*A Rigorous Introduction for the Mathematically Untrained*

**Author**: Øyvind Grøn,Arne Næss

**Publisher:**Springer Science & Business Media

**ISBN:**9781461407065

**Category:**Science

**Page:**341

**View:**2479

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# Search Results for: einstein-s-theory-a-rigorous-introduction-for-the-mathematically-untrained

*A Rigorous Introduction for the Mathematically Untrained*

**Author**: Øyvind Grøn,Arne Næss

**Publisher:** Springer Science & Business Media

**ISBN:** 9781461407065

**Category:** Science

**Page:** 341

**View:** 2479

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.
*A Rigorous Introduction for the Mathematically Untrained*

**Author**: Oyvind Gron,Arne Naess

**Publisher:** Springer

**ISBN:** 9781489997326

**Category:** Science

**Page:** 341

**View:** 8743

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.
*A Rigorous Introduction for the Mathematically Untrained*

**Author**: Oyvind Gron,Arne Naess

**Publisher:** Springer

**ISBN:** 9781461407072

**Category:** Science

**Page:** 341

**View:** 1485

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.
*With Modern Applications in Cosmology*

**Author**: Øyvind Grøn,Sigbjorn Hervik

**Publisher:** Springer Science & Business Media

**ISBN:** 0387692002

**Category:** Science

**Page:** 538

**View:** 5818

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.
*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:** 5643

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.
*Life Without Special Relativity*

**Author**: Eric Baird

**Publisher:** Chocolate Tree Books

**ISBN:** 0955706807

**Category:** Science

**Page:** 378

**View:** 6811

Relativity theory has become one of the icons of Twentieth Century science. It's reckoned to be a difficult subject, taught as a layered series of increasingly difficult mathematics and increasingly abstract concepts. We're told that relativity theory is supposed to be this complicated and counter-intuitive. But how much of this historical complexity is really necessary? Can we bypass the interpretations and paradoxes and pseudoparadoxes of Einstein's special theory and jump directly to a deeper and more intuitive description of reality? What if curvature is a fundamental part of physics, and a final theory of relativity shouldn't reduce to Einstein's "flat" 1905 theory //on principle//? "Relativity..." takes us on a whistlestop tour of Twentieth Century physics - from black holes, quantum mechanics, wormholes and the Big Bang to the workings of the human mind, and asks: what would physics look like without special relativity? 394 printed pages, 234156 mm, ~200 figures and illustrations, includes bibliography and index www.relativitybook.com
*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:** 8606

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.

**Author**: Pavel Grinfeld

**Publisher:** Springer Science & Business Media

**ISBN:** 1461478677

**Category:** Mathematics

**Page:** 302

**View:** 4392

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.
*An Introduction*

**Author**: RichardL. Faber

**Publisher:** Routledge

**ISBN:** 1351455141

**Category:** Mathematics

**Page:** 272

**View:** 2217

Differentilil Geometry and Relativity Theory: An Introduction approaches relativity asa geometric theory of space and time in which gravity is a manifestation of space-timecurvature, rathe1 than a force. Uniting differential geometry and both special and generalrelativity in a single source, this easy-to-understand text opens the general theory of relativityto mathematics majors having a backgr.ound only in multivariable calculus and linearalgebra.The book offers a broad overview of the physical foundations and mathematical details ofrelativity, and presents concrete physical interpretations of numerous abstract concepts inRiemannian geometry. The work is profusely illustrated with diagrams aiding in the understandingof proofs and explanations. Appendices feature important material on vectoranalysis and hyperbolic functions.Differential Geometry and Relativity Theory: An Introduction serves as the ideal textfor high-level undergraduate couues in mathematics and physics, and includes a solutionsmanual augmenting classroom study. It is an invaluable reference for mathematicians interestedin differential and IUemannian geometry, or the special and general theories ofrelativity

**Author**: Robert P. Crease

**Publisher:** W. W. Norton & Company

**ISBN:** 0393337936

**Category:** Mathematics

**Page:** 320

**View:** 9701

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.
*An Overview of the New Physics*

**Author**: Gary Zukav

**Publisher:** Harper Collins

**ISBN:** 0061926388

**Category:** Science

**Page:** 416

**View:** 8450

“The most exciting intellectual adventure I've been on since reading Robert Pirsig’s Zen and the Art of Motorcycle Maintenance.” —Christopher Lehmann-Haupt, New York Times Gary Zukav’s timeless, humorous, New York Times bestselling masterpiece, The Dancing Wu Li Masters, is arguably the most widely acclaimed introduction to quantum physics ever written. Scientific American raves: “Zukav is such a skilled expositor, with such an amiable style, that it is hard to imagine a layman who would not find his book enjoyable and informative.” Accessible, edifying, and endlessly entertaining, The Dancing Wu Li Masters is back in a beautiful new edition—and the doors to the fascinating, dazzling, remarkable world of quantum physics are opened to all once again, no previous mathematical or technical expertise required.
*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:** 1466

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.

**Author**: David Bohm

**Publisher:** Routledge

**ISBN:** 1134438729

**Category:** Philosophy

**Page:** 304

**View:** 1255

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.

