*A Rigorous Introduction for the Mathematically Untrained*

**Author**: Øyvind Grøn,Arne Næss

**Publisher:**Springer Science & Business Media

**ISBN:**9781461407065

**Category:**Science

**Page:**341

**View:**5444

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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:** 5444

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:** 553

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:** 7456

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.

**Author**: Andrew M. Steane

**Publisher:** Oxford University Press

**ISBN:** 0199662851

**Category:** Science

**Page:** 419

**View:** 7143

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.
*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:** 5245

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**: Pavel Grinfeld

**Publisher:** Springer Science & Business Media

**ISBN:** 1461478677

**Category:** Mathematics

**Page:** 302

**View:** 4320

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.

**Author**: Daniel F. Styer

**Publisher:** JHU Press

**ISBN:** 1421401258

**Category:** Science

**Page:** 200

**View:** 8087

The appendixes provide helpful hints, basic answers to the sample problems, and materials to stimulate further exploration.
*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:** 1920

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**: Robert P. Crease

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

**ISBN:** 0393337936

**Category:** Mathematics

**Page:** 320

**View:** 1540

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:** 5770

“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.
*Contributions of Contemporary Physics and Philosophy*

**Author**: Robert J. Spitzer

**Publisher:** Wm. B. Eerdmans Publishing

**ISBN:** 0802863833

**Category:** Religion

**Page:** 319

**View:** 1477

Responding to contemporary popular atheism, Robert J. Spitzer's New Proofs for the Existence of God examines the considerable evidence for God and creation that has come to light from physics and philosophy during the last forty years. An expert in diverse areas, including theology, physics, metaphysics, and ethics, Spitzer offers in this text the most contemporary, complete, and integrated approach to rational theism currently available. "Skepticism about the possibility of proving the existence of God often relies on data from modern science. In this splendid new book Father Robert Spitzer explores the implications of the latest discoveries in big bang cosmology, string theory, quantum physics, and the ontology of time to craft a series of convincing philosophical arguments. To paraphrase a popular commercial, this is not your father's old 'natural theology' textbook ù it's a gripping and compelling account of the best current arguments for theism."ùJoseph W. Koterski, S.J., Foidham University "A most original and insightful case for the existence of God.... Fr. Spitzer's new proofs pose a serious and compelling challenge to the unconscious hegemony of naturalism in the worlds of both philosophy and the sciences."ùFrancis J. Beckwith, Baylor University "Rare is the theologian who keeps abreast of the latest developments in fundamental physics, and even rarer the one who can discuss them with the theological and philosophical sophistication that Fr. Spitzer displays in this book. A challenging and original work."ùStephen M. Barr, University of Delaware, author of Modern Physics and Ancient Faith

**Author**: Arne Naess

**Publisher:** ReadHowYouWant.com

**ISBN:** 1458759849

**Category:**

**Page:** 608

**View:** 2638

The Ecology of Wisdom is a definitive collection of essays by Norwegian philosopher Arne Naess, a founder of the Deep Ecology movement and one of the leading thinkers of modern environmentalism. Drengson and Devall provide a comprehensive and accessible portrait of Naess's philosophy and activism, and showcase his enthusiasm, wit, and spiritual fascination with nature.

**Author**: David Bohm

**Publisher:** Routledge

**ISBN:** 1134438729

**Category:** Philosophy

**Page:** 304

**View:** 9354

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.
*The Loss of Certainty*

**Author**: Morris Kline

**Publisher:** Oxford University Press, USA

**ISBN:** 9780195030853

**Category:** Mathematics

**Page:** 366

**View:** 1073

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
*The Logic of Science*

**Author**: E. T. Jaynes

**Publisher:** Cambridge University Press

**ISBN:** 1139435167

**Category:** Science

**Page:** N.A

**View:** 5828

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.
*How a Godless Cosmos Creates*

