**A Mathematical Approach To Special Relativity**

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### The Special Theory of Relativity

- Author : Farook Rahaman
- Publisher : Springer Nature
- Release Date : 2022-05-12
- Total pages : 337
- ISBN : 9789811904974
- File Size : 51,9 Mb
- Total Download : 551
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Download The Special Theory of Relativity in PDF, Epub, and Kindle

This textbook 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 text discusses the relativistic effect on photons. A new chapter on electromagnetic waves as well as several new problems and examples have been included in the second edition of the book. Using the mathematical approach, the text offers graduate students a clear, concise view of the special theory of relativity. Organized into 15 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 text provides numerous relevant worked-out examples in every chapter. The mathematical approach of the text helps students in their independent study and motivates them to research the topic further.

### A Mathematical Approach to Special Relativity

- Author : Ahmad Shariati
- Publisher : Elsevier
- Release Date : 2022-09-19
- Total pages : 352
- ISBN : 9780323997096
- File Size : 12,8 Mb
- Total Download : 859
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Download A Mathematical Approach to Special Relativity in PDF, Epub, and Kindle

A Mathematical Approach to Special Relativity introduces the mathematical formalisms of special and general relativity. Developed from the author’s experience teaching physics to students across all levels, the valuable resource introduces key concepts, building in complexity and using increasingly advanced mathematical tools as it progresses. Without assuming a background in calculus, the text begins with symmetry, before delving more deeply into Galilean relativity. Throughout, the book provides examples and useful "Guides to the Literature." This unique text emphasizes the experimental consequences and verifications of the underpinning theory in order to provide students with a solid foundation in this key area. Based on the professor’s 25+ years of experience teaching physics students at every level Covers key topics in special relativity, including some group theory, as well as an introduction to general relativity and basic differential geometry Contains numerous worked examples and "Guides to the Literature" throughout the text

### The General Theory of Relativity

- Author : Farook Rahaman
- Publisher : Cambridge University Press
- Release Date : 2021-09-30
- Total pages : 427
- ISBN : 9781108837996
- File Size : 51,6 Mb
- Total Download : 853
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Discusses the general theory of relativity, Lie derivatives, rotating black holes, with a focus on basics of cosmology and astrophysics.

### The Physical and Mathematical Foundations of the Theory of Relativity

- Author : Antonio Romano,Mario Mango Furnari
- Publisher : Birkhäuser
- Release Date : 2019-10-07
- Total pages : 496
- ISBN : 3030272362
- File Size : 41,8 Mb
- Total Download : 542
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Download The Physical and Mathematical Foundations of the Theory of Relativity in PDF, Epub, and Kindle

This unique textbook offers a mathematically rigorous presentation of the theory of relativity, emphasizing the need for a critical analysis of the foundations of general relativity in order to best study the theory and its implications. The transitions from classical mechanics to special relativity and then to general relativity are explored in detail as well, helping readers to gain a more profound and nuanced understanding of the theory as a whole. After reviewing the fundamentals of differential geometry and classical mechanics, the text introduces special relativity, first using the physical approach proposed by Einstein and then via Minkowski’s mathematical model. The authors then address the relativistic thermodynamics of continua and electromagnetic fields in matter – topics which are normally covered only very briefly in other treatments – in the next two chapters. The text then turns to a discussion of general relativity by means of the authors’ unique critical approach, underlining the difficulty of recognizing the physical meaning of some statements, such as the physical meaning of coordinates and the derivation of physical quantities from those of space-time. Chapters in this section cover the model of space-time proposed by Schwarzschild; black holes; the Friedman equations and the different cosmological models they describe; and the Fermi-Walker derivative. Well-suited for graduate students in physics and mathematics who have a strong foundation in real analysis, classical mechanics, and general physics, this textbook is appropriate for a variety of graduate-level courses that cover topics in relativity. Additionally, it will interest physicists and other researchers who wish to further study the subtleties of these theories and understand the contemporary scholarly discussions surrounding them.

### Einstein's Theory of Special Relativity

- Author : George Trimble
- Publisher : Unknown
- Release Date : 2015-06-20
- Total pages : 160
- ISBN : 1514285630
- File Size : 11,8 Mb
- Total Download : 261
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Download Einstein's Theory of Special Relativity in PDF, Epub, and Kindle

RelativitySimple, Shocking, WorthwhileThe mathematics is SIMPLE. Only high school algebra is used. It is the concepts that are difficult to grasp because they require you to set aside commonly held notions about reality and accept truths that are profoundly counterintuitive. Special Relativity is shocking. From simple premises come mind-bending corollaries that excite the imagination. Ideas like time travel, length contraction, time dilation, and the twin paradox are all easily understood with an understanding of Einstein's great theorem.While conceptually challenging, it is worth the effort! Dr. Trimble will make Einstein's theory of special relativity entertaining, engaging and attainable. Plan for some enjoyable afternoons of fun and learning.

