-base. The theoretical approach draws on the modern theory of the firm and related ideas in order to better define the concept of the business model, which is employed to guide the case studies and empirical analysis in the book. The author shows that while traditional pharmaceutical companies have successfully adjusted their business models to meet the challenges of biotechnology, biopharmaceutical start-ups have experienced more problems. Despite the poor financial performance of the vast majority of these firms, the biopharmaceutical sector as a whole has created significant value. However, this has been captured disproportionately by a handful of large, fully-integrated biopharmaceutical firms and, to a lesser extent, by the largest dozen pharmaceutical companies. This highly focused book will be a captivating read for innovation and biopharmaceutical industry analysts, as well as advisers formulating policies to support the development of the biopharmaceutical sector. Academics working on innovation and biotechnology, as well as scientists engaged in research in the life sciences, will also find this book of particular interest.
As its name implies, this book deals with clinical information systems. The clinical information system (or CIS) is an automated system with a long term database containing clinical information used for patient care. This definition excludes business systems (no clinical data), physiological monitoring systems (no long term database), and many research systems (not used in patient care). The theses of this book are (a) that CIS technology is mature, (b) that the CIS will have a major impact upon patient care and the health delivery system, and (c) that the number of commercial systems which now offer these potential benefits is very small. The objective of this book is to establish the above theses and thereby (a) inform both users and developers, (b) increase the demand for more sophisticated products, and finally, (c) provide marketplace incentives to advance the state of the art. The CIS is an application of computer technology for a specific class of problems. Its development requires a knowledge of the technology with an understanding of the application area. As with any tool-based application, the scope of the product will be limited by the capability of the tool. In the case of the CIS, reliable computers with comprehensive database facilities became com mercially available in the early 1970s. By the mid 1970s there was a maturation of the literature, and evaluations of 5-years' use began to appear. As will be shown, there have been surprisingly few new ideas introduced since the 1970s.
This text provides a detailed presentation of the main results for infinite products, as well as several applications. The target readership is a student familiar with the basics of real analysis of a single variable and a first course in complex analysis up to and including the calculus of residues. The book provides a detailed treatment of the main theoretical results and applications with a goal of providing the reader with a short introduction and motivation for present and future study. While the coverage does not include an exhaustive compilation of results, the reader will be armed with an understanding of infinite products within the course of more advanced studies, and, inspired by the sheer beauty of the mathematics. The book will serve as a reference for students of mathematics, physics and engineering, at the level of senior undergraduate or beginning graduate level, who want to know more about infinite products. It will also be of interest to instructors who teach courses that involve infinite products as well as mathematicians who wish to dive deeper into the subject. One could certainly design a special-topics class based on this book for undergraduates. The exercises give the reader a good opportunity to test their understanding of each section.
The second episode in this award-winning trilogy impressively shows how the Union and Confederacy, slowly and inexorably, reconciled themselves to an all-out war—an epic struggle for freedom. In Terrible Swift Sword, Bruce Catton tells the story of the Civil War as never before—of two turning points which changed the scope and meaning of the war. First, he describes how the war slowly but steadily got out of control. This would not be the neat, short, “limited” war both sides had envisioned. And then the author reveals how the sweeping force of all-out conflict changed the war’s purpose, in turning it into a war for human freedom. It was not initially a war against slavery. Instead, this was, Mr. Lincoln kept insisting, a fight to reunite the United States. At first, it was not even much of a fight. Cautious generals; inexperienced, incompetent, or jealous administrators; shortages of good people and supplies; excess of both gloom and optimism, kept each side from swinging into decisive action. As the buildup began, there were maddening delays. The earliest engagements were halting and inconclusive. After these first tests at arms, reputations began to crumble. Buell, Halleck, Beauregard Albert Sidney Johnston. Failed to drive ahead—for reasons good and bad. General McClellan (impaled in these pages on the arrogant words of his letters) captured more imaginations than enemies, and continued to accept serious over estimates of Confederate strength while becoming more and more fatally estranged from his own government.
The era from 1890 to 1930 constituted a building boom for American art museums designed in a monumental, classical style; both the proliferation of the buildings and the ubiquity of the style seem to indicate an architectural as well as a sociocultural phenomenon. The present work is an attempt to place the American art museum building of this period into its historical milieu, and employs over one hundred illustrations and sociocultural analysis to explain the significance of both the institutions and the structures housing them to those who came into regular contact with them, including architects, patrons, journalists, and museum personnel.
