Einstein's Theory

A Rigorous Introduction for the Mathematically Untrained

Author: Øyvind Grøn,Arne Næss

Publisher: Springer Science & Business Media

ISBN: 9781461407065

Category: Science

Page: 341

View: 9407


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.

Einstein's General Theory of Relativity

With Modern Applications in Cosmology

Author: Øyvind Grøn,Sigbjorn Hervik

Publisher: Springer Science & Business Media

ISBN: 0387692002

Category: Science

Page: 538

View: 7904


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.

Relativity Made Relatively Easy

Author: Andrew M. Steane

Publisher: Oxford University Press

ISBN: 0199662851

Category: Science

Page: 419

View: 2556


This book unfolds the subject of Relativity for undergraduate students of physics. It is intended to allow an undergraduate physics course to extend somewhat further and wider in this area than has traditionally been the case, while ensuring that the mainstream of students can handle the material. Introducing Lorentz invariants and four-vectors early on, but postponing tensor notation till it is needed, the aim is to make manageable what would otherwise beregarded as hard; to make derivations as simple as possible and physical ideas as transparent as possible.

Introduction to Tensor Analysis and the Calculus of Moving Surfaces

Author: Pavel Grinfeld

Publisher: Springer Science & Business Media

ISBN: 1461478677

Category: Mathematics

Page: 302

View: 6557


This textbook is distinguished from other texts on the subject by the depth of the presentation and the discussion of the calculus of moving surfaces, which is an extension of tensor calculus to deforming manifolds. Designed for advanced undergraduate and graduate students, this text invites its audience to take a fresh look at previously learned material through the prism of tensor calculus. Once the framework is mastered, the student is introduced to new material which includes differential geometry on manifolds, shape optimization, boundary perturbation and dynamic fluid film equations. The language of tensors, originally championed by Einstein, is as fundamental as the languages of calculus and linear algebra and is one that every technical scientist ought to speak. The tensor technique, invented at the turn of the 20th century, is now considered classical. Yet, as the author shows, it remains remarkably vital and relevant. The author’s skilled lecturing capabilities are evident by the inclusion of insightful examples and a plethora of exercises. A great deal of material is devoted to the geometric fundamentals, the mechanics of change of variables, the proper use of the tensor notation and the discussion of the interplay between algebra and geometry. The early chapters have many words and few equations. The definition of a tensor comes only in Chapter 6 – when the reader is ready for it. While this text maintains a consistent level of rigor, it takes great care to avoid formalizing the subject. The last part of the textbook is devoted to the Calculus of Moving Surfaces. It is the first textbook exposition of this important technique and is one of the gems of this text. A number of exciting applications of the calculus are presented including shape optimization, boundary perturbation of boundary value problems and dynamic fluid film equations developed by the author in recent years. Furthermore, the moving surfaces framework is used to offer new derivations of classical results such as the geodesic equation and the celebrated Gauss-Bonnet theorem.

Relativity for the Questioning Mind

Author: Daniel F. Styer

Publisher: JHU Press

ISBN: 1421401258

Category: Science

Page: 200

View: 6587


The appendixes provide helpful hints, basic answers to the sample problems, and materials to stimulate further exploration.

Inside Interesting Integrals

A Collection of Sneaky Tricks, Sly Substitutions, and Numerous Other Stupendously Clever, Awesomely Wicked, and Devilishly Seductive Maneuvers for Computing Nearly 200 Perplexing Definite Integrals From Physics, Engineering, and Mathematics (Plus 60 Challenge Problems with Complete, Detailed Solutions)

Author: Paul J. Nahin

Publisher: Springer

ISBN: 1493912771

Category: Science

Page: 412

View: 5874


What’s the point of calculating definite integrals since you can’t possibly do them all?. What makes doing the specific integrals in this book of value aren’t the specific answers we’ll obtain, but rather the methods we’ll use in obtaining those answers; methods you can use for evaluating the integrals you will encounter in the future. This book is written in a light-hearted manner for students who have completed the first year of college or high school AP calculus and have just a bit of exposure to the concept of a differential equation. Every result is fully derived. If you are fascinated by definite integrals, then this is a book for you.

General Relativity

Author: Robert M. Wald

Publisher: University of Chicago Press

ISBN: 9780226870373

Category: Science

Page: 506

View: 7565


"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

Quantum Mechanics

Author: Eugene D. Commins

Publisher: Cambridge University Press

ISBN: 110706399X

Category: Science

Page: 720

View: 2163


A self-contained introduction for advanced students in physics who want to acquire serious knowledge and understanding of quantum mechanics.

