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A Mathematical Journey To Relativity
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Book Synopsis A Mathematical Journey to Relativity by : Wladimir-Georges Boskoff
Download or read book A Mathematical Journey to Relativity written by Wladimir-Georges Boskoff and published by Springer Nature. This book was released on 2020-06-01 with total page 412 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book opens with an axiomatic description of Euclidean and non-Euclidean geometries. Euclidean geometry is the starting point to understand all other geometries and it is the cornerstone for our basic intuition of vector spaces. The generalization to non-Euclidean geometry is the following step to develop the language of Special and General Relativity. These theories are discussed starting from a full geometric point of view. Differential geometry is presented in the simplest way and it is applied to describe the physical world. The final result of this construction is deriving the Einstein field equations for gravitation and spacetime dynamics. Possible solutions, and their physical implications are also discussed: the Schwarzschild metric, the relativistic trajectory of planets, the deflection of light, the black holes, the cosmological solutions like de Sitter, Friedmann-Lemaître-Robertson-Walker, and Gödel ones. Some current problems like dark energy are also scketched. The book is self-contained and includes details of all proofs. It provides solutions or tips to solve problems and exercises. It is designed for undergraduate students and for all readers who want a first geometric approach to Special and General Relativity.
Book Synopsis A Mathematical Journey to Relativity by : Wladimir-Georges Boskoff
Download or read book A Mathematical Journey to Relativity written by Wladimir-Georges Boskoff and published by Springer Nature. This book was released on with total page 556 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis A Mathematical Journey to Quantum Mechanics by : Salvatore Capozziello
Download or read book A Mathematical Journey to Quantum Mechanics written by Salvatore Capozziello and published by Springer Nature. This book was released on 2021-09-27 with total page 294 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an itinerary to quantum mechanics taking into account the basic mathematics to formulate it. Specifically, it features the main experiments and postulates of quantum mechanics pointing out their mathematical prominent aspects showing how physical concepts and mathematical tools are deeply intertwined. The material covers topics such as analytic mechanics in Newtonian, Lagrangian, and Hamiltonian formulations, theory of light as formulated in special relativity, and then why quantum mechanics is necessary to explain experiments like the double-split, atomic spectra, and photoelectric effect. The Schrödinger equation and its solutions are developed in detail. It is pointed out that, starting from the concept of the harmonic oscillator, it is possible to develop advanced quantum mechanics. Furthermore, the mathematics behind the Heisenberg uncertainty principle is constructed towards advanced quantum mechanical principles. Relativistic quantum mechanics is finally considered.The book is devoted to undergraduate students from University courses of Physics, Mathematics, Chemistry, and Engineering. It consists of 50 self-contained lectures, and any statement and theorem are demonstrated in detail. It is the companion book of "A Mathematical Journey to Relativity", by the same Authors, published by Springer in 2020.
Book Synopsis The Road to Relativity by : Hanoch Gutfreund
Download or read book The Road to Relativity written by Hanoch Gutfreund and published by Princeton University Press. This book was released on 2017-05-09 with total page 257 pages. Available in PDF, EPUB and Kindle. Book excerpt: An annotated facsimile edition of Einstein's handwritten manuscript on the foundations of general relativity This richly annotated facsimile edition of "The Foundation of General Relativity" introduces a new generation of readers to Albert Einstein's theory of gravitation. Written in 1915, this remarkable document is a watershed in the history of physics and an enduring testament to the elegance and precision of Einstein's thought. Presented here is a beautiful facsimile of Einstein's original handwritten manuscript, along with its English translation and an insightful page-by-page commentary that places the work in historical and scientific context. Hanoch Gutfreund and Jürgen Renn's concise introduction traces Einstein's intellectual odyssey from special to general relativity, and their essay "The Charm of a Manuscript" provides a delightful meditation on the varied afterlife of Einstein's text. Featuring a foreword by John Stachel, this handsome edition also includes a biographical glossary of the figures discussed in the book, a comprehensive bibliography, suggestions for further reading, and numerous photos and illustrations throughout.
