Mathematical / Computational / Theoretical physics Books

Book SynopsisA groundbreaking work in the field of physics and mathematics. In this monumental work, Newton formulated the laws of motion and universal gravitation, laying the foundation for classical mechanics and revolutionizing our understanding of the physical world. The Principia remains one of the most significant scientific books ever written, influencing generations of scientists, and shaping the course of modern physics and mathematics. The Groundbreaking Work of Sir Isaac Newton Mathematical proofs and equations. Comprehensive coverage of planetary motion. Helps in understanding the principles of motion. Logical and rigorous approach to scientific inquiry. Studied and revered as a seminal work in the field of science.

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Book SynopsisThe latest volume in The New York Times bestselling physics series explains Einstein''s masterpiece: the general theory of relativityHe taught us classical mechanics, quantum mechanics and special relativity. Now, physicist Leonard Susskind, assisted by a new collaborator, André Cabannes, returns to tackle Einstein''s general theory of relativity. Starting from the equivalence principle and covering the necessary mathematics of Riemannian spaces and tensor calculus, Susskind and Cabannes explain the link between gravity and geometry. They delve into black holes, establish Einstein field equations and solve them to describe gravity waves. The authors provide vivid explanations that, to borrow a phrase from Einstein himself, are as simple as possible (but no simpler).An approachable yet rigorous introduction to one of the most important topics in physics, General Relativity is a must-read for anyone who wants a deeper knowledge of the universe''s real structure.

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Book SynopsisThis modern text combines fundamental principles with advanced topics and recent techniques in a rigorous and self-contained treatment of quantum field theory.Beginning with a review of basic principles, starting with quantum mechanics and special relativity, students can refresh their knowledge of elementary aspects of quantum field theory and perturbative calculations in the Standard Model. Results and tools relevant to many applications are covered, including canonical quantization, path integrals, non-Abelian gauge theories, and the renormalization group. Advanced topics are explored, with detail given on effective field theories, quantum anomalies, stable extended field configurations, lattice field theory, and field theory at a finite temperature or in the strong field regime. Two chapters are dedicated to new methods for calculating scattering amplitudes (spinor-helicity, on-shell recursion, and generalized unitarity), equipping students with practical skills for research. AccesTrade Review'Quantum Field Theory: From Basics to Modern Topics, by François Gelis, is a very welcome addition to the canon of literature on quantum field theory, impressive both in its breadth and depth. It covers, in a succinct fashion, foundational material in the subject and then treats many more modern developments: effective field theories, anomaly matching, recursion relations for gauge and gravitational amplitudes, strong fields, and more.' Laurence Yaffe, University of Washington'Though there are many books on quantum field theory, I have found this book valuable for its readable treatment of a diverse selection of modern topics from a uniform viewpoint. Subjects introduced well in this book that are hard to find elsewhere include Schwinger-Keldysh and finite-temperature field theory, modern tools for scattering amplitudes, worldline methods, as well as effective field theory. The discussion is illustrated with a rich set of examples, mainly from high energy physics.' John McGreevy, University of California, San DiegoTable of ContentsPreface; 1. Basics of quantum field theory; 2. Peturbation theory; 3. Quantum electrodynamics; 4. Spontaneous symmetry breaking; 5. Functional quantization; 6. Path integrals for fermions and photons; 7. Non-Abelian gauge symmetry; 8. Quantization of Yang–Mills theory; 9. Renormalization of gauge theories; 10. Renormalization group; 11. Effective field theories; 12. Quantum anomalies; 13. Localized field configurations; 14. Modern tools for tree amplitudes; 15. Wordline formalism; 16. Lattice field theory; 17. Quantum field theory at finite temperature; 18. Strong fields and semi-classical methods; 19. From trees to loops; Further reading; Index.

