*A Mathematical Approach*

**Author**: Farook Rahaman

**Publisher:**Springer

**ISBN:**8132220803

**Category:**Science

**Page:**249

**View:**2570

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# Search Results for: the-special-theory-of-relativity-a-mathematical-approach

*A Mathematical Approach*

**Author**: Farook Rahaman

**Publisher:** Springer

**ISBN:** 8132220803

**Category:** Science

**Page:** 249

**View:** 2570

The book expounds the major topics in the special theory of relativity. It provides a detailed examination of the mathematical foundation of the special theory of relativity, relativistic mass, relativistic mechanics and relativistic electrodynamics. As well as covariant formulation of relativistic mechanics and electrodynamics, the book discusses the relativistic effect on photons. Using a mathematical approach, the text offers graduate students a clear, concise view of the special theory of relativity. Organized into 14 chapters and two appendices, the content is presented in a logical order, and every topic has been dealt with in a simple and lucid manner. To aid understanding of the subject, the book provides numerous relevant worked examples in every chapter. The book’s mathematical approach helps students in their independent study and motivates them to research the topic further.
*A Mathematical Exposition*

**Author**: Anadijiban Das

**Publisher:** Springer Science & Business Media

**ISBN:** 1461208939

**Category:** Science

**Page:** 232

**View:** 5474

Based on courses taught at the University of Dublin, Carnegie Mellon University, and mostly at Simon Fraser University, this book presents the special theory of relativity from a mathematical point of view. It begins with the axioms of the Minkowski vector space and the flat spacetime manifold. Then it discusses the kinematics of special relativity in terms of Lorentz tranformations, and treats the group structure of Lorentz transformations. Extending the discussion to spinors, the author shows how a unimodular mapping of spinor (vector) space can induce a proper, orthochronous Lorentz mapping on the Minkowski vector space. The second part begins with a discussion of relativistic particle mechanics from both the Lagrangian and Hamiltonian points of view. The book then turns to the relativistic (classical) field theory, including a proof of Noether's theorem and discussions of the Klein-Gordon, electromagnetic, Dirac, and non-abelian gauge fields. The final chapter deals with recent work on classical fields in an eight-dimensional covariant phase space.
*A New Approach to Einstein*

**Author**: Hermann Bondi

**Publisher:** Courier Corporation

**ISBN:** 9780486240213

**Category:** Science

**Page:** 177

**View:** 381

This radically reoriented and popular presentation of Einstein's Special Theory of Relativity derives its concepts from Newtonian ideas rather than by opposing them. It demonstrates that time is relative rather than absolute, that high speeds affect the nature of time, and that acceleration affects speed, time, and mass. Very little mathematics is required, and 60 illustrations augment the text.
*A Mathematical Exposition*

**Author**: Anadijiban Das,Andrew DeBenedictis

**Publisher:** Springer Science & Business Media

**ISBN:** 1461436583

**Category:** Science

**Page:** 678

**View:** 9056

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.
*With Modern Applications in Cosmology*

**Author**: Øyvind Grøn,Sigbjorn Hervik

**Publisher:** Springer Science & Business Media

**ISBN:** 0387692002

**Category:** Science

**Page:** 538

**View:** 7366

This book introduces the general theory of relativity and includes applications to cosmology. The book provides a thorough introduction to tensor calculus and curved manifolds. After the necessary mathematical tools are introduced, the authors offer a thorough presentation of the theory of relativity. Also included are some advanced topics not previously covered by textbooks, including Kaluza-Klein theory, Israel's formalism and branes. Anisotropic cosmological models are also included. The book contains a large number of new exercises and examples, each with separate headings. The reader will benefit from an updated introduction to general relativity including the most recent developments in cosmology.
*A Textbook for Undergraduates*

**Author**: Jrgen Freund

**Publisher:** World Scientific

**ISBN:** 981277159X

**Category:** Science

**Page:** 314

**View:** 5636

This book, first appearing in German in 2004 under the title Spezielle Relativittstheorie fr Studienanfnger, offers access to the special theory of relativity for readers with a background in mathematics and physics comparable to a high school honors degree. All mathematical and physical competence required beyond that level is gradually developed through the book, as more advanced topics are introduced. The full tensor formalism, however, is dispensed with as it would only be a burden for the problems to be dealt with. Eventually, a substantial and comprehensive treatise on special relativity emerges which, with its gray-shaded formulary, is an invaluable reference manual for students and scientists alike.Some crucial results are derived more than once with different approaches: the Lorentz transformation in one spatial direction three times, the Doppler formula four times, the Lorentz transformation in two directions twice; also twice the unification of electric and magnetic forces, the velocity addition formula, as well as the aberration formula. Beginners will be grateful to find several routes to the goal; moreover, for a theory like relativity, it is of fundamental importance to demonstrate that it is self-contained and without contradictions.Author's website: www.relativity.ch.
*A Simplified Approach to Einstein's Theories*

