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“Newton’s Gravity” conveys the power of simple mathematics to tell the fundamental truth about nature. Many people know the tides are caused by the pull of the Moon and to a lesser extent the Sun. But very few can explain exactly how and why that happens. Fewer still can calculate the  actual pulls of the Moon and Sun on the oceans. This book shows in clear detail how to do this with simple tools. It uniquely crosses disciplines – history, astronomy, physics and mathematics – and takes pains to explain things frequently passed over or taken for granted in other books. Using a problem-based approach, “Newton’s Gravity” explores the surprisingly basic mathematics behind gravity, the most fundamental force that governs the movements of satellites, planets, and the stars.

Astrophysics. --- Gravitational waves. --- Celestial mechanics --- Gravity --- Astronomy & Astrophysics --- Physical Sciences & Mathematics --- Astronomy - General --- Astrophysics --- Theoretical Astronomy --- Gravitational astronomy --- Mechanics, Celestial --- Physics. --- Planetology. --- Mathematical physics. --- Astronomy. --- Cosmology. --- Astronomy, Astrophysics and Cosmology. --- Mathematical Applications in the Physical Sciences. --- Planetary sciences --- Planetology --- Celestial mechanics. --- Gravity. --- Physical mathematics --- Physics --- Astronomical physics --- Astronomy --- Cosmic physics --- Mathematics

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The basic idea, simple and revolutionary at the same time, to replace the concept of a point particle with a one-dimensional string, has opened up a whole new field of research. Even today, four decades later, its multifaceted consequences are still not fully conceivable. Up to now string theory has offered a new way to view particles as different excitations of the same fundamental object. It has celebrated success in discovering the graviton in its spectrum, and it has naturally led scientists to posit space-times with more than four dimensions—which in turn has triggered numerous interesting developments in fields as varied as condensed matter physics and pure mathematics. This book collects pedagogical lectures by leading experts in string theory, introducing the non-specialist reader to some of the newest developments in the field. The carefully selected topics are at the cutting edge of research in string theory and include new developments in topological strings, AdS/CFT dualities, as well as newly emerging subfields such as doubled field theory and holography in the hydrodynamic regime. The contributions to this book have been selected and arranged in such a way as to form a self-contained, graduate level textbook.

String models --- Physics --- Physical Sciences & Mathematics --- Atomic Physics --- Nuclear Physics --- String models. --- Research. --- Models, String --- String theory --- Physics. --- Mathematical physics. --- Quantum field theory. --- String theory. --- Quantum Field Theories, String Theory. --- Mathematical Physics. --- Mathematical Applications in the Physical Sciences. --- Mathematical Methods in Physics. --- Nuclear reactions --- Physical mathematics --- Mathematics --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- Dynamics --- Relativistic quantum field theory --- Field theory (Physics) --- Quantum theory --- Relativity (Physics)

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 The General Theory of Relativity: A Mathematical Exposition will serve readers as a modern mathematical introduction to the general theory of relativity. Throughout the book, examples, worked-out problems, and exercises (with hints and solutions) are furnished. Topics in this book include, but are not limited to: • tensor analysis • the special theory of relativity • the general theory of relativity and Einstein’s field equations • spherically symmetric solutions and experimental confirmations • static and stationary space-time domains • black holes • cosmological models • algebraic classifications and the Newman-Penrose equations • the coupled Einstein-Maxwell-Klein-Gordon equations • appendices covering mathematical supplements and special topics Mathematical rigor, yet very clear presentation of the topics make this book a unique text for both university students and research scholars. Anadijiban Das has taught courses on Relativity Theory at The University College of Dublin, Ireland; Jadavpur University, India; Carnegie-Mellon University, USA; and Simon Fraser University, Canada. His major areas of research include, among diverse topics, the mathematical aspects of general relativity theory. Andrew DeBenedictis has taught courses in Theoretical Physics at Simon Fraser University, Canada, and is also a member of The Pacific Institute for the Mathematical Sciences. His research interests include quantum gravity, classical gravity, and semi-classical gravity.