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Book SynopsisThese lecture notes provide a systematic introduction to matrix models of quantum field theories with non-commutative and fuzzy geometries. The book initially focuses on the matrix formulation of non-commutative and fuzzy spaces, followed by a description of the non-perturbative treatment of the corresponding field theories. As an example, the phase structure of non-commutative phi-four theory is treated in great detail, with a separate chapter on the multitrace approach. The last chapter offers a general introduction to non-commutative gauge theories, while two appendices round out the text. Primarily written as a self-study guide for postgraduate students – with the aim of pedagogically introducing them to key analytical and numerical tools, as well as useful physical models in applications – these lecture notes will also benefit experienced researchers by providing a reference guide to the fundamentals of non-commutative field theory with an emphasis on matrix models and fuzzy geometries.Trade Review“The book collects almost all that has been achieved on the topic within the recent years, including all major results of many authors. As such, it is a nice reference work for graduate students and beginning researchers who want to pursue research in this area. Having all the results and different approaches collected in one place, together with the exhaustive list of references make this a valuable compendium to everyone working on noncommutative models of quantum field theory.” (Andrzej Sitarz, zbMATH 1371.81013, 2017)Table of ContentsPreface.- Introductory Remarks.- The Non-Commutative Moyal-Weyl Spaces Rd.- The Fuzzy Sphere.- Quantum Non-Commutative Phi-Four.- The Multitrace Approach.- Non-Commutative Gauge Theory.- Appendix A - The Landau States.- Appendix B - The Traces TrtAtB and TrtAtBtCtD.- Index.

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Book SynopsisNew concise edition with a new introduction, abridged for the modern reader. The Principia. Mathematical Principles of Natural Philosophy is one of the most important scientific works ever to have been written and has had a profound impact on modern science. Consisting of three separate books, the Principia states Newton’s laws of motion and Newton’s law of universal gravitation. Understanding and acceptance of these theories was not immediate, however by the end of the seventeenth century no one could deny that Newton had far exceeded all previous works and revolutionised scientific thinking. The FLAME TREE Foundations series features core publications which together have shaped the cultural landscape of the modern world, with cutting-edge research distilled into pocket guides designed to be both accessible and informative.

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Book SynopsisIntroduces advanced undergraduates to Riemannian geometry and mathematical general relativity. The overall strategy of the book is to explain the concept of curvature via the Jacobi equation which, through discussion of tidal forces, further helps motivate the Einstein field equations.Table of Contents Introduction to Riemannian geometry Differential calculus with tensors Curvature General relativity Introduction to geometry analysis Bibliography Index

