Böcker utgivna av Springer International Publishing

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 onfinite difference and finite element methods. Computer-aided calculation with Maple¿ 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.

This book provides a thorough analysis focused on the sound expression produced by human-crafted musical instrument ¿ a pipe organ, in which various components blend into a complex whole to produce a wide range of timbres. The sound produced by wooden and metal pipes of a variety of sizes is an integral part of the instrument¿s unique character, while the organ stop is like its signature, from which one can judge about the size and style of the instrument, an organ building school or even an organ master, to which it is attributable. Precise identification of the name of the stop in accordance to both the pipework itself and the authentic inscriptions on the pipes is instrumental in investigating the geographic origins and authorship of an organ. The monograph focuses on the craftsmanship of complex and historically influential organ stop Vox humana. Its research and definition provides specific information distinguishing particular features in the variety of organ building traditions and discussing the differences in organ sound perception and production. The volume is aimed at art and music historians, as well as musicologists and scholars researching restoration techniques.The book contains supplemental material with video and audio material as well as photo-documentation of authentic Vox humana examples. The material is placed in the online catalog, which may be accessed by scanning the QR code in the appendix of the book.dsgdsgds

This book asks if it is time to ¿reboot¿ the fundamental institutions of global international society. The volume revisits Hedley Bull¿s seminal contribution The Anarchical Society by exploring the interconnected nature of change, contestation and resilience for maintaining order in today¿s uncertain and complex environment. The volume adds to Bull¿s theorizing by recognizing that order demands change, that contestation should be welcomed, and that resilience is anchored in local and agent-led forms of ordering. The contributors to Part One of the book focus on theoretical and conceptual issues related to order in the global international society, whilst the contributors to Part Two of the book focus on the primary institutions as listed by Hedley Bull with the addition of a chapter on the market adding a distinctive commentary on new and important dynamics of change, contestation and resilience of the existing institutions.

This book exposes, for the first time in modern scholarship, the role that the rise of the Carry Trade played in British financial crises between 1825 and 1866, how in reaction the Bank of England improved its management of monetary policy after 1866 and how those lessons have been forgotten since the 1970s. Britain is one of the few major capitalist economies in the world to have avoided policy-induced systemic financial crises for more than 100 years of its history¿between 1866 and 1973. Beforehand, it suffered a series of serious banking panics, in 1825, 1837, 1847, 1857-58 and 1866. Since the 1970s banking instability has returned again, with the global financial crisis of 2007-09 hitting Britain hard. Economists and policymakers have asked what can be learnt from Britain¿s experience of the disappearance and reappearance of crises to help efforts to prevent future ones. This book answers that question with a major reassessment of Britain¿s financial history over the past two centuries. It does so by applying the long-neglected ideas of the British Banking School to explain how crises can occur because of the Carry Trade. This book is essential reading for economists and historians of modern Britain, practitioners and policymakers, as well as anyone who is affected by financial crises and their consequences.