Although there are many textbooks on stochastic calculus applied to finance, this volume earns its place with a pedagogical approach. The text presents a quick (but by no means "dirty") road to the tools required for advanced finance in continuous time, including option pricing by martingale methods, term structure models in a HJM-framework and the Libor market model. The reader should be familiar with elementary real analysis and basic probability theory.

Involving rigorous analysis, computational dexterity, and a breadth of applications, this text is ideal for an undergraduate honors calculus course or for an introduction to analysis. This fourth edition includes corrections as well as some additional material.

In recent years fractional calculus has played an important role in various fields such as mechanics, electricity, chemistry, biology, economics, modeling, identification, control theory and signal processing. The scope of this book is to present the state of the art in the study of fractional systems and the application of fractional differentiation. Furthermore, the manufacture of nanowires is important for the design of nanosensors and the development of high-yield thin films is vital in procuring clean solar energy.

"Elegantly written, with obvious appreciation for fine points of higher mathematics…most notable is [the] author's effort to weave classical probability theory into [a] quantum framework." – The American Mathematical Monthly

The calculus of variations has a long history of interaction with other branches of mathematics such as geometry and differential equations, and with physics, particularly mechanics. More recently, the calculus of variations has found applications in other fields such as economics and electrical engineering. Much of the mathematics underlying control theory, for instance, can be regarded as part of the calculus of variations.

<i>This book presents a functional calculus for <i>n</i>-tuples of not necessarily commuting linear operators. In particular, a functional calculus for quaternionic linear operators is developed. These calculi are based on a new theory of hyperholomorphicity for functions with values in a Clifford algebra: the so-called slice monogenic functions which are carefully described in the book. In the case of functions with values in the algebra of quaternions these functions are named slice regular functions.

Although the calculus of variations has ancient origins in questions of Ar­ istotle and Zenodoros, its mathematical principles first emerged in the post­ calculus investigations of Newton, the Bernoullis, Euler, and Lagrange. Its results now supply fundamental tools of exploration to both mathematicians and those in the applied sciences. (Indeed, the macroscopic statements ob­ tained through variational principles may provide the only valid mathemati­ cal formulations of many physical laws. ) Because of its classical origins, variational calculus retains the spirit of natural philosophy common to most mathematical investigations prior to this century.

reason for delaying its study has to do with the question of mathematical maturity. * No use is made here of trigonometric, logarithmic, or expo­ nential functions except in occasional optional material indicating how such functions can be handled. A perceptive remark made by George P6lya suggests how we can simultaneously learn mathematics and learn "about" mathematics-i.e., about the nature of mathematics and how it is developed: If the learning of mathematics reflects to any degree the invention of mathematics, it must have a place for guessing, for plausible inference. The reader will find plenty of opportunity here for guessing. The early chapters go at a gentle pace and invite the reader to enter into the spirit of the investigation. Exercises asking the reader to "make a guess" should be taken in this spirit-as simply an invitation to speculate about what is the likely truth in a given situation without feeling any pressure to guess "correctly". Readers will soon realize that a matter about which they are asked to guess will likely be a topic of serious discussion later on.

Electron microscopy has revolutionized our understanding the extraordinary intellectual demands required of the mi­ of materials by completing the processing-structure-prop­ croscopist in order to do the job properly: crystallography, erties links down to atomistic levels. It now is even possible diffraction, image contrast, inelastic scattering events, and to tailor the microstructure (and meso structure ) of materials spectroscopy. Remember, these used to be fields in them­ to achieve specific sets of properties; the extraordinary abili­ selves.
Today, one has to understand the fundamentals ties of modem transmission electron microscopy-TEM­ of all of these areas before one can hope to tackle signifi­ instruments to provide almost all of the structural, phase, cant problems in materials science. TEM is a technique of and crystallographic data allow us to accomplish this feat. characterizing materials down to the atomic limits. It must Therefore, it is obvious that any curriculum in modem mate­ be used with care and attention, in many cases involving rials education must include suitable courses in electron mi­ teams of experts from different venues. The fundamentals croscopy. It is also essential that suitable texts be available are, of course, based in physics, so aspiring materials sci­ for the preparation of the students and researchers who must entists would be well advised to have prior exposure to, for carry out electron microscopy properly and quantitatively.

The updated textbook is intended to serve as an advanced and detailed treatment of the evolution of the subject of stratigraphy from its disparate beginnings as separate studies of sedimentology, lithostratigraphy, chronostratigraphy, etc., into a modern integrated discipline in which all components are necessary.
There is a historical introduction, which now includes information about the timeline of the evolution of the components of modern stratigraphy. The elements of the various components (facies analysis, sequence stratigraphy, mapping methods, chronostratigraphic methods, etc.) are outlined, and a chapter discussing the modern synthesis is included near the end of the book, which closes with a discussion of future research trends in the study of time as preserved in the stratigraphic record.

This updated and expanded second edition covers all of the diagnostic areas where FNAC is used today. Each chapter follows a similar, practical format: diagnostic criteria with an emphasis of differential diagnoses; diagnostic problems and pitfalls; and relevant findings of ancillary methods. Authoritative discussions will reflect accepted international viewpoints. The interaction of the cytologist or cytopathologist with other specialists (radiologists, oncologists and surgeons) is emphasized and illustrated throughout.
With contributions from experts in the field internationally and many new colour images Atlas of Fine Needle Aspiration Cytology, Second Edition provides a comprehensive and up-to-date guide to FNAC for pathologists, cytopathologists, radiologists, oncologists, surgeons and others involved in the diagnosis and treatment of patients with suspicious mass lesions.

The Encyclopedia of Nanotechnology provides a comprehensive and multi-disciplinary reference to the many fields relevant to the general field of nanotechnology. It aims to be a comprehensive and genuinely international reference work and will be aimed at graduate students, researchers, and practitioners.

This book addresses the highly differentiated spatial, social, cultural and demographic structure(s) of Germany, with a particular focus on the reciprocal relations between different levels of spatial development.
The historical development of Germany serves as a background in order to provide context for the development of spatially relevant ideas and ideals (whether in relation to politics, landscape, or culture). In this regard, questions of divergence and convergence become highly salient.

This book contains select proceedings of the International Conference on Smart Technologies for Energy, Environment, and Sustainable Development (ICSTEESD 2020). The book is broadly divided into the themes of energy, environment, and sustainable development; and discusses the significance and solicitations of intelligent technologies in the domain of energy and environmental systems engineering.

This book presents the latest advances in research to analyze mechanical damage and its detection in multilayer systems. The contents are linked to the Rilem TC241 - MCD scientific activities and the proceedings of the 8th RILEM International Conference on Mechanisms of Cracking and Debonding in Pavements (MCD2016).