The Great Equations: Breakthroughs in Science from Pythagoras to Heisenberg

Author: Robert P. Crease

Publisher: W. W. Norton & Company

ISBN: 0393337936

Category: Mathematics

Page: 320

View: 5373


Shares behind-the-scenes stories for ten of the most significant equations in human history, covering a range of topics, from Feynman's statement about Maxwell's pivotal electromagnetic equations and the influence of Newton's law of gravitation to the reason Euler's formula has been called "God's equation" and Heisenberg's uncertainty principle. 20,000 first printing.

The Survival of a Mathematician

From Tenure-track to Emeritus

Author: Steven George Krantz

Publisher: American Mathematical Soc.

ISBN: 0821846299

Category: Mathematics

Page: 310

View: 4285


"One of the themes of the book is how to have a fulfilling professional life. In order to achieve this goal, Krantz discusses keeping a vigorous scholarly program going and finding new challenges, as well as dealing with the everyday tasks of research, teaching, and administration." "In short, this is a survival manual for the professional mathematician - both in academics and in industry and government agencies. It is a sequel to the author's A Mathematician's Survival Guide."--BOOK JACKET.

Skin in the Game

Hidden Asymmetries in Daily Life

Author: Nassim Nicholas Taleb

Publisher: N.A

ISBN: 042528462X


Page: 304

View: 4398


The phrase "skin in the game" means that you do not pay attention to what people say, only to what they do, and to how much of their necks they are putting on the line. This willingness to accept one's own risks is an essential attribute of people in all walks of life. Taleb challenges long-held beliefs about those who control our military, finances, religions, and so much more-- and shows how "skin in the game" applies to all aspects of our lives.


Author: Steven Weinberg

Publisher: Oxford University Press

ISBN: 0198526822

Category: Nature

Page: 593

View: 1494


This is a uniquely comprehensive and detailed treatment of the theoretical and observational foundations of modern cosmology, by a Nobel Laureate in Physics. It gives up-to-date and self contained accounts of the theories and observations that have made the past few decades a golden age of cosmology.

The Landscape of Theoretical Physics: A Global View

From Point Particles to the Brane World and Beyond in Search of a Unifying Principle

Author: M. Pavsic

Publisher: Springer Science & Business Media

ISBN: 0306471361

Category: Science

Page: 374

View: 5294


Today many important directions of research are being pursued more or less independently of each other. These are, for instance, strings and mem branes, induced gravity, embedding of spacetime into a higher dimensional space, the brane world scenario, the quantum theory in curved spaces, Fock Schwinger proper time formalism, parametrized relativistic quantum the ory, quantum gravity, wormholes and the problem of “time machines”, spin and supersymmetry, geometric calculus based on Clifford algebra, various interpretations of quantum mechanics including the Everett interpretation, and the recent important approach known as “decoherence”. A big problem, as I see it, is that various people thoroughly investigate their narrow field without being aware of certain very close relations to other fields of research. What we need now is not only to see the trees but also the forest. In the present book I intend to do just that: to carry out a first approximation to a synthesis of the related fundamental theories of physics. I sincerely hope that such a book will be useful to physicists. From a certain viewpoint the book could be considered as a course in the oretical physics in which the foundations of all those relevant fundamental theories and concepts are attempted to be thoroughly reviewed. Unsolved problems and paradoxes are pointed out. I show that most of those ap proaches have a common basis in the theory of unconstrained membranes. The very interesting and important concept of membrane space, the tensor calculus in and functional transformations in are discussed.

Wholeness and the Implicate Order

Author: David Bohm

Publisher: Routledge

ISBN: 1134438729

Category: Philosophy

Page: 304

View: 5782


David Bohm was one of the foremost scientific thinkers and philosophers of our time. Although deeply influenced by Einstein, he was also, more unusually for a scientist, inspired by mysticism. Indeed, in the 1970s and 1980s he made contact with both J. Krishnamurti and the Dalai Lama whose teachings helped shape his work. In both science and philosophy, Bohm's main concern was with understanding the nature of reality in general and of consciousness in particular. In this classic work he develops a theory of quantum physics which treats the totality of existence as an unbroken whole. Writing clearly and without technical jargon, he makes complex ideas accessible to anyone interested in the nature of reality.

Teaching As a Subversive Activity

A No-Holds-Barred Assault on Outdated Teaching Methods-with Dramatic and Practical Proposals on How Education Can Be Made Relevant to Today's World

Author: Neil Postman

Publisher: Delta

ISBN: 0307491706

Category: Education

Page: 240

View: 6038


A no-holds-barred assault on outdated teaching methods--with dramatic and practical proposals on how education can be made relevant to today's world. From the Trade Paperback edition.