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Book SynopsisUpdating one of the most widely used introductory textbooks on Einstein's general relativity, this third edition includes the latest updates on gravitational waves, black holes, and cosmology. It introduces the science of relativity to final-year undergraduates and graduate students, requiring only a minimal background in mathematics.Trade ReviewPraise for the second edition: 'Bernard Schutz's textbook A First Course in General Relativity quickly became a classic, notable for its use of the geometrical approach to the subject, combined with a refreshing succinctness. Since its first publication in 1985, the field of general relativity has exploded … Schutz has done a masterful job of incorporating these new developments into a revised edition, which is sure to become a new 'classic'.' Clifford M. Will, McDonnell Center for the Space Sciences, Washington University, St. LouisPraise for the second edition: 'This new edition retains all of the original's clarity and insight into the mathematical foundations of general relativity, but thoroughly updates the accounts of the application of the theory in astrophysics and cosmology. The result is an indispensable volume and this new edition will no doubt become a classic text in its own right.' Mike Hobson, Cavendish Laboratory, University of CambridgePraise for the second edition: 'Schutz has updated his eminently readable and eminently teachable A First Course in General Relativity. This text will be appreciated by any upper-level undergraduate with an interest in cosmology, astrophysics, or experimentation in gravitational physics.' Richard Matzner, The Center for Relativity, University of Texas at AustinPraise for the second edition: ' … marvellous … very clear … I cannot recommend this book highly enough to any physicist who wants a good introduction to general relativity.' David Burton, The ObservatoryPraise for the first edition: 'Schutz has such mastery of the material that it soon becomes clear that one is in authoritative hands, and topics are selected and developed only to a point where they prove adequate for future needs.' The Times Higher Education SupplementPraise for the first edition: '… ought to inspire more physicists and astronomers to teach and learn the other half of the twentieth century's revolution in physics.' Foundations of PhysicsPraise for the first edition: 'The book is a goldmine of cleverly constructed problems and exercises (and solutions!).' NaturePraise for the first edition: '… provides the first step into general relativity for undergraduate students with a minimal background in mathematics.' Zentralblatt MATH'Several generations of students have benefitted from the first two editions of Professor Bernard Schutz' beautiful introductory textbook on tensor algebra, manifolds, physics in curved space times, and Einstein's field equations. Why another edition now? The answer is that, in the last years, precision measurements of stellar orbits around the central massive black hole in the Galactic Center, the detection of gravitational waves from in-spiraling binary black holes and neutron stars with LIGO, and the detection of the central 'radio wave shadow' of the supermassive black hole in the galaxy M87 have suddenly opened the magical world of strongly curved spacetime to precision experimental tests. These experiments and much more to come from ground- and space-based gravitational wave studies have started a renaissance of interest in Einstein's theory.' Reinhard Genzel, Max Planck Institute for Extraterrestrial Physics'Students and teachers of general relativity will welcome this new edition of Schutz' hugely popular text, significantly broadened to cover the astonishing discoveries of gravitational-wave astronomy and their implications. A pioneer of the geometrical approach to undergraduate-level teaching of GR, the book remains unmatched in its highly readable style. With vim and authority, Schutz leads his readers masterfully from mathematical foundations to the forefront of research in astronomy and cosmology, providing them with the tools to understand future discoveries. With this new edition, Schutz' classic text remains as fresh and relevant as ever.' Leor Barack, University of Southampton'An outstanding textbook on general relativity written with the author's customary clarity and in his engaging style. It includes not only the basics of general relativity, but also recent developments in the direct detection of gravitational waves. A clear exposition of the essential ideas and methods.' Rong-Gen Cai, Chinese Academy of Sciences'Professor Schutz' informal style bewitches the reader into absorbing profound and complex concepts effortlessly. Physics is explained in a lucid style with minimal mathematics, without compromising on rigour. The recent excitement in the field of gravitational waves and its implications for astronomy and cosmology is adeptly conveyed. This edition has been enriched with several more exercises which the student or the young researcher will find illuminating and instructive.' Sanjeev Dhurandhar, Inter University Centre for Astronomy and Astrophysics'When I first taught from this book in the 1980s, my students and I loved it for its unusual combination of clarity and brevity. This third edition is not quite as brief because so much has happened in the subject! But for an all-around text with clear writing and an engaging style, it is still top of the class.' Clifford Will, University of Florida'A First Course in General Relativity by Bernard Schutz is an outstanding introductory text on Einstein's theory of general relativity and offers an invaluable resource for students interested in understanding the formal and physical foundations of modern spacetime theory.' Karim Thebault, University of Bristol'As with its previous editions, this textbook provides a fantastically accessible introduction to the key physical concepts of general relativity and the formalism used by its practitioners. The third edition gives a much-needed update accounting for discoveries since the previous edition, with the chapters on gravitational waves in particular serving as outstanding tutorials for students who are interested in astronomical applications of this subject.' Scott Hughes, Massachusetts Institute of TechnologyTable of ContentsPreface to the third edition page; Preface to the second edition; Preface to the first edition; 1. Special relativity; 2. Vector analysis in special relativity; 3. Tensor analysis in special relativity; 4. Perfect fluids in special relativity; 5. Preface to curvature; 6. Curved manifolds; 7. Physics in a curved spacetime; 8. The Einstein field equations; 9. Fundamentals of Gravitational Radiation; 10. Spherical solutions for stars; 11. Schwarzschild geometry and black holes; 12. Gravitational wave astronomy; 13. Cosmology; Appendix A. Summary of linear algebra; References; Index.

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Book SynopsisIn his monumental 1687 work, Philosophiae Naturalis Principia Mathematica, known familiarly as the Principia, Isaac Newton laid out in mathematical terms the principles of time, force, and motion that have guided the development of modern physical science. This is a modern translation based on the 1726 edition.

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Book SynopsisThis textbook uses insight from differential equations to analyse fundamental subjects of modern theoretical physics, including classical and quantum mechanics, thermodynamics, electromagnetism, superconductivity, gravitational physics, and quantum field theories.Table of ContentsPreface Notation and Convention 1: Hamiltonian Systems and Applications 2: Schrödinger Equation and Quantum Mechanics 3: Maxwell Equations, Dirac Monopole, and Gauge Fields 4: Special Relativity 5: Abelian Gauge Field Equations 6: Dirac Equations 7: GinzburgDSLandau Equations for Superconductivity 8: Magnetic Vortices in Abelian Higgs Theory 9: Non-Abelian Gauge Field Equations 10: Einstein Equations and Related Topics 11: Charged Vortices and ChernDSSimons Equations 12: Skyrme Model and Related Topics 13: Strings and Branes 14: BornDSInfeld Theory of Electromagnetism 15: Canonical Quantization of Fields Appendices Bibliography Index