### Special Relativity

- Author : Michael Tsamparlis
- Publisher : Springer Science & Business Media
- Release Date : 2010-05-17
- Total pages : 595
- ISBN : 9783642038372
- File Size : 27,6 Mb
- Total Download : 880
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Download Special Relativity in PDF, Epub, and Kindle

Writing a new book on the classic subject of Special Relativity, on which numerous important physicists have contributed and many books have already been written, can be like adding another epicycle to the Ptolemaic cosmology. Furthermore, it is our belief that if a book has no new elements, but simply repeats what is written in the existing literature, perhaps with a different style, then this is not enough to justify its publication. However, after having spent a number of years, both in class and research with relativity, I have come to the conclusion that there exists a place for a new book. Since it appears that somewhere along the way, mathem- ics may have obscured and prevailed to the degree that we tend to teach relativity (and I believe, theoretical physics) simply using “heavier” mathematics without the inspiration and the mastery of the classic physicists of the last century. Moreover current trends encourage the application of techniques in producing quick results and not tedious conceptual approaches resulting in long-lasting reasoning. On the other hand, physics cannot be done a ́ la carte stripped from philosophy, or, to put it in a simple but dramatic context A building is not an accumulation of stones! As a result of the above, a major aim in the writing of this book has been the distinction between the mathematics of Minkowski space and the physics of r- ativity.

### Elementary Approach to Special Relativity

- Author : Helmut Günther
- Publisher : Springer Nature
- Release Date : 2020-05-16
- Total pages : 362
- ISBN : 9789811531682
- File Size : 39,8 Mb
- Total Download : 531
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Download Elementary Approach to Special Relativity in PDF, Epub, and Kindle

This book presents an alternative representation of Einstein's Special Theory of Relativity, which makes Special Relativity much more comprehensible. Moreover, one will come across a fundamental relationship between the Special Theory of Relativity and the mechanics of space lattice. In all previous formulations, the Einsteinian special principle of relativity, in one or the other form is used as the starting point for Special Relativity. In correspondence to this principle, one takes it as granted apriori, that all observers independent of their uniform motion to each other measure one and the same propagation velocity of a light signal. This book is thought of as a lecture for physicists, mathematicians and computer scientists and concentrates on the students of these fields. The book should reach a broad circle of interested readers from the fields of natural sciences and philosophy and provide and invigorating experience for engineers.

### The Physical and Mathematical Foundations of the Theory of Relativity

- Author : Antonio Romano,Mario Mango Furnari
- Publisher : Springer Nature
- Release Date : 2019-09-25
- Total pages : 496
- ISBN : 9783030272371
- File Size : 39,9 Mb
- Total Download : 463
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Download The Physical and Mathematical Foundations of the Theory of Relativity in PDF, Epub, and Kindle

This unique textbook offers a mathematically rigorous presentation of the theory of relativity, emphasizing the need for a critical analysis of the foundations of general relativity in order to best study the theory and its implications. The transitions from classical mechanics to special relativity and then to general relativity are explored in detail as well, helping readers to gain a more profound and nuanced understanding of the theory as a whole. After reviewing the fundamentals of differential geometry and classical mechanics, the text introduces special relativity, first using the physical approach proposed by Einstein and then via Minkowski’s mathematical model. The authors then address the relativistic thermodynamics of continua and electromagnetic fields in matter – topics which are normally covered only very briefly in other treatments – in the next two chapters. The text then turns to a discussion of general relativity by means of the authors’ unique critical approach, underlining the difficulty of recognizing the physical meaning of some statements, such as the physical meaning of coordinates and the derivation of physical quantities from those of space-time. Chapters in this section cover the model of space-time proposed by Schwarzschild; black holes; the Friedman equations and the different cosmological models they describe; and the Fermi-Walker derivative. Well-suited for graduate students in physics and mathematics who have a strong foundation in real analysis, classical mechanics, and general physics, this textbook is appropriate for a variety of graduate-level courses that cover topics in relativity. Additionally, it will interest physicists and other researchers who wish to further study the subtleties of these theories and understand the contemporary scholarly discussions surrounding them.