The Loss of Certainty

Author: Morris Kline

Publisher: Oxford University Press, USA

ISBN: 9780195030853

Category: Mathematics

Page: 366

View: 1699


Refuting the accepted belief that mathematics is exact and infallible, the author examines the development of conflicting concepts of mathematics and their implications for the physical, applied, social, and computer sciences


Improving Decisions About Health, Wealth, and Happiness

Author: Richard H. Thaler,Cass R. Sunstein

Publisher: Penguin

ISBN: 1101655097

Category: Business & Economics

Page: 320

View: 2416


From the winner of the 2017 Nobel Prize in Economics, Richard H. Thaler, and Cass R. Sunstein: a revelatory look at how we make decisions—for fans of Malcolm Gladwell’s Blink and Daniel Kahneman’s Thinking Fast and Slow New York Times bestseller Named a Best Book of the Year by The Economist and the Financial Times Every day we make choices—about what to buy or eat, about financial investments or our children’s health and education, even about the causes we champion or the planet itself. Unfortunately, we often choose poorly. Nudge is about how we make these choices and how we can make better ones. Using dozens of eye-opening examples and drawing on decades of behavioral science research, Nobel Prize winner Richard H. Thaler and Harvard Law School professor Cass R. Sunstein show that no choice is ever presented to us in a neutral way, and that we are all susceptible to biases that can lead us to make bad decisions. But by knowing how people think, we can use sensible “choice architecture” to nudge people toward the best decisions for ourselves, our families, and our society, without restricting our freedom of choice. More than 750,000 copies sold

Revolutions in Twentieth-Century Physics

Author: David J. Griffiths

Publisher: Cambridge University Press

ISBN: 1107602173

Category: Science

Page: 182

View: 4670


"The conceptual changes brought by modern physics are important, radical and fascinating, yet they are only vaguely understood by people working outside the field. Exploring the four pillars of modern physics - relativity, quantum mechanics, elementary particles and cosmology - this clear and lively account will interest anyone who has wondered what Einstein, Bohr, Schrèodinger and Heisenberg were really talking about. The book discusses quarks and leptons, antiparticles and Feynman diagrams, curved space-time, the Big Bang and the expanding Universe. Suitable for undergraduate students in non-science as well as science subjects, it uses problems and worked examples to help readers develop an understanding of what recent advances in physics actually mean"--

The Economics Anti-Textbook

A Critical Thinker's Guide to Microeconomics

Author: Rod Hill,Professor Tony Myatt

Publisher: Zed Books Ltd.

ISBN: 1848138296

Category: Business & Economics

Page: 320

View: 5326


Mainstream textbooks present economics as an objective science free from value judgements; that settles disputes by testing hypotheses; that applies a pre-determined body of principles; and contains policy prescriptions supported by a consensus of professional opinion. The Economics Anti-Textbook argues that this is a myth - one which is not only dangerously misleading but also bland and boring. It challenges the mainstream textbooks' assumptions, arguments, models and evidence. It puts the controversy and excitement back into economics to reveal a fascinating and a vibrant field of study - one which is more an 'art of persuasion' than it is a science. The Economics Anti-Textbook's chapters parallel the major topics in the typical text, beginning with a boiled-down account of them before presenting an analysis and critique. Drawing on the work of leading economists, the Anti-Textbook lays bare the blind spots in the texts and their sins of omission and commission. It shows where hidden value judgements are made and when contrary evidence is ignored. It shows the claims made without any evidence and the alternative theories that aren't mentioned. It shows the importance of power, social context and legal framework. The Economics Anti-Textbook is the students' guide to decoding the textbooks and shows how real economics is much more interesting than most economists are willing to let on.

Quantum Mechanics

The Theoretical Minimum

Author: Leonard Susskind,Art Friedman

Publisher: Basic Books

ISBN: 0465036678

Category: Science

Page: 384

View: 2041


From the bestselling author of The Theoretical Minimum, a DIY introduction to the math and science of quantum physics First he taught you classical mechanics. Now, physicist Leonard Susskind has teamed up with data engineer Art Friedman to present the theory and associated mathematics of the strange world of quantum mechanics. In this follow-up to The Theoretical Minimum, Susskind and Friedman provide a lively introduction to this famously difficult field, which attempts to understand the behavior of sub-atomic objects through mathematical abstractions. Unlike other popularizations that shy away from quantum mechanics’ weirdness, Quantum Mechanics embraces the utter strangeness of quantum logic. The authors offer crystal-clear explanations of the principles of quantum states, uncertainty and time dependence, entanglement, and particle and wave states, among other topics, and each chapter includes exercises to ensure mastery of each area. Like The Theoretical Minimum, this volume runs parallel to Susskind’s eponymous Stanford University-hosted continuing education course. An approachable yet rigorous introduction to a famously difficult topic, Quantum Mechanics provides a tool kit for amateur scientists to learn physics at their own pace.