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Book SynopsisBlack holes present one of the most fascinating predictions of Einstein''s general theory of relativity. There is strong evidence of their existence through observation of active galactic nuclei, including the centre of our galaxy, observations of gravitational waves, and others.There exists a large scientific literature on black holes, including many excellent textbooks at various levels. However, most of these steer clear from the mathematical niceties needed to make the theory of black holes a mathematical theory. Those which maintain a high mathematical standard are either focused on specific topics, or skip many details. The objective of this book is to fill this gap and present a detailed, mathematically oriented, extended introduction to the subject.The book provides a wide background to the current research on all mathematical aspects of the geometry of black hole spacetimes.Trade ReviewWritten with a high standard of rigor and care, with very good treatments of many topics that are hard to find elsewhere. * Robert Wald, University of Chicago *Including some very interesting and unique material, the book is written in a manner that will be accessible for students, and provide a valuable resource for experts working in mathematical general relativity. * Greg Galloway, University of Miami *This text is an excellent research level monograph exploring the detailed and rich structure of black holes in mathematical physics. * Kymani Armstrong-Williams, Physics Book Reviews *Table of ContentsPART I GLOBAL LORENTZIAN GEOMETRY 1: Basic Notions 2: Elements of causality 3: Some applications PART II BLACK HOLES 4: An introduction to black holes 5: Further selected solutions 6: Extensions, conformal diagrams 7: Projection diagrams 8: Dynamical black holes

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Book SynopsisThe Nature of Complex Networks provides a systematic introduction to the statistical mechanics of complex networks and the different theoretical achievements in the field that are now finding strands in common.The book presents a wide range of networks and the processes taking place on them, including recently developed directions, methods, and techniques. It assumes a statistical mechanics view of random networks based on the concept of statistical ensembles but also features the approaches and methods of modern random graph theory and their overlaps with statistical physics.This book will appeal to graduate students and researchers in the fields of statistical physics, complex systems, graph theory, applied mathematics, and theoretical epidemiology.Trade ReviewThe current volume by Dorogovtsev and Mendes takes quite a broad view of complex networks to include the analysis of finite and infinite graphs, directed and undirected graphs, multigraphs, hypergraphs, and even simplicial complexes, as networks scale according to increasing N or in some other fashion. The writing style is that of physics and especially statistical mechanics with frequent connections made to physical concepts such as Bose-Einstein condensation...The current volume can especially serve as a useful reference on complex networks from a physics perspective. * Lenwood S. Heath, MathSciNet *Table of ContentsPreface 1: First insight 2: Graphs 3: Classical random graphs 4: Equilibrium networks 5: Evolving networks 6: Connected components 7: Epidemics and spreading phenomena 8: Networks of networks 9: Spectra and communities 10: Walks and search 11: Temporal networks 12: Cooperative systems on networks 13: Inference and reconstruction 14: What's next? Further Reading Appendices A-G References

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Book SynopsisTable of Contents1. Galilean relativity 2. Lorentz Boosts 3. Development of the Formalism 4. Electrodynamics 5. Gravity 6. Experiments and Applications Part II: Mathematics 7. Mathematics of Translations 8. The Rotation Group 9. The Lorentz Group

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Book SynopsisWaves are an important topic in the fields of mechanics, electromagnetism, and quantum theory, but many students struggle with the mathematical aspects. Written to complement course textbooks, this book focuses on the topics that students find most difficult. Retaining the highly popular approach used in Fleisch''s other Student''s Guides, the book uses plain language to explain fundamental ideas in a simple and clear way. Exercises and fully-worked examples help readers test their understanding of the concepts, making this an ideal book for undergraduates in physics and engineering trying to get to grips with this challenging subject. The book is supported by a suite of online resources available at www.cambridge.org/9781107643260. These include interactive solutions for every exercise and problem in the text and a series of video podcasts in which the authors explain the important concepts of every section of the book.Trade Review'I recommend this supplementary textbook as a clear tutorial for understanding the basic concepts of waves and the wave equation with its applications to mechanics, electromagnetic waves and the Schrӧdinger equation. … It is written for undergraduates in physics and engineering, but it also has exceptional value to a wider readership. … Physical insights that are helpful for a deep understanding of waves are uniquely presented. The text is supplemented with clear and useful graphs. The book's website contains additional resources: worked solutions to all problems, animated graphics, a few errata, and author podcasts to augment all the chapters.' Barry R. Masters, Optics and Photonics NewsTable of ContentsIntroduction; 1. Wave fundamentals; 2. The wave equation; 3. Wave components; 4. The mechanical wave equation; 5. The electromagnetic wave equation; 6. The quantum wave equation; References; Index.