**Author**: Leo Sartori

**Publisher:** Univ of California Press

**ISBN:** 9780520916241

**Category:** Science

**Page:** 376

**View:** 5672

Nonspecialists with no prior knowledge of physics and only reasonable proficiency with algebra can now understand Einstein's special theory of relativity. Effectively diagrammed and with an emphasis on logical structure, Leo Sartori's rigorous but simple presentation will guide interested readers through concepts of relative time and relative space. Sartori covers general relativity and cosmology, but focuses on Einstein's theory. He tracks its history and implications. He explores illuminating paradoxes, including the famous twin paradox, the "pole-in-the-barn" paradox, and the Loedel diagram, which is an accessible, graphic approach to relativity. Students of the history and philosophy of science will welcome this concise introduction to the central concept of modern physics.
*An Illustrated Guide*

**Author**: Sander Bais

**Publisher:** Harvard University Press

**ISBN:** 9780674026117

**Category:** Mathematics

**Page:** 120

**View:** 5537

Using a series of easy-to-follow diagrams and elementary geometry, this visual guide to Einstein's Theory of Relativity explores fundamental concepts such as simultaneity, causality, and time dilation.

**Author**: Tevian Dray

**Publisher:** CRC Press

**ISBN:** 1466510471

**Category:** Mathematics

**Page:** 150

**View:** 4852

The Geometry of Special Relativity provides an introduction to special relativity that encourages readers to see beyond the formulas to the deeper geometric structure. The text treats the geometry of hyperbolas as the key to understanding special relativity. This approach replaces the ubiquitous γ symbol of most standard treatments with the appropriate hyperbolic trigonometric functions. In most cases, this not only simplifies the appearance of the formulas, but also emphasizes their geometric content in such a way as to make them almost obvious. Furthermore, many important relations, including the famous relativistic addition formula for velocities, follow directly from the appropriate trigonometric addition formulas. The book first describes the basic physics of special relativity to set the stage for the geometric treatment that follows. It then reviews properties of ordinary two-dimensional Euclidean space, expressed in terms of the usual circular trigonometric functions, before presenting a similar treatment of two-dimensional Minkowski space, expressed in terms of hyperbolic trigonometric functions. After covering special relativity again from the geometric point of view, the text discusses standard paradoxes, applications to relativistic mechanics, the relativistic unification of electricity and magnetism, and further steps leading to Einstein’s general theory of relativity. The book also briefly describes the further steps leading to Einstein’s general theory of relativity and then explores applications of hyperbola geometry to non-Euclidean geometry and calculus, including a geometric construction of the derivatives of trigonometric functions and the exponential function.
*Man's New Perspective on the Cosmos*

**Author**: Stan Gibilisco

**Publisher:** Courier Corporation

**ISBN:** 9780486266596

**Category:** Science

**Page:** 200

**View:** 8818

Clear, concise exposition of both the special and general theories of relativity, intended for nonscientific readers with a knowledge of high school math. Topics include simultaneity, time dilation, length contraction, the possibility of travel to a distant star, non-Euclidean geometries, black holes, and the structure of the universe. 158 illustrations.
*From Newton’s Attractive Gravity to the Repulsive Gravity of Vacuum Energy*

**Author**: Øyvind Grøn

**Publisher:** Springer Science & Business Media

**ISBN:** 0387881344

**Category:** Science

**Page:** 252

**View:** 7162

This book collects lectures on the general theory of relativity given by Dr. Øyvind Grøn at the University of Oslo, Norway. This accessible text allows students to follow the deductions all the way throughout the book.

**Author**: David Bohm

**Publisher:** Routledge

**ISBN:** 1136747605

**Category:** Philosophy

**Page:** 304

**View:** 5042

In these inspiring lectures David Bohm explores Albert Einstein’s celebrated Theory of Relativity that transformed forever the way we think about time and space. Yet for Bohm the implications of the theory were far more revolutionary both in scope and impact even than this. Stepping back from dense theoretical and scientific detail in this eye-opening work, Bohm describes how the notion of relativity strikes at the heart of our very conception of the universe, regardless of whether we are physicists or philosophers.

**Author**: Valerio Faraoni

**Publisher:** Springer Science & Business Media

**ISBN:** 3319011073

**Category:** Science

**Page:** 304

**View:** 5054

This book offers an essential bridge between college-level introductions and advanced graduate-level books on special relativity. It begins at an elementary level, presenting and discussing the basic concepts normally covered in college-level works, including the Lorentz transformation. Subsequent chapters introduce the four-dimensional worldview implied by the Lorentz transformations, mixing time and space coordinates, before continuing on to the formalism of tensors, a topic usually avoided in lower-level courses. The book’s second half addresses a number of essential points, including the concept of causality; the equivalence between mass and energy, including applications; relativistic optics; and measurements and matter in Minkowski space-time. The closing chapters focus on the energy-momentum tensor of a continuous distribution of mass-energy and its co-variant conservation; angular momentum; a discussion of the scalar field of perfect fluids and the Maxwell field; and general coordinates. Every chapter is supplemented by a section with numerous exercises, allowing readers to practice the theory. These exercises constitute an essential part of the textbook, and the solutions to approximately half of them are provided in the appendix.
*A Rigorous Introduction for the Mathematically Untrained*

