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Author : Wladimir-Georges Boskoff
Publisher : Springer Nature
ISBN 13 : 303154823X
Total Pages : 556 pages
Book Rating : 4.0/5 (315 download)
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:
Author : Wladimir-Georges Boskoff
Publisher : Springer Nature
ISBN 13 : 3030478947
Total Pages : 412 pages
Book Rating : 4.0/5 (34 download)
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.
Author : Salvatore Capozziello
Publisher : Springer Nature
ISBN 13 : 3030860981
Total Pages : 294 pages
Book Rating : 4.0/5 (38 download)
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.
Author : Arthur Mazer
Publisher : John Wiley & Sons
ISBN 13 : 1118108310
Total Pages : 266 pages
Book Rating : 4.1/5 (181 download)
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.
Author : Anadijiban Das
Publisher : Springer Science & Business Media
ISBN 13 : 1461436583
Total Pages : 694 pages
Book Rating : 4.4/5 (614 download)
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.
Author : Lillian R. Lieber
Publisher : Paul Dry Books
ISBN 13 : 1589880447
Total Pages : 370 pages
Book Rating : 4.5/5 (898 download)
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.
Author : Amol Sasane
Publisher : World Scientific Publishing Company
ISBN 13 : 9789811256721
Total Pages : pages
Book Rating : 4.2/5 (567 download)
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.
Author : Louis S. Jagerman
Publisher : Trafford Publishing
ISBN 13 : 155212567X
Total Pages : 456 pages
Book Rating : 4.5/5 (521 download)
Download or read book The Mathematics of Relativity for the Rest of Us written by Louis S. Jagerman and published by Trafford Publishing. This book was released on 2001 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Mathematics of Relativity for the Rest of Us is intended to give the generally educated reader a thorough and factual understanding of Einstein's theory of relativity - including the difficult mathematical concepts, even if the reader is not trained in higher mathematics.
Author : Don Koks
Publisher : Springer Science & Business Media
ISBN 13 : 0387309438
Total Pages : 549 pages
Book Rating : 4.3/5 (873 download)
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.
Author : George Yuri Rainich
Publisher : Courier Corporation
ISBN 13 : 0486783251
Total Pages : 193 pages
Book Rating : 4.4/5 (867 download)
Download or read book Mathematics of Relativity written by George Yuri Rainich and published by Courier Corporation. This book was released on 2014-11-19 with total page 193 pages. Available in PDF, EPUB and Kindle. Book excerpt: Based on the ideas of Einstein and Minkowski, this concise treatment is derived from the author's many years of teaching the mathematics of relativity at the University of Michigan. Geared toward advanced undergraduates and graduate students of physics, the text covers old physics, new geometry, special relativity, curved space, and general relativity. Beginning with a discussion of the inverse square law in terms of simple calculus, the treatment gradually introduces increasingly complicated situations and more sophisticated mathematical tools. Changes in fundamental concepts, which characterize relativity theory, and the refinements of mathematical technique are incorporated as necessary. The presentation thus offers an easier approach without sacrifice of rigor. Dover (2014) republication of the edition published by John Wiley & Sons, New York, 1950. See every Dover book in print at www.doverpublications.com
Author : Hermann Weyl
Publisher : Courier Corporation
ISBN 13 : 0486318427
Total Pages : 368 pages
Book Rating : 4.4/5 (863 download)
Download or read book Space, Time, Matter written by Hermann Weyl and published by Courier Corporation. This book was released on 2013-04-26 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: Excellent introduction probes deeply into Euclidean space, Riemann's space, Einstein's general relativity, gravitational waves and energy, and laws of conservation. "A classic of physics." — British Journal for Philosophy and Science.
Author : Farook Rahaman
Publisher : Cambridge University Press
ISBN 13 : 1108837999
Total Pages : 427 pages
Book Rating : 4.1/5 (88 download)
Download or read book The General Theory of Relativity written by Farook Rahaman and published by Cambridge University Press. This book was released on 2021-09-30 with total page 427 pages. Available in PDF, EPUB and Kindle. Book excerpt: Discusses the general theory of relativity, Lie derivatives, rotating black holes, with a focus on basics of cosmology and astrophysics.