Book Synopsis Shifting the Earth by : Arthur Mazer
Download or read book Shifting the Earth written by Arthur Mazer and published by John Wiley & Sons. This book was released on 2011-09-09 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: Discover how mathematics and science have propelled history From Ancient Greece to the Enlightenment and then on to modern times, Shifting the Earth: The Mathematical Quest to Understand the Motion of the Universe takes readers on a journey motivated by the desire to understand the universe and the motion of the heavens. The author presents a thought-provoking depiction of the sociopolitical environment in which some of the most prominent scientists in history lived and then provides a mathematical account of their contributions. From Eudoxus to Einstein, this fascinating book describes how, beginning in ancient times, pioneers in the sciences and mathematics have dramatically changed our vision of who we are as well as our place in the universe. Readers will discover how Ptolemy's geocentric model evolved into Kepler's heliocentric model, with Copernicus as the critical intermediary. The author explains how one scientific breakthrough set the stage for the next one, and he also places the scientists and their discoveries within the context of history, including: Archimedes, Apollonius, and the Punic Wars Ptolemy and the rise of Christianity Copernicus and the Renaissance Kepler and the Counter-Reformation Newton and the Enlightenment Einstein and the detonation of the atom bomb Each chapter presents the work of a single scientist or mathematician, building on the previous chapters to demonstrate the evolutionary process of discovery. Chapters begin with a narrative section and conclude with a mathematical presentation of one of the scientist's original works. Most of these mathematical presentations, including the section on Einstein's special relativity, are accessible using only basic mathematics; however, readers can skip the mathematical sections and still follow the evolution of science and mathematics. Shifting the Earth is an excellent book for anyone interested in the history of mathematics and how the quest to understand the motion of the heavens has influenced the broader history of humankind.
Book Synopsis Our Mathematical Universe by : Max Tegmark
Download or read book Our Mathematical Universe written by Max Tegmark and published by Vintage. This book was released on 2015-02-03 with total page 434 pages. Available in PDF, EPUB and Kindle. Book excerpt: Max Tegmark leads us on an astonishing journey through past, present and future, and through the physics, astronomy and mathematics that are the foundation of his work, most particularly his hypothesis that our physical reality is a mathematical structure and his theory of the ultimate multiverse. In a dazzling combination of both popular and groundbreaking science, he not only helps us grasp his often mind-boggling theories, but he also shares with us some of the often surprising triumphs and disappointments that have shaped his life as a scientist. Fascinating from first to last—this is a book that has already prompted the attention and admiration of some of the most prominent scientists and mathematicians.
Book Synopsis Einstein’s Italian Mathematicians: Ricci, Levi-Civita, and the Birth of General Relativity by : Judith R. Goodstein
Download or read book Einstein’s Italian Mathematicians: Ricci, Levi-Civita, and the Birth of General Relativity written by Judith R. Goodstein and published by American Mathematical Soc.. This book was released on 2018-07-20 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: In the first decade of the twentieth century as Albert Einstein began formulating a revolutionary theory of gravity, the Italian mathematician Gregorio Ricci was entering the later stages of what appeared to be a productive if not particularly memorable career, devoted largely to what his colleagues regarded as the dogged development of a mathematical language he called the absolute differential calculus. In 1912, the work of these two dedicated scientists would intersect—and physics and mathematics would never be the same. Einstein's Italian Mathematicians chronicles the lives and intellectual contributions of Ricci and his brilliant student Tullio Levi-Civita, including letters, interviews, memoranda, and other personal and professional papers, to tell the remarkable, little-known story of how two Italian academicians, of widely divergent backgrounds and temperaments, came to provide the indispensable mathematical foundation—today known as the tensor calculus—for general relativity.