**Author**: Øyvind Grøn,Arne Næss

**Publisher:** Springer Science & Business Media

**ISBN:** 9781461407065

**Category:** Science

**Page:** 341

**View:** 8904

This book provides an introduction to the theory of relativity and the mathematics used in its processes. Three elements of the book make it stand apart from previously published books on the theory of relativity. First, the book starts at a lower mathematical level than standard books with tensor calculus of sufficient maturity to make it possible to give detailed calculations of relativistic predictions of practical experiments. Self-contained introductions are given, for example vector calculus, differential calculus and integrations. Second, in-between calculations have been included, making it possible for the non-technical reader to follow step-by-step calculations. Thirdly, the conceptual development is gradual and rigorous in order to provide the inexperienced reader with a philosophically satisfying understanding of the theory. The goal of this book is to provide the reader with a sound conceptual understanding of both the special and general theories of relativity, and gain an insight into how the mathematics of the theory can be utilized to calculate relativistic effects.
*From Particles to Astrophysics*

**Author**: Eric Gourgoulhon

**Publisher:** Springer Science & Business Media

**ISBN:** 3642372767

**Category:** Science

**Page:** 784

**View:** 9750

Special relativity is the basis of many fields in modern physics: particle physics, quantum field theory, high-energy astrophysics, etc. This theory is presented here by adopting a four-dimensional point of view from the start. An outstanding feature of the book is that it doesn’t restrict itself to inertial frames but considers accelerated and rotating observers. It is thus possible to treat physical effects such as the Thomas precession or the Sagnac effect in a simple yet precise manner. In the final chapters, more advanced topics like tensorial fields in spacetime, exterior calculus and relativistic hydrodynamics are addressed. In the last, brief chapter the author gives a preview of gravity and shows where it becomes incompatible with Minkowsky spacetime. Well illustrated and enriched by many historical notes, this book also presents many applications of special relativity, ranging from particle physics (accelerators, particle collisions, quark-gluon plasma) to astrophysics (relativistic jets, active galactic nuclei), and including practical applications (Sagnac gyrometers, synchrotron radiation, GPS). In addition, the book provides some mathematical developments, such as the detailed analysis of the Lorentz group and its Lie algebra. The book is suitable for students in the third year of a physics degree or on a masters course, as well as researchers and any reader interested in relativity. Thanks to the geometric approach adopted, this book should also be beneficial for the study of general relativity. “A modern presentation of special relativity must put forward its essential structures, before illustrating them using concrete applications to specific dynamical problems. Such is the challenge (so successfully met!) of the beautiful book by Éric Gourgoulhon.” (excerpt from the Foreword by Thibault Damour)
*The Foundation of Macroscopic Physics*

**Author**: W. G. Dixon

**Publisher:** CUP Archive

**ISBN:** 9780521272414

**Category:** Science

**Page:** 272

**View:** 2667

The book aims to illuminate the importance of special relativity in the examination of dynamics, thermodynamics and electromagnetism.

**Author**: James Hammond Smith

**Publisher:** Courier Corporation

**ISBN:** 048668895X

**Category:** Science

**Page:** 218

**View:** 8199

Concise, well-written treatment of epochal theory of modern physics covers classical relativity and the relativity postulate, time dilation, the twin paradox, momentum and energy, particles of zero mass, electric and magnetic fields and forces and more. Only high school math needed. Replete with examples, ideal for self-study. Introduction. 70 illustrations.

**Author**: Alladi Ramakrishnan

**Publisher:** Egully.com

**ISBN:** N.A

**Category:** Science

**Page:** 151

**View:** 3068

*An Introduction to Special and General Relativity*

**Author**: Rafael Ferraro

**Publisher:** Springer Science & Business Media

**ISBN:** 0387699473

**Category:** Science

**Page:** 310

**View:** 9027

This excellent textbook offers a unique take on relativity theory, setting it in its historical context. Ideal for those interested in relativity and the history of physics, the book contains a complete account of special relativity that begins with the historical analysis of the reasons that led to a change in our view of space and time. Its aim is to foster a deep understanding of relativistic spacetime and its consequences for Dynamics.
*The Special and the General Theory*

**Author**: Albert Einstein,Robert W. Lawson,Amit Hagar

**Publisher:** Barnes & Noble Publishing

**ISBN:** 9780760759219

**Category:** Science

**Page:** 125

**View:** 4616

Albert Einstein's Relativity: The Special and the General Theory (1920) is a cornerstone of modern physics. Einstein intended this book for "those readers who, from a general scientific and philosophical point of view, are interested in the theory, but who are not conversant with the mathematical apparatus." Indeed, within the vast literature on the philosophy of space and time, Einstein's Relativity shall remain an illuminable and intelligible exposition, highly quotable as one of the most lucid presentations of the subject matter, and a launching pad for any further inquiry on the fascinating features of our universe.

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