Much of what is known about the universe came from the study of celestial shadows. This book looks in detail at the way eclipses and other celestial shadows have given us amazing insights into the nature of the objects in our solar system and how they are even helping us discover and analyze planets that orbit stars other than our Sun. A variety of eclipses, transits, and occultations of the mooons of Jupiter and Saturn, Pluto and its satellite Charon, asteroids and stars have helped astronomers to work out their dimensions, structures, and shapes - even the existence of atmospheres and structures of exoplanets. Long before Columbus set out to reach the Far East by sailing West, the curved shadow of the Earth on the Moon during a lunar eclipse revealed that we inhabit a round world, a globe. More recently, comparisons of the sunlit and Earthlit parts of the Moon have been used to determine changes in the Earth's brightness as a way of monitoring possible effects in cloud coverage which may be related to global warming. Shadows were used by the Greek mathematician Eratosthenes to work out the first estimate of the circumference of the Earth, by Galileo to measure the heights of the lunar mountains and by eighteenth century astronomers to determine the scale of the Solar System itself. Some of the rarest and most wonderful shadows of all are those cast onto Earth by the lovely "Evening Star" Venus as it goes between the Earth and the Sun. These majestic transits of Venus occur at most two in a century; after the 2012 transit, there is not a chance to observe this phenomenon until 2117, while the more common sweep of a total solar eclipse creates one of the most dramatic and awe-inspiring events of nature. Though it may have once been a source of consternation or dread, solar eclipses now lead thousands of amateur astronomers and "eclipse-chasers" to travel the globe in order to experience the dramatic view under "totality." These phenomena are among the most spectacular available to observers and are given their full due in Westfall and Sheehan's comprehensive study.
The New Cambridge Shakespeare appeals to students worldwide for its up-to-date scholarship and emphasis on performance. The series features line-by-line commentaries and textual notes on the plays and poems. Introductions are regularly refreshed with accounts of new critical, stage and screen interpretations. In his Introduction to this second edition of As You Like It, its editor, Michael Hattaway accounts for what makes this popular play both innocent and dangerous. In performance it can appear bright or sombre: a feast of language and a delight for comic actors, or a risk-taking exploration of gender roles. This edition includes a new section on recent critical interpretations and dramatic productions of the play as well as an appendix on an early court performance of As You Like It in 1599. Commentary on the play's language, an updated reading list and an account of the play in performance are also included.
This extensively revised second edition is a rigorous introduction to the construction and criticism of arguments about questions of fact, and to the marshalling and evaluation of evidence at all stages of litigation. It covers the principles underlying the logic of proof; the uses and dangers of story-telling; standards for decision and the relationship between probabilities and proof; the chart method and other methods of analyzing and ordering evidence in fact-investigation, in preparing for trial, and in connection with other important decisions in legal processes and in criminal investigation and intelligence analysis. Most of the chapters in this new edition have been rewritten; the treatment of fact investigation, probabilities and narrative has been extended; and new examples and exercises have been added. Designed as a flexible tool for undergraduate and postgraduate courses on evidence and proof, students, practitioners and teachers alike will find this book challenging but rewarding.
This book explores both the practical and theoretical aspects of the Discrete Fourier Transform, one of the most widely used tools in science, engineering, and computational mathematics. Designed to be accessible to an audience with diverse interests and mathematical backgrounds, the book is written in an informal style and is supported by many examples, figures, and problems. Conceived as an "owner's" manual, this comprehensive book covers such topics as the history of the DFT, derivations and properties of the DFT, comprehensive error analysis, issues concerning the implementation of the DFT in one and several dimensions, symmetric DFTs, a sample of DFT applications, and an overview of the FFT.
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