Author : Peter Lorimer
Publisher : World Scientific
ISBN 13 : 9814506869
Total Pages : 116 pages
Book Rating : 4.8/5 (145 download)
Download or read book The Special Theory Of Relativity For Mathematics Students written by Peter Lorimer and published by World Scientific. This book was released on 1990-07-05 with total page 116 pages. Available in PDF, EPUB and Kindle. Book excerpt: One of the problems facing mathematics and physics is that mathematicians and physicists speak languages that the others find hard to understand. These notes take a fundamental part of physics, the special theory of relativity and describe it in terms that can be understood by mathematics students who have studied the two basic undergraduate topics, linear algebra and multivariable calculus. It gives a full description of the geometry of space-time and the foundations of the theory of electromagnetism in terms they are familiar with.
Author : R. K. Sachs
Publisher : Dover Publications
ISBN 13 : 9780486461533
Total Pages : 304 pages
Book Rating : 4.4/5 (615 download)
Download or read book General Relativity for Mathematicians written by R. K. Sachs and published by Dover Publications. This book was released on 2007-01 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt: Geared toward mathematically sophisticated readers with a solid background in differential geometry, this text was written by two noted teachers at the University of California, Berkeley. It offers a firm foundation in the principles of general relativity, particularly in terms of singularity theorems and the quantization of gravity. Starting with preliminaries that include notation, physics background, and a preview of relativity, the text advances to spacetimes and observers. A three-part treatment of electromagnetism and matter progresses from basic concepts to interactions and other matter models. Subsequent chapters explore the Einstein field equation, photons, cosmology, and applications. Exercises appear at the end of each section, and the text concludes with optional drills offering further explorations of relativity and Newtonian analogues.
Author : Richard Lighthouse
Publisher : Richard Lighthouse
ISBN 13 : 1311382305
Total Pages : 10 pages
Book Rating : 4.3/5 (113 download)
Download or read book Time Travel written by Richard Lighthouse and published by Richard Lighthouse. This book was released on with total page 10 pages. Available in PDF, EPUB and Kindle. Book excerpt: This short technical note describes an approximate mathematical solution for Time Travel involving relativity and very brief time intervals. Limitations of the solution are discussed including possible error sources. Assumptions are made for small changes in the speed of light and for the Lighthouse Frequency, which has been described in previous papers. This paper will only be meaningful to those with a background in calculus, physics, and/or engineering. Each reader must comprehend that our universe blinks off and on, more than 1 trillion times every second.
Author : Nirmala Prakash
Publisher : World Scientific Publishing Company
ISBN 13 : 1911298240
Total Pages : 864 pages
Book Rating : 4.9/5 (112 download)
Download or read book Mathematical Perspectives on Theoretical Physics written by Nirmala Prakash and published by World Scientific Publishing Company. This book was released on 2003-09-02 with total page 864 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the basics of mathematics that are needed for learning the physics of today. It describes briefly the theories of groups and operators, finite- and infinite-dimensional algebras, concepts of symmetry and supersymmetry, and then delineates their relations to theories of relativity and black holes, classical and quantum physics, electroweak fields and Yang-Mills. It concludes with a chapter on (the complex theory of) strings and superstrings and their link to black holes — an idea that fascinates both the physicist and the mathematician. Contents:Complex Functions, Riemann Surfaces and Two-Dimensional Conformal Field Theory (an Introduction)Elements of Group Theory and Group RepresentationsA Primer on OperatorsBasics of Algebras and Related ConceptsInfinite-Dimensional AlgebrasThe Role of Symmetry in Physics and MathematicsAll That's Super — An IntroductionGravitation, Relativity and Black HolesBasics of Quantum TheoryTheory of Yang–Mills and the Yang–Mills–Higgs MechanismStrings and Superstrings (Elementary Aspects) Readership: Upper level undergraduates, graduate students, lecturers and researchers in theoretical physics, mathematical physics, quantum physics and astrophysics as well as Yang-Mills and superstring theory.
Author : Yvonne Choquet-Bruhat
Publisher : Oxford University Press
ISBN 13 : 0199230722
Total Pages : 812 pages
Book Rating : 4.1/5 (992 download)
Download or read book General Relativity and the Einstein Equations written by Yvonne Choquet-Bruhat and published by Oxford University Press. This book was released on 2009 with total page 812 pages. Available in PDF, EPUB and Kindle. Book excerpt: General Relativity has passed all experimental and observational tests to model the motion of isolated bodies with strong gravitational fields, though the mathematical and numerical study of these motions is still in its infancy. It is believed that General Relativity models our cosmos, with a manifold of dimensions possibly greater than four and debatable topology opening a vast field of investigation for mathematicians and physicists alike. Remarkable conjectures have been proposed, many results have been obtained but many fundamental questions remain open. In this monograph, aimed at researchers in mathematics and physics, the author overviews the basic ideas in General Relativity, introduces the necessary mathematics and discusses some of the key open questions in the field.