### A Mathematical Journey to Relativity

- Author : Wladimir-Georges Boskoff,Salvatore Capozziello
- Publisher : Springer Nature
- Release Date : 2020-06-01
- Total pages : 397
- ISBN : 9783030478940
- File Size : 44,7 Mb
- Total Download : 836
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Download A Mathematical Journey to Relativity in PDF, Epub, and Kindle

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.

### The Geometry of Special Relativity

- Author : Tevian Dray
- Publisher : CRC Press
- Release Date : 2021-06-15
- Total pages : 167
- ISBN : 9781351663205
- File Size : 18,8 Mb
- Total Download : 263
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Download The Geometry of Special Relativity in PDF, Epub, and Kindle

This unique book presents a particularly beautiful way of looking at special relativity. The author encourages students to see beyond the formulas to the deeper structure. The unification of space and time introduced by Einstein’s special theory of relativity is one of the cornerstones of the modern scientific description of the universe. Yet the unification is counterintuitive because we perceive time very differently from space. Even in relativity, time is not just another dimension, it is one with different properties The book treats the geometry of hyperbolas as the key to understanding special relativity. The author simplifies the formulas and emphasizes their geometric content. Many important relations, including the famous relativistic addition formula for velocities, then follow directly from the appropriate (hyperbolic) trigonometric addition formulas. Prior mastery of (ordinary) trigonometry is sufficient for most of the material presented, although occasional use is made of elementary differential calculus, and the chapter on electromagnetism assumes some more advanced knowledge. Changes to the Second Edition The treatment of Minkowski space and spacetime diagrams has been expanded. Several new topics have been added, including a geometric derivation of Lorentz transformations, a discussion of three-dimensional spacetime diagrams, and a brief geometric description of "area" and how it can be used to measure time and distance. Minor notational changes were made to avoid conflict with existing usage in the literature. Table of Contents Preface 1. Introduction. 2. The Physics of Special Relativity. 3. Circle Geometry. 4. Hyperbola Geometry. 5. The Geometry of Special Relativity. 6. Applications. 7. Problems III. 8. Paradoxes. 9. Relativistic Mechanics. 10. Problems II. 11. Relativistic Electromagnetism. 12. Problems III. 13. Beyond Special Relativity. 14. Three-Dimensional Spacetime Diagrams. 15. Minkowski Area via Light Boxes. 16. Hyperbolic Geometry. 17. Calculus. Bibliography. Author Biography Tevian Dray is a Professor of Mathematics at Oregon State University. His research lies at the interface between mathematics and physics, involving differential geometry and general relativity, as well as nonassociative algebra and particle physics; he also studies student understanding of "middle-division" mathematics and physics content. Educated at MIT and Berkeley, he held postdoctoral positions in both mathematics and physics in several countries prior to coming to OSU in 1988. Professor Dray is a Fellow of the American Physical Society for his work in relativity, and an award-winning teacher.

### FUNDAMENTALS OF SPECIAL AND GENERAL RELATIVITY, Revised Edition

- Author : KRORI, K. D.
- Publisher : PHI Learning Pvt. Ltd.
- Release Date : 2023
- Total pages : 332
- ISBN : 9789388028684
- File Size : 23,7 Mb
- Total Download : 735
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Download FUNDAMENTALS OF SPECIAL AND GENERAL RELATIVITY, Revised Edition in PDF, Epub, and Kindle

Relativity, apart from quantum mechanics, is the greatest wonder in science, unfolded single-handedly in the 20th century by Albert Einstein. The scientist developed general relativity as a logical sequel to special relativity. This comprehensive book presents explication of the conceptual evolution and mathematical derivations of the theories of special and general relativity. The book follows an Einsteinian approach while explaining the concepts and the theories of relativity. Divided into 14 chapters, the revised edition of the book covers elementary concepts of Special relativity, as well as the advanced studies on General relativity. The recent theories like Kerr geometry, Sagnac effect, Vaidya geometry, Raychaudhuri equation and Gravitation physics vis-à-vis Quantum physics are presented in easy-to-understand language and simple style. In addition to it, the book gives an in-depth analysis on the applications of advanced theories like Vaidya-Krori-Barua solution from author’s own research works. Apart from that, the book also discusses some of the isotropic and anisotropic cosmological models, in detail. The salient topics discussed in the revised edition of the book are extrinsic curvature, detection of gravitational waves, early universe, evolution of a dead star into a white dwarf or a neutron star or a black hole, dark matter and dark energy. This book is intended for the undergraduate and postgraduate students of Physics and Mathematics. KEY FEATURES • Step-by-step derivation of equations • Easy demagogic approach • Review questions to widen the analytical understanding of the students