Book Synopsis Spacetime and Geometry by : Sean M. Carroll
Download or read book Spacetime and Geometry written by Sean M. Carroll and published by Cambridge University Press. This book was released on 2019-08-08 with total page 529 pages. Available in PDF, EPUB and Kindle. Book excerpt: An accessible introductory textbook on general relativity, covering the theory's foundations, mathematical formalism and major applications.
Book Synopsis The Einstein Theory of Relativity by : Lillian R. Lieber
Download or read book The Einstein Theory of Relativity written by Lillian R. Lieber and published by Paul Dry Books. This book was released on 2008 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt: "A clear and vivid exposition of the essential ideas and methods of the theory of relativity...can be warmly recommended especially to those who cannot spend too much time on the subject." -- Albert Einstein. Using "just enough mathematics to help and not to hinder the lay reader", Lillian Lieber provides a thorough explanation of Einstein's theory of relativity. Her delightful style, in combination with her husband's charming illustrations, makes for an interesting and accessible read about one of the greatest ideas of all times.
Book Synopsis The General Theory of Relativity by : Anadijiban Das
Download or read book The General Theory of Relativity written by Anadijiban Das and published by Springer Science & Business Media. This book was released on 2012-06-26 with total page 694 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Semi-Riemannian Geometry by : Stephen C. Newman
Download or read book Semi-Riemannian Geometry written by Stephen C. Newman and published by John Wiley & Sons. This book was released on 2019-07-30 with total page 656 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to semi-Riemannian geometry as a foundation for general relativity Semi-Riemannian Geometry: The Mathematical Language of General Relativity is an accessible exposition of the mathematics underlying general relativity. The book begins with background on linear and multilinear algebra, general topology, and real analysis. This is followed by material on the classical theory of curves and surfaces, expanded to include both the Lorentz and Euclidean signatures. The remainder of the book is devoted to a discussion of smooth manifolds, smooth manifolds with boundary, smooth manifolds with a connection, semi-Riemannian manifolds, and differential operators, culminating in applications to Maxwell’s equations and the Einstein tensor. Many worked examples and detailed diagrams are provided to aid understanding. This book will appeal especially to physics students wishing to learn more differential geometry than is usually provided in texts on general relativity.
Book Synopsis Mathematics of Relativity by : George Yuri Rainich
Download or read book Mathematics of Relativity written by George Yuri Rainich and published by Courier Corporation. This book was released on 2014-08-20 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt: Concise treatment, based on ideas of Einstein and Minkowski, geared toward advanced undergraduates and graduate students of physics. Topics include old physics, new geometry, special relativity, curved space, and general relativity. 1950 edition.
Book Synopsis The Wave Equation on a Curved Space-Time by : F. G. Friedlander
Download or read book The Wave Equation on a Curved Space-Time written by F. G. Friedlander and published by Cambridge University Press. This book was released on 1975 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives a rigourous discussion of the local effects of curvature on the behaviour of waves. In the course of this discussion many techniques are developed which are also needed for a study of more general problems, in which the gravitational field itself plays a dynamical role.
Book Synopsis The Mathematical Theory of Relativity by : Arthur Stanley Eddington
Download or read book The Mathematical Theory of Relativity written by Arthur Stanley Eddington and published by Mjp Publishers. This book was released on 2023-02-15 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Book Synopsis Explorations in Mathematical Physics by : Don Koks
Download or read book Explorations in Mathematical Physics written by Don Koks and published by Springer Science & Business Media. This book was released on 2006-09-15 with total page 549 pages. Available in PDF, EPUB and Kindle. Book excerpt: Have you ever wondered why the language of modern physics centres on geometry? Or how quantum operators and Dirac brackets work? What a convolution really is? What tensors are all about? Or what field theory and lagrangians are, and why gravity is described as curvature? This book takes you on a tour of the main ideas forming the language of modern mathematical physics. Here you will meet novel approaches to concepts such as determinants and geometry, wave function evolution, statistics, signal processing, and three-dimensional rotations. You will see how the accelerated frames of special relativity tell us about gravity. On the journey, you will discover how tensor notation relates to vector calculus, how differential geometry is built on intuitive concepts, and how variational calculus leads to field theory. You will meet quantum measurement theory, along with Green functions and the art of complex integration, and finally general relativity and cosmology. The book takes a fresh approach to tensor analysis built solely on the metric and vectors, with no need for one-forms. This gives a much more geometrical and intuitive insight into vector and tensor calculus, together with general relativity, than do traditional, more abstract methods. Don Koks is a physicist at the Defence Science and Technology Organisation in Adelaide, Australia. His doctorate in quantum cosmology was obtained from the Department of Physics and Mathematical Physics at Adelaide University. Prior work at the University of Auckland specialised in applied accelerator physics, along with pure and applied mathematics.
