Although Galileo Galilei lived and died centuries ago, his story is more relevant to our lives than we might realize. Today we face enormous challenges such as climate change that are disregarded or questioned by those who fear that their implications will damage business profitability. Others posit a false dichotomy between religion and science in order to reject scientific evidence whose implications they fear. Galileo confronted this problem 400 years ago. His discoveries were based on observation and experiment. His telescopes revealed previously unknown planets, moons orbiting other planets, and other discoveries that essentially confirmed the Copernican universe that the Church had rejected as heretical because Church theologians insisted on a literal reading of the Bible. Even St. Augustine in the fifth century maintained that the Bible pertained to the realm of faith, not reason. But when Galileo argued essentially the same position before an ecclesiastical court in Rome, he was forbidden from publishing any more books. Livio's life of Galileo shows us how the great thinker made his discoveries about the heavens and also formulated fundamental laws of physics. As an astrophysicist, Livio brings insight into how Galileo reasoned his way to his conclusions, which we know today were accurate. Along with Newton, Galileo remains one of the two great figures at the dawn of the scientific revolution. He insisted on reaching the widest audience possible, publishing his work in Italian rather than Latin as had been the case until his time, when vernacular languages were rapidly replacing Latin throughout Europe. Galileo believed that every educated person should know science as well as literature. Did Galileo actually say at the end of his trial when he was forced to recant his discoveries, as legend has it, And still it moves, referring to the motion of the earth around the sun? Not likely, says Livio, but Galileo nonetheless remains an inspiration to scientists and those who value open-minded inquiry, which as Livio reminds us, remains threatened even today.

This book grew out of the need to provide students with a solid introduction to modern fluid dynamics. It offers a broad grounding in the underlying principles and techniques used, with some emphasis on applications in astrophysics and planetary science. The book comprehensively covers recent developments, methods and techniques, including, for example, new ideas on transitions to turbulence (via transiently growing stable linear modes), new approaches to turbulence (which remains the enigma of fluid dynamics), and the use of asymptotic approximation methods, which can give analytical or semi-analytical results and complement fully numerical treatments. The authors also briefly discuss some important considerations to be taken into account when developing a numerical code for computer simulation of fluid flows. Although the text is populated throughout with examples and problems from the field of astrophysics and planetary science, the text is eminently suitable as a general introduction to fluid dynamics. It is assumed that the readers are mathematically equipped with a reasonable knowledge in analysis, including basics of ordinary and partial differential equations and a good command of vector calculus and linear algebra. Each chapter concludes with bibliographical notes in which the authors briefly discuss the chapter's essential literature and give recommendations for further, deeper reading. Included in each chapter are a number of problems, some of them relevant to astrophysics and planetary science. The book is written for advanced undergraduate and graduate students, but will also prove a valuable source of reference for established researchers.