July 2014 - a new updated edition of this book is now available globally from Amazon and other retailers. Reader reviews (1) "Fantastic book ... very easy to follow and leads you gradually and gently to the full mathematical detail of general relativity." (2) "Highly recommended for anyone willing to invest some time and effort." - Amazon.com (1) " ... do not be put off by the title! This is a great book on relativity which nicely bridges the gap between those books catering for readers who know little or nothing about relativity and those texts intended for physics mathematical specialists." (2) "A new gold standard for physics books." (3) "A unique book. Well done the author." - Amazon.co.uk Synopsis Based on the concept of four-dimensional spacetime - curved in the vicinity of mass-energy, flat in its absence - Einstein's theories of special and general relativity together form a cornerstone of modern physics. Special relativity has some strangely counter-intuitive consequences, including time dilation, length contraction, the relativity of simultaneity and mass-energy equivalence, whilst general relativity is at the heart of our understanding of black holes and the evolution of the universe. Using straightforward, accessible language, with numerous fully solved problems and clear derivations and explanations, this book is aimed at the enthusiastic general reader who wants to move beyond maths-lite popularisations and tackle the essential mathematics of this fascinating theory. (To paraphrase Euclid, there is no royal road to relativity - you have to do the mathematics.) For those with minimal mathematical background, the first chapter provides a crash course in foundation mathematics. The reader is then taken gently by the hand and guided through a wide range of fundamental topics, including Newtonian mechanics; the Lorentz transformations; tensor calculus; the Einstein field equations; the Schwarzschild solution; the four classical tests of general relativity; simple black holes; the mysteries of dark energy and the cosmological constant; and the Friedmann equations and Friedmann-Robertson-Walker cosmological models. Understand even the basics of Einstein's amazing theory and the world will never seem the same again. Contents Preface Introduction 1 Foundation mathematics 2 Newtonian mechanics 3 Special relativity 4 Introducing the manifold 5 Scalars, vectors, one-forms and tensors 6 More on curvature 7 General relativity 8 The Newtonian limit 9 The Schwarzschild metric 10 Schwarzschild black holes 11 Cosmology Bibliography Appendix - Planetary motion data Acknowledgements

A Most Incomprehensible Thing: Notes Towards a Very Gentle Introduction to the Mathematics of Relativity

Science & Math

Peter Collier

Physics

Incomprehensible Books

Teach yourself the mathematics of relativity – THE AMAZON BESTSELLER To really understand Einstein's theory of relativity – one of the cornerstones of modern physics – you have to get to grips with the underlying mathematics. A Most Incomprehensible Thing is aimed at the general reader who is motivated to tackle that not insignificant challenge. With a user-friendly style, clear step-by-step mathematical derivations, many fully solved problems and numerous diagrams, this self-study guide provides an accessible introduction to a fascinating but complex subject. For those with minimal mathematical background, the first chapter gives a crash course in foundation mathematics. The reader is then taken gently by the hand and guided through a wide range of fundamental topics, including Newtonian mechanics; the Lorentz transformations; the all important metric tensor gμν; tensor calculus; the Einstein field equations; the Schwarzschild solution (which gives a good approximation of the spacetime of our Solar System); black holes, relativistic cosmology and gravitational waves.<ul>
<li>
Special relativity helps explain a huge range of non-gravitational physical phenomena and has some strangely counter-intuitive consequences. These include time dilation, length contraction, the relativity of simultaneity, mass-energy equivalence and an absolute speed limit.</li> <li>
General relativity, the leading theory of gravity, is at the heart of our understanding of cosmology and black holes. Summed up in the words of eminent theoretical physicist John Archibald Wheeler: “Matter tells space how to curve. Space tells matter how to move.”</li>
</ul>“I must observe that the theory of relativity resembles a building consisting of two separate stories, the special theory and the general theory. The special theory, on which the general theory rests, applies to all physical phenomena with the exception of gravitation; the general theory provides the law of gravitation and its relations to the other forces of nature.” – Albert Einstein, 1919 Understand even the basics of Einstein's amazing theory and the world will never seem the same again. Contents Preface Introduction 1 Foundation mathematics 2 Newtonian mechanics 3 Special relativity 4 Introducing the manifold 5 Scalars, vectors, one-forms and tensors 6 More on curvature 7 General relativity 8 The Newtonian limit 9 The Schwarzschild metric 10 Schwarzschild black holes 11 Cosmology 12 Gravitational waves Appendix: The Riemann curvature tensor Bibliography Acknowledgements January 2019 – this revised printing includes new Chapter 11 (cosmology) sections on a scale factor and a spacetime diagram for our universe.

COLLIER, Peter

Astronomy & Space Science

Differential forms eat tangent vectors, spit out numbers and do this in an alternating multilinear fashion. These properties make differential forms an essential tool for doing calculus on manifolds and thus of great interest to mathematicians and physicists. This book is aimed at the general reader who is interested in tackling a relaxed but wide-ranging introduction to this fascinating subject. The only prerequisite is a reasonable foundation in advanced, school-level mathematics. The text includes numerous worked problems. Topics covered include: An introduction to basic concepts. How differential forms eat tangent vectors and spit out numbers. Manipulating differential forms, including the wedge product, differentiation and integration. How differential forms provide an alternative means of understanding three-dimensional vector calculus. The generalised Stoke's theorem, which applies to manifolds of any dimension. Maxwell's equations in the language of differential forms. Using differential forms to prove three nice topological theorems, including the famous hairy ball theorem.

A Beginner's Guide to Differential Forms

Mathematics

This book is aimed at the general reader who wishes to understand the mathematics behind a range of interesting astronomical calculations that relate to the motion and position of celestial bodies. The calculations are structured around 29 freely downloadable Excel spreadsheets. Using the spreadsheets, the reader can determine a planet's position, the Sun's rising and setting times, the Moon's phase, and much more. No prior astronomical knowledge is required, though you will need a background in secondary/high school mathematics. Because the emphasis is on understanding the underlying mathematics, easy to follow derivations of most of the astronomical equations used in the book are included. Topics covered include: The celestial sphere. The different ways astronomers have of measuring time. Astronomical coordinate systems. Rising and setting times. Elliptical orbits. Predicting the position of the planets and periodic comets. Calculating times of sunrise and sunset for any location on Earth. The equation of time. The Moon's orbit and phases. Numerical integration of a celestial object's equations of motion. Understanding and deriving the astronomical equations used in the calculations. By the author of A Most Incomprehensible Thing: Notes Towards a Very Gentle Introduction to the Mathematics of Relativity (ISBN 9780957389465) and A Beginner’s Guide to Differential Forms (ISBN 9780957389472).

Movement of the Spheres: Basic Astronomical Calculations Explained With 29 Spreadsheets

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Books by Incomprehensible Books

See the best price to sell, buy or rent books by the Incomprehensible Books publisher. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

A Most Incomprehensible Thing: Notes Towards a Very Gentle Introduction to the Mathematics of Relativity

A Most Incomprehensible Thing: Notes Towards a Very Gentle Introduction to the Mathematics of Relativity

A Beginner's Guide to Differential Forms

Movement of the Spheres: Basic Astronomical Calculations Explained With 29 Spreadsheets