**Author**: Howard Bloom

**Publisher:** Prometheus Books

**ISBN:** 1616145528

**Category:** Religion

**Page:** 708

**View:** 951

God’s war crimes, Aristotle’s sneaky tricks, Einstein’s pajamas, information theory’s blind spot, Stephen Wolfram’s new kind of science, and six monkeys at six typewriters getting it wrong. What do these have to do with the birth of a universe and with your need for meaning? Everything, as you’re about to see. How does the cosmos do something it has long been thought only gods could achieve? How does an inanimate universe generate stunning new forms and unbelievable new powers without a creator? How does the cosmos create? That’s the central question of this book, which finds clues in strange places. Why A does not equal A. Why one plus one does not equal two. How the Greeks used kickballs to reinvent the universe. And the reason that Polish-born Benoît Mandelbrot—the father of fractal geometry—rebelled against his uncle. You’ll take a scientific expedition into the secret heart of a cosmos you’ve never seen. Not just any cosmos. An electrifyingly inventive cosmos. An obsessive-compulsive cosmos. A driven, ambitious cosmos. A cosmos of colossal shocks. A cosmos of screaming, stunning surprise. A cosmos that breaks five of science’s most sacred laws. Yes, five. And you’ll be rewarded with author Howard Bloom’s provocative new theory of the beginning, middle, and end of the universe—the Bloom toroidal model, also known as the big bagel theory—which explains two of the biggest mysteries in physics: dark energy and why, if antimatter and matter are created in equal amounts, there is so little antimatter in this universe. Called "truly awesome" by Nobel Prize–winner Dudley Herschbach, The God Problem will pull you in with the irresistible attraction of a black hole and spit you out again enlightened with the force of a big bang. Be prepared to have your mind blown. From the Hardcover edition.
*Improving Decisions About Health, Wealth, and Happiness*

**Author**: Richard H. Thaler,Cass R. Sunstein

**Publisher:** Penguin

**ISBN:** 1101655097

**Category:** Business & Economics

**Page:** 320

**View:** 2538

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

**Author**: David J. Griffiths

**Publisher:** Cambridge University Press

**ISBN:** 1107602173

**Category:** Science

**Page:** 182

**View:** 3518

"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"--
*50th Anniversary Edition*

**Author**: Thomas S. Kuhn

**Publisher:** University of Chicago Press

**ISBN:** 0226458148

**Category:** Science

**Page:** 264

**View:** 9751

A good book may have the power to change the way we see the world, but a great book actually becomes part of our daily consciousness, pervading our thinking to the point that we take it for granted, and we forget how provocative and challenging its ideas once were—and still are. The Structure of Scientific Revolutions is that kind of book. When it was first published in 1962, it was a landmark event in the history and philosophy of science. Fifty years later, it still has many lessons to teach. With The Structure of Scientific Revolutions, Kuhn challenged long-standing linear notions of scientific progress, arguing that transformative ideas don’t arise from the day-to-day, gradual process of experimentation and data accumulation but that the revolutions in science, those breakthrough moments that disrupt accepted thinking and offer unanticipated ideas, occur outside of “normal science,” as he called it. Though Kuhn was writing when physics ruled the sciences, his ideas on how scientific revolutions bring order to the anomalies that amass over time in research experiments are still instructive in our biotech age. This new edition of Kuhn’s essential work in the history of science includes an insightful introduction by Ian Hacking, which clarifies terms popularized by Kuhn, including paradigm and incommensurability, and applies Kuhn’s ideas to the science of today. Usefully keyed to the separate sections of the book, Hacking’s introduction provides important background information as well as a contemporary context. Newly designed, with an expanded index, this edition will be eagerly welcomed by the next generation of readers seeking to understand the history of our perspectives on science.

**Author**: Richard A. Muller

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

**ISBN:** 0393285243

**Category:** Science

**Page:** 352

**View:** 9697

From the celebrated author of the best-selling Physics for Future Presidents comes “a provocative, strongly argued book on the fundamental nature of time” (Lee Smolin). You are reading the word “now” right now. But what does that mean? What makes the ephemeral moment “now” so special? Its enigmatic character has bedeviled philosophers, priests, and modern-day physicists from Augustine to Einstein and beyond. Einstein showed that the flow of time is affected by both velocity and gravity, yet he despaired at his failure to explain the meaning of “now.” Equally puzzling: why does time flow? Some physicists have given up trying to understand, and call the flow of time an illusion, but the eminent experimentalist physicist Richard A. Muller protests. He says physics should explain reality, not deny it. In Now, Muller does more than poke holes in past ideas; he crafts his own revolutionary theory, one that makes testable predictions. He begins by laying out—with the refreshing clarity that made Physics for Future Presidents so successful—a firm and remarkably clear explanation of the physics building blocks of his theory: relativity, entropy, entanglement, antimatter, and the Big Bang. With the stage then set, he reveals a startling way forward. Muller’s monumental work will spark major debate about the most fundamental assumptions of our universe, and may crack one of physics’s longest-standing enigmas.

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