The aim of the Managing Global Insecurity project is to launch a reform effort of the global security system in 2009. That task is both ambitious and urgent.... The time to act is now."—from the Foreword by Javier Solana The twenty-first century will be defined by security threats unconstrained by borders—from economic instability, climate change, and nuclear proliferation to conflict, poverty, terrorism, and disease. The greatest test of global leadership will be building partnerships and institutions for cooperation that can meet the challenge. Power and Responsibility describes how American leadership can rebuild international order to promote global security and prosperity for today's transnational world. Power & Responsibility establishes a new foundation for international security: "responsible sovereignty," or the notion that sovereignty entails obligations and duties toward other states as well as one's own citizens. Governments must cooperate across borders to safeguard common resources and tackle common threats. Power & Responsibility argues that in order to advance its own interests, the United States must learn to govern in an interdependent world, exercise leadership through cooperation, and create new institutions with today's traditional and emerging powers. The result of a collaborative project on Managing Global Insecurity, the book also reflects the MGI project's global dialogue—extensive consultations in the United States and in regions around the world as well as discussions with the MGI project's Advisory Group, composed of prominent U.S. and international figures. "The 2008 financial crisis has brought our global interconnectedness close to home. But economic insecurity is just one concern. Power and Responsibility provides a road map for building effective policies and legitimate global institutions to tackle today's suite of transnational challenges."—Kemal Dervis, administrator, UN Develo
This text gives a rigorous treatment of the foundations of calculus. In contrast to more traditional approaches, infinite sequences and series are placed at the forefront. The approach taken has not only the merit of simplicity, but students are well placed to understand and appreciate more sophisticated concepts in advanced mathematics. The authors mitigate potential difficulties in mastering the material by motivating definitions, results and proofs. Simple examples are provided to illustrate new material and exercises are included at the end of most sections. Noteworthy topics include: an extensive discussion of convergence tests for infinite series, Wallis’s formula and Stirling’s formula, proofs of the irrationality of π and e and a treatment of Newton’s method as a special instance of finding fixed points of iterated functions.
This volume was part of a short-lived series to encompass the 1810 and 1820 federal censuses for the state of Louisiana. In both volumes the census schedules are transcribed from the original returns, and they include the name of the head of each household, the number of persons in each family, their approximate ages, and their sex. In addition to listing the page reference for the names appearing in the text, each index also includes the years and the parishes under which the names appear.
The availability of inexpensive steel, so crucial to the United States' emergence as a leading industrial power in the late nineteenth century, relied upon the rise of an ore transport system on the Great Lakes that would feed American industry as a whole and come to alter the face of the region. This detailed history recounts innovations in shipping, the improvement of channels and harbors, the creation of locks, technical advances in loading and unloading equipment, and the ability to attract capital and government support to fund the various projects. When government support was lacking, reinterpretations of the Constitution were introduced to justify federal involvement. These changes, which often functioned symbiotically, represent one of the key untold stories in the spectacular rise of American industry.
The fundamental purpose of this book is to synthesise the divergent literature on aquatic lipids into a co-ordinated, digestible form. A large part of the book addresses lipid composition and production in freshwater organisms, with chapters on phytoplankton, zooplankton and benthic invertebrates. A common theme throughout the book is the function of lipids in aquatic food webs, with a chapter devoted exclusively to lipids as indicators of health in fish populations. A complementary chapter highlights the role of lipids and essential fatty acids in mariculture. Methodologies to determine the lipid content of aquatic samples and suggestions as to the utility of fatty acids as trophic markers are included, as is one chapter on the role of lipids in the bioaccumulation and bioconcentration of toxicants and another on the relationships between lipids and surface films and foams. The final chapter highlights the similarities and differences between lipids of marine and freshwater origin. Students and researchers in ecology, phycology, aquatic toxicology, physiological ecology and limnology will find this an invaluable guide and reference.
• Stories of the best known of the Garden State's cryptid population • From the bustling cities and Down the Shore to the creepy Pine Barrens • Research from the world's leading cryptozoologist • Extensive section on the state's most infamous creature, the Jersey Devil • Also includes Big Red Eye of the Great Swamp in Somerset County, Hoboken Monkey-Man, Lake Hopatcong Monster, Cape May Sea Serpent, the Wooo-wooo, and the Lizardman of Great Meadows
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