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Book SynopsisThis clear and pedagogical text delivers a concise overview of classical and quantum statistical physics. Essential Statistical Physics shows students how to relate the macroscopic properties of physical systems to their microscopic degrees of freedom, preparing them for graduate courses in areas such as biophysics, condensed matter physics, atomic physics and statistical mechanics. Topics covered include the microcanonical, canonical, and grand canonical ensembles, Liouville''s Theorem, Kinetic Theory, non-interacting Fermi and Bose systems and phase transitions, and the Ising model. Detailed steps are given in mathematical derivations, allowing students to quickly develop a deep understanding of statistical techniques. End-of-chapter problems reinforce key concepts and introduce more advanced applications, and appendices provide a detailed review of thermodynamics and related mathematical results. This succinct book offers a fresh and intuitive approach to one of the most challengingTrade Review'At last a textbook that contains all the required elements for a modern advanced undergraduate course on statistical physics: foundations, quantum statistical mechanics, phase transitions and dynamics. I particularly like the derivation of ensembles through maximization of Gibbs entropy and the Langevin description of Brownian motion. Plenty of instructive problems within ten digestible chapters make this a text I can recommend to my students.' Martin Evans, University of Edinburgh'Statistical mechanics is a vast and fascinating topic, sometimes intimidating beginning students. Kennett succeeds in delivering an agile, fresh and modern exposition of the essential ideas and methods, in addition to a well-thought selection of examples and applications borrowed from all branches of physics. Students and teachers alike will enjoy the carefully organized table of contents for self-study and lecture preparation.' Roberto Raimondi, Roma Tre University'This book incorporates, into a single course, ideas and theoretical techniques in statistical physics and quantum mechanics that are connected by the physical phenomena they are meant to describe. Yet they are rarely all found in the same text. Professor Kennett offers students of theoretical physics a rare opportunity to acquire a mature understanding of their impact and meaning.' Herbert Fertig, Indiana University, BloomingtonTable of ContentsPreface; 1. Introduction; 2. The microcanonical ensemble; 3. Liouville's theorem; 4. The canonical ensemble; 5. Kinetic theory; 6. The grand canonical ensemble; 7. Quantum statistical mechanics; 8. Fermions; 9. Bosons; 10. Phase transitions and order; Appendix A Gaussian integrals and stirling's formula; Appendix B Primer on thermal physics; Appendix C Heat capacity cusp in Bose systems; References; Index.

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Book SynopsisThe revised and updated 2nd edition of this established textbook provides a self-contained introduction to the general theory of relativity, describing not only the physical principles and applications of the theory, but also the mathematics needed, in particular the calculus of differential forms.Updated throughout, the book contains more detailed explanations and extended discussions of several conceptual points, and strengthened mathematical deductions where required. It includes examples of work conducted in the ten years since the first edition of the book was published, for example the pedagogically helpful concept of a "river of space" and a more detailed discussion of how far the principle of relativity is contained in the general theory of relativity. Also presented is a discussion of the concept of the 'gravitational field' in Einstein's theory, and some new material concerning the 'twin paradox' in the theory of relativity. Finally, the book contains a new section about gravitational waves, exploring the dramatic progress in this field following the LIGO observations. Based on a long-established masters course, the book serves advanced undergraduate and graduate level students, and also provides a useful reference for researchers.Table of ContentsNewton’s law of universal gravitation.- The force law of gravitation.- Newton’s law of gravitation in local form.- Tidal forces.- The principle of equivalence.- The general principle of relativity.- The covariance principle.- Mach’s principle.- The special theory of relativity.- Coordinate systems