Book Synopsis A Mathematical Odyssey by : Steven G. Krantz
Download or read book A Mathematical Odyssey written by Steven G. Krantz and published by Springer. This book was released on 2014-05-10 with total page 382 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics is a poem. It is a lucid, sensual, precise exposition of beautiful ideas directed to specific goals. It is worthwhile to have as broad a cross-section of mankind as possible be conversant with what goes on in mathematics. Just as everyone knows that the Internet is a powerful and important tool for communication, so everyone should know that the Poincaré conjecture gives us important information about the shape of our universe. Just as every responsible citizen realizes that the mass-production automobile was pioneered by Henry Ford, so everyone should know that the P/NP problem has implications for security and data manipulation that will affect everyone. This book endeavors to tell the story of the modern impact of mathematics, of its trials and triumphs and insights, in language that can be appreciated by a broad audience. It endeavors to show what mathematics means for our lives, how it impacts all of us, and what new thoughts it should cause us to entertain. It introduces new vistas of mathematical ideas and shares the excitement of new ideas freshly minted. It discusses the significance and impact of these ideas, and gives them meaning that will travel well and cause people to reconsider their place in the universe. Mathematics is one of mankind's oldest disciplines. Along with philosophy, it has shaped the very modus of human thought. And it continues to do so. To be unaware of modern mathematics is to miss out on a large slice of life. It is to be left out of essential modern developments. We want to address this point, and do something about it. This is a book to make mathematics exciting for people of all interests and all walks of life. Mathematics is exhilarating, it is ennobling, it is uplifting, and it is fascinating. We want to show people this part of our world, and to get them to travel new paths.
Book Synopsis A Mathematical Introduction to General Relativity by : Amol Sasane
Download or read book A Mathematical Introduction to General Relativity written by Amol Sasane and published by World Scientific Publishing Company. This book was released on 2021-08-31 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: The book aims to give a mathematical presentation of the theory of general relativity (that is, spacetime-geometry-based gravitation theory) to advanced undergraduate mathematics students. Mathematicians will find spacetime physics presented in the definition-theorem-proof format familiar to them. The given precise mathematical definitions of physical notions help avoiding pitfalls, especially in the context of spacetime physics describing phenomena that are counter-intuitive to everyday experiences.In the first part, the differential geometry of smooth manifolds, which is needed to present the spacetime-based gravitation theory, is developed from scratch. Here, many of the illustrating examples are the Lorentzian manifolds which later serve as spacetime models. This has the twofold purpose of making the physics forthcoming in the second part relatable, and the mathematics learnt in the first part less dry. The book uses the modern coordinate-free language of semi-Riemannian geometry. Nevertheless, to familiarise the reader with the useful tool of coordinates for computations, and to bridge the gap with the physics literature, the link to coordinates is made through exercises, and via frequent remarks on how the two languages are related.In the second part, the focus is on physics, covering essential material of the 20th century spacetime-based view of gravity: energy-momentum tensor field of matter, field equation, spacetime examples, Newtonian approximation, geodesics, tests of the theory, black holes, and cosmological models of the universe.Prior knowledge of differential geometry or physics is not assumed. The book is intended for self-study, and the solutions to the (over 200) exercises are included.