Diatomic molecules. --- General relativity (Physics). --- Quantum theory. --- General relativity (Physics) --- Physics --- Physical Sciences & Mathematics --- Atomic Physics --- Mathematics --- Mathematics. --- Relativistic theory of gravitation --- Relativity theory, General --- Physics. --- Global analysis (Mathematics). --- Manifolds (Mathematics). --- Mathematical physics. --- Gravitation. --- Cosmology. --- Classical and Quantum Gravitation, Relativity Theory. --- Mathematical Physics. --- Mathematical Applications in the Physical Sciences. --- Global Analysis and Analysis on Manifolds. --- Gravitation --- Relativity (Physics) --- Global analysis. --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic --- Geometry, Differential --- Topology --- Astronomy --- Deism --- Metaphysics --- Physical mathematics --- Field theory (Physics) --- Matter --- Antigravity --- Centrifugal force --- Properties

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This volume contains the invited contributions from talks delivered in the Fall 2011 series of the Seminar on Mathematical Sciences and Applications 2011 at Virginia State University. Contributors to this volume, who are leading researchers in their fields, present their work in a way to generate genuine interdisciplinary interaction. Thus all articles therein are selective, self-contained, and are pedagogically exposed and help to foster student interest in science, technology, engineering and mathematics and to stimulate graduate and undergraduate research and collaboration between researchers in different areas.   This work is suitable for both students and researchers in a variety of interdisciplinary fields namely, mathematics as it applies to engineering, physical-chemistry, nanotechnology, life sciences, computer science, finance, economics, and game theory.

Discrete groups. --- Mathematics -- Congresses. --- Mathematics. --- Mathematics --- Technology --- Statistics --- Engineering & Applied Sciences --- Physical Sciences & Mathematics --- Mathematical Theory --- Computer Science --- Engineering --- Construction --- Math --- Computer science --- Computer mathematics. --- Mathematical physics. --- Convex geometry. --- Discrete geometry. --- Physics. --- Mathematical Applications in Computer Science. --- Mathematical Applications in the Physical Sciences. --- Numerical and Computational Physics. --- Convex and Discrete Geometry. --- Mathematical Physics. --- Industrial arts --- Science --- Numerical and Computational Physics, Simulation. --- Groups, Discrete --- Infinite groups --- Discrete mathematics --- Computer science—Mathematics. --- Convex geometry . --- Geometry --- Combinatorial geometry --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- Dynamics --- Physical mathematics --- Physics --- Computer mathematics --- Electronic data processing

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The aim of this book is to facilitate the use of Stokes' Theorem in applications.  The text takes a differential geometric point of view and provides for the student a bridge between pure and applied mathematics by carefully building a formal rigorous development of the topic and following this through to concrete applications in two and three variables.  Several practical methods and many solved exercises are provided. This book tries to show that vector analysis and vector calculus are not always at odds with one another.   Key topics include: -vectors and vector fields; -line integrals; -regular k-surfaces; -flux of a vector field; -orientation of a surface; -differential forms; -Stokes' theorem; -divergence theorem.   This book is intended for upper undergraduate students who have completed a standard introduction to differential and integral calculus for functions of several variables.  The book can also be useful to engineering and physics students who know how to handle the theorems of Green, Stokes and Gauss, but would like to explore the topic further.

Calculus of variations. --- Stokes' theorem. --- Vector analysis. --- Vector analysis --- Stokes' theorem --- Calculus of variations --- Civil & Environmental Engineering --- Mathematics --- Engineering & Applied Sciences --- Physical Sciences & Mathematics --- Operations Research --- Geometry --- Isoperimetrical problems --- Variations, Calculus of --- Mathematics. --- Global analysis (Mathematics). --- Manifolds (Mathematics). --- Mathematical physics. --- Differential geometry. --- Global Analysis and Analysis on Manifolds. --- Differential Geometry. --- Mathematical Applications in the Physical Sciences. --- Differential geometry --- Physical mathematics --- Physics --- Geometry, Differential --- Topology --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic --- Math --- Science --- Maxima and minima --- Integrals --- Vector valued functions --- Algebra, Universal --- Numbers, Complex --- Quaternions --- Spinor analysis --- Vector algebra --- Global analysis. --- Global differential geometry.