### Geometry: from Isometries to Special Relativity

- Author : Nam-Hoon Lee
- Publisher : Springer Nature
- Release Date : 2020-04-28
- Total pages : 258
- ISBN : 9783030421014
- File Size : 12,9 Mb
- Total Download : 841
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This textbook offers a geometric perspective on special relativity, bridging Euclidean space, hyperbolic space, and Einstein’s spacetime in one accessible, self-contained volume. Using tools tailored to undergraduates, the author explores Euclidean and non-Euclidean geometries, gradually building from intuitive to abstract spaces. By the end, readers will have encountered a range of topics, from isometries to the Lorentz–Minkowski plane, building an understanding of how geometry can be used to model special relativity. Beginning with intuitive spaces, such as the Euclidean plane and the sphere, a structure theorem for isometries is introduced that serves as a foundation for increasingly sophisticated topics, such as the hyperbolic plane and the Lorentz–Minkowski plane. By gradually introducing tools throughout, the author offers readers an accessible pathway to visualizing increasingly abstract geometric concepts. Numerous exercises are also included with selected solutions provided. Geometry: from Isometries to Special Relativity offers a unique approach to non-Euclidean geometries, culminating in a mathematical model for special relativity. The focus on isometries offers undergraduates an accessible progression from the intuitive to abstract; instructors will appreciate the complete instructor solutions manual available online. A background in elementary calculus is assumed.

### Relativity: The Special and General Theory

- Author : Albert Einstein
- Publisher : DigiCat
- Release Date : 2022-05-28
- Total pages : 113
- ISBN : EAN:8596547022763
- File Size : 49,8 Mb
- Total Download : 288
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Relativity: The Special and General Theory is a book by physicist and writer Albert Einstein. It provides an insight into the theory of relativity to those readers who are not familiar with the mathematical mechanisms of theoretical physics, but still exhibit an interest at the subject.

### The Mathematical Theory of Relativity

- Author : A S Eddington
- Publisher : Unknown
- Release Date : 2019-12-02
- Total pages : 440
- ISBN : 1670853136
- File Size : 11,6 Mb
- Total Download : 225
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PDF book entitled The Mathematical Theory of Relativity written by A S Eddington and published by Unknown which was released on 2019-12-02 with total hardcover pages 440, the book become popular and critical acclaim.

### Special Relativity and Classical Field Theory

- Author : Leonard Susskind,Art Friedman
- Publisher : Basic Books
- Release Date : 2017-09-26
- Total pages : 448
- ISBN : 9780465093359
- File Size : 40,9 Mb
- Total Download : 878
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Download Special Relativity and Classical Field Theory in PDF, Epub, and Kindle

The third volume in the bestselling physics series cracks open Einstein's special relativity and field theory Physicist Leonard Susskind and data engineer Art Friedman are back. This time, they introduce readers to Einstein's special relativity and Maxwell's classical field theory. Using their typical brand of real math, enlightening drawings, and humor, Susskind and Friedman walk us through the complexities of waves, forces, and particles by exploring special relativity and electromagnetism. It's a must-read for both devotees of the series and any armchair physicist who wants to improve their knowledge of physics' deepest truths.

### Special Relativity

- Author : Sadri Hassani
- Publisher : Elsevier
- Release Date : 2017-05-09
- Total pages : 380
- ISBN : 9780128104248
- File Size : 41,8 Mb
- Total Download : 509
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Special Relativity: A Heuristic Approach provides a qualitative exposition of relativity theory on the basis of the constancy of the speed of light. Using Einstein's signal velocity as the defining idea for the notion of simultaneity and the fact that the speed of light is independent of the motion of its source, chapters delve into a qualitative exposition of the relativity of time and length, discuss the time dilation formula using the standard light clock, explore the Minkowski four-dimensional space-time distance based on how the time dilation formula is derived, and define the components of the two-dimensional space-time velocity, amongst other topics. Provides a heuristic derivation of the Minkowski distance formula Uses relativistic photography to see Lorentz transformation and vector algebra manipulation in action Includes worked examples to elucidate and complement the topic being discussed Written in a very accessible style

