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This volume presents original papers ranging from an experimental study on cavitation jets to an up-to-date mathematical analysis of the Navier-Stokes equations for free boundary problems, reflecting topics featured at the International Conference on Mathematical Fluid Dynamics, Present and Future, held 11–14 November 2014 at Waseda University in Tokyo. The contributions address subjects in one- and two-phase fluid flows, including cavitation, liquid crystal flows, plasma flows, and blood flows. Written by internationally respected experts, these papers highlight the connections between mathematical, experimental, and computational fluid dynamics. The book is aimed at a wide readership in mathematics and engineering, including researchers and graduate students interested in mathematical fluid dynamics.

Partial differential equations. --- Fluid mechanics. --- Mathematical physics. --- Partial Differential Equations. --- Engineering Fluid Dynamics. --- Mathematical Applications in the Physical Sciences.

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This textbook develops the essential tools of linear algebra, with the goal of imparting technique alongside contextual understanding. Applications go hand-in-hand with theory, each reinforcing and explaining the other. This approach encourages students to develop not only the technical proficiency needed to go on to further study, but an appreciation for when, why, and how the tools of linear algebra can be used across modern applied mathematics. Providing an extensive treatment of essential topics such as Gaussian elimination, inner products and norms, and eigenvalues and singular values, this text can be used for an in-depth first course, or an application-driven second course in linear algebra. In this second edition, applications have been updated and expanded to include numerical methods, dynamical systems, data analysis, and signal processing, while the pedagogical flow of the core material has been improved. Throughout, the text emphasizes the conceptual connections between each application and the underlying linear algebraic techniques, thereby enabling students not only to learn how to apply the mathematical tools in routine contexts, but also to understand what is required to adapt to unusual or emerging problems. No previous knowledge of linear algebra is needed to approach this text, with single-variable calculus as the only formal prerequisite. However, the reader will need to draw upon some mathematical maturity to engage in the increasing abstraction inherent to the subject. Once equipped with the main tools and concepts from this book, students will be prepared for further study in differential equations, numerical analysis, data science and statistics, and a broad range of applications. The first author’s text, Introduction to Partial Differential Equations, is an ideal companion volume, forming a natural extension of the linear mathematical methods developed here.

Mathematics. --- Matrix theory. --- Algebra. --- Mathematical physics. --- Linear and Multilinear Algebras, Matrix Theory. --- Mathematical Applications in the Physical Sciences. --- Algebras, Linear. --- Physical mathematics --- Physics --- Mathematics --- Mathematical analysis --- Algebras, Linear

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This book is designed to serve as a core text for courses in advanced engineering mathematics required by many engineering departments. The style of presentation is such that the student, with a minimum of assistance, can follow the step-by-step derivations. Liberal use of examples and homework prob­lems aid the student in the study of the topics presented. Ordinary differential equations, including a number of physical applica­tions, are reviewed in Chapter One. The use of series methods are presented in Chapter Two, Subsequent chapters present Laplace transforms, matrix theory and applications, vector analysis, Fourier series and transforms, partial differential equations, numerical methods using finite differences, complex vari­ables, and wavelets. The material is presented so that four or five subjects can be covered in a single course, depending on the topics chosen and the completeness of coverage. Incorporated in this textbook is the use of certain computer software packages. Short tutorials on Maple, demonstrating how problems in engineering mathematics can be solved with a computer algebra system, are included in most sections of the text. Problems have been identified at the end of sections to be solved specifically with Maple, and there are computer laboratory activities, which are more difficult problems designed for Maple. In addition, MATLAB and Excel have been included in the solution of problems in several of the chapters. There is a solutions manual available for those who select the text for their course. This text can be used in two semesters of engineering mathematics. The many helpful features make the text relatively easy to use in the classroom. .

Engineering mathematics. --- Engineering Mathematics. --- Mathematical Applications in the Physical Sciences. --- Theoretical, Mathematical and Computational Physics. --- Engineering --- Engineering analysis --- Mathematical analysis --- Mathematics --- Mathematical physics. --- Physical mathematics --- Physics

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This book presents a selection of Prof. Matteo Campanella’s writings on the interpretative aspects of quantum mechanics and on a possible derivation of Born's rule – one of the key principles of the probabilistic interpretation of quantum mechanics – that is independent of any priori probabilistic interpretation. This topic is of fundamental interest, and as such is currently an active area of research. Starting from a natural method of defining such a state, Campanella found that it can be characterized through a partial density operator, which occurs as a consequence of the formalism and of a number of reasonable assumptions connected with the notion of a state. The book demonstrates that the density operator arises as an orbit invariant that has to be interpreted as probabilistic, and that its quantitative implementation is equivalent to Born's rule. The appendices present various mathematical details, which would have interrupted the continuity of the discussion if they had been included in the main text. For instance, they discuss baricentric coordinates, mapping between Hilbert spaces, tensor products between linear spaces, orbits of vectors of a linear space under the action of its structure group, and the class of Hilbert space as a category.

Mathematical physics. --- Quantum physics. --- Mathematical Applications in the Physical Sciences. --- Quantum Physics. --- Physical mathematics --- Physics --- Mathematics --- Quantum dynamics --- Quantum mechanics --- Quantum physics --- Mechanics --- Thermodynamics

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To the naked eye, the most evident defining feature of the planets is their motion across the night sky. It was this motion that allowed ancient civilizations to single them out as different from fixed stars. But how does the geometry of the Solar System give rise to the observed motions of the planets and their moons? Although the motions of the planets may be described as simple elliptical orbits around the Sun, they must be observed from a particular vantage point--the Earth, which spins daily on its axis and circles around the Sun each year, resulting in more complicated patterns. The Observer’s Guide to Planetary Motion provides accurate tables of the best time for observing each planet, together with other notable events in their orbits, helping amateur astronomers plan when and what to observe. Along the way, many questions are answered: Why does Mars take over two years between apparitions (the times when it is visible from Earth) in the night sky, while Uranus and Neptune take almost exactly a year? Why do planets appear higher in the night sky when they’re visible in the winter months? Why do Saturn’s rings appear to open and close every 15 years? This book places seemingly disparate astronomical events into an understandable three-dimensional  structure.

Planets --- Astronomy --- Astronomy. --- Astronomy, Observations and Techniques. --- Popular Science in Astronomy. --- Mathematical Applications in the Physical Sciences. --- Observations, Astronomical. --- Astronomy—Observations. --- Mathematical physics. --- Physical mathematics --- Physics --- Astronomical observations --- Observations, Astronomical --- Mathematics