**Author**: Lewis Wolpert

**Publisher:** Harvard University Press

**ISBN:** 9780674929814

**Category:** Science

**Page:** 191

**View:** 6768

How is it that nobody--except maybe scientists--sees science for what it is? In this entertaining and provocative book, Lewis Wolpert draws on the entire history of science, from Thales of Miletus to Watson and Crick, from the study of eugenics to the discovery of the double helix. The result is a scientist's view of the culture of science, authoritative and informed and at the same time mercifully accessible to those who find cohabiting with this culture a puzzling experience. Science is arguably the defining feature of our age. For anyone who hopes to understand its nature, this lively and thoughtful book provides the perfect starting point.
*The Logic of Science*

**Author**: E. T. Jaynes

**Publisher:** Cambridge University Press

**ISBN:** 1139435167

**Category:** Science

**Page:** N.A

**View:** 2440

The standard rules of probability can be interpreted as uniquely valid principles in logic. In this book, E. T. Jaynes dispels the imaginary distinction between 'probability theory' and 'statistical inference', leaving a logical unity and simplicity, which provides greater technical power and flexibility in applications. This book goes beyond the conventional mathematics of probability theory, viewing the subject in a wider context. New results are discussed, along with applications of probability theory to a wide variety of problems in physics, mathematics, economics, chemistry and biology. It contains many exercises and problems, and is suitable for use as a textbook on graduate level courses involving data analysis. The material is aimed at readers who are already familiar with applied mathematics at an advanced undergraduate level or higher. The book will be of interest to scientists working in any area where inference from incomplete information is necessary.
*Scientists--Their Passions and Professions*

**Author**: Joseph C. Hermanowicz

**Publisher:** University of Chicago Press

**ISBN:** 9780226327679

**Category:** Science

**Page:** 268

**View:** 8517

Based on sixty interviews with physicists at universities across the United States, The Stars are Not Enough offers a detailed and intimate account of the worlds in which scientists work. Joseph C. Hermanowicz looks at a range of scientists from young graduate students to older professionals well into their careers. The result is a colorful portrait of a profession and its diverse cast of characters. These deeply personal narratives reveal dreams of fame and glory, in which scientists confess their ambitions of becoming the next Newton or Einstein. However, these scientists also discuss the meaning of success and failure. We hear their stories of aspiration and anxiety, disappointment and tragedy, hope and achievement; we are privy to their doubts and to what they consider to be their limitations and weaknesses. As the scientists age in their professions, the specter of failure often visits them, and they have to accept something less than scientific immortality or even the Nobel Prize. Ultimately these stories give us more than an inside look at the details of careers in science, they also examine ambition by uncovering the forces that drive people in their professions and by describing how these forces persist or fade over time. Ambition for greatness often ignites a career and often sustains it. Yet, as Hermanowicz's study reveals, greatness eludes nearly all people in their heroic quests for extraordinary achievement. The Stars Are Not Enough offers a fascinating account that will appeal to anyone interested in how people's dreams blossom and evolve.
*Hidden Asymmetries in Daily Life*

**Author**: Nassim Nicholas Taleb

**Publisher:** N.A

**ISBN:** 042528462X

**Category:** Business & Economics

**Page:** 304

**View:** 9142

Discusses how the willingness to accept one's own risks is an essential attribute for defining what it means to understand the world, succeed in life, contribute to a fair and just society, and influence others.

**Author**: Bill Bryson

**Publisher:** Anchor Canada

**ISBN:** 0385674503

**Category:** Science

**Page:** 560

**View:** 4770

One of the world’s most beloved and bestselling writers takes his ultimate journey -- into the most intriguing and intractable questions that science seeks to answer. In A Walk in the Woods, Bill Bryson trekked the Appalachian Trail -- well, most of it. In In A Sunburned Country, he confronted some of the most lethal wildlife Australia has to offer. Now, in his biggest book, he confronts his greatest challenge: to understand -- and, if possible, answer -- the oldest, biggest questions we have posed about the universe and ourselves. Taking as territory everything from the Big Bang to the rise of civilization, Bryson seeks to understand how we got from there being nothing at all to there being us. To that end, he has attached himself to a host of the world’s most advanced (and often obsessed) archaeologists, anthropologists, and mathematicians, travelling to their offices, laboratories, and field camps. He has read (or tried to read) their books, pestered them with questions, apprenticed himself to their powerful minds. A Short History of Nearly Everything is the record of this quest, and it is a sometimes profound, sometimes funny, and always supremely clear and entertaining adventure in the realms of human knowledge, as only Bill Bryson can render it. Science has never been more involving or entertaining. From the Hardcover edition.

**Author**: Lincoln Barnett,Albert Einstein

**Publisher:** Courier Corporation

**ISBN:** 0486445194

**Category:** Science

**Page:** 128

**View:** 3423

Acclaimed by Einstein himself, this is among the clearest, most readable expositions of relativity theory. It explains the problems Einstein faced, the experiments that led to his theories, and what his findings reveal about the forces that govern the universe. 1957 edition.
*Science in the Classroom*

**Author**: Committee on How People Learn: A Targeted Report for Teachers,Board on Behavioral, Cognitive, and Sensory Sciences,Division of Behavioral and Social Sciences and Education,National Research Council

**Publisher:** National Academies Press

**ISBN:** 0309089506

**Category:** Education

**Page:** 264

**View:** 2732

How Students Learn: Science in the Classroom builds on the discoveries detailed in the best-selling How People Learn. Now these findings are presented in a way that teachers can use immediately, to revitalize their work in the classroom for even greater effectiveness. Organized for utility, the book explores how the principles of learning can be applied in science at three levels: elementary, middle, and high school. Leading educators explain in detail how they developed successful curricula and teaching approaches, presenting strategies that serve as models for curriculum development and classroom instruction. Their recounting of personal teaching experiences lends strength and warmth to this volume. This book discusses how to build straightforward science experiments into true understanding of scientific principles. It also features illustrated suggestions for classroom activities.

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