### The Geometry of Minkowski Spacetime

- Author : Gregory L. Naber
- Publisher : Courier Corporation
- Release Date : 2003-01-01
- Total pages : 276
- ISBN : 0486432351
- File Size : 37,5 Mb
- Total Download : 756
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Download The Geometry of Minkowski Spacetime in PDF, Epub, and Kindle

This mathematically rigorous treatment examines Zeeman's characterization of the causal automorphisms of Minkowski spacetime and the Penrose theorem concerning the apparent shape of a relativistically moving sphere. Other topics include the construction of a geometric theory of the electromagnetic field; an in-depth introduction to the theory of spinors; and a classification of electromagnetic fields in both tensor and spinor form. Appendixes introduce a topology for Minkowski spacetime and discuss Dirac's famous "Scissors Problem." Appropriate for graduate-level courses, this text presumes only a knowledge of linear algebra and elementary point-set topology. 1992 edition. 43 figures.

### Very Special Relativity

- Author : Sander Bais
- Publisher : Harvard University Press
- Release Date : 2007
- Total pages : 128
- ISBN : 067402611X
- File Size : 52,5 Mb
- Total Download : 979
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Download Very Special Relativity in PDF, Epub, and Kindle

Einstein's Special Theory of Relativity, first published in 1905, radically changed our understanding of the world. Familiar notions of space and time and energy were turned on their head, and our struggle with Einstein's counterintuitive explanation of these concepts was under way. The task is no easier today than it was a hundred years ago, but in this book Sander Bais has found an original and uniquely effective way to convey the fundamental ideas of Einstein's Special Theory. Bais's previous book, The Equations, was widely read and roundly praised for its clear and commonsense explanation of the math in physics. Very Special Relativity brings the same accessible approach to Einstein's theory. Using a series of easy-to-follow diagrams and employing only elementary high school geometry, Bais conducts readers through the quirks and quandaries of such fundamental concepts as simultaneity, causality, and time dilation. The diagrams also illustrate the difference between the Newtonian view, in which time was universal, and the Einsteinian, in which the speed of light is universal. Following Bais's straightforward sequence of simple, commonsense arguments, readers can tinker with the theory and its great paradoxes and, finally, arrive at a truly deep understanding of Einstein's interpretation of space and time. An intellectual journey into the heart of the Special Theory, the book offers an intimate look at the terms and ideas that define our reality.

### The Geometry of Special Relativity

- Author : Tevian Dray
- Publisher : CRC Press
- Release Date : 2012-07-02
- Total pages : 151
- ISBN : 9781466510470
- File Size : 40,7 Mb
- Total Download : 906
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Download The Geometry of Special Relativity in PDF, Epub, and Kindle

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.

### Second Year Calculus

- Author : David M. Bressoud
- Publisher : Springer Science & Business Media
- Release Date : 2012-12-06
- Total pages : 404
- ISBN : 9781461209591
- File Size : 14,9 Mb
- Total Download : 980
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Download Second Year Calculus in PDF, Epub, and Kindle

Second Year Calculus: From Celestial Mechanics to Special Relativity covers multi-variable and vector calculus, emphasizing the historical physical problems which gave rise to the concepts of calculus. The book guides us from the birth of the mechanized view of the world in Isaac Newton's Mathematical Principles of Natural Philosophy in which mathematics becomes the ultimate tool for modelling physical reality, to the dawn of a radically new and often counter-intuitive age in Albert Einstein's Special Theory of Relativity in which it is the mathematical model which suggests new aspects of that reality. The development of this process is discussed from the modern viewpoint of differential forms. Using this concept, the student learns to compute orbits and rocket trajectories, model flows and force fields, and derive the laws of electricity and magnetism. These exercises and observations of mathematical symmetry enable the student to better understand the interaction of physics and mathematics.

### General Relativity

- Author : Robert M. Wald
- Publisher : University of Chicago Press
- Release Date : 2010-05-15
- Total pages : 506
- ISBN : 0226870375
- File Size : 24,5 Mb
- Total Download : 499
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"Wald's book is clearly the first textbook on general relativity with a totally modern point of view; and it succeeds very well where others are only partially successful. The book includes full discussions of many problems of current interest which are not treated in any extant book, and all these matters are considered with perception and understanding."—S. Chandrasekhar "A tour de force: lucid, straightforward, mathematically rigorous, exacting in the analysis of the theory in its physical aspect."—L. P. Hughston, Times Higher Education Supplement "Truly excellent. . . . A sophisticated text of manageable size that will probably be read by every student of relativity, astrophysics, and field theory for years to come."—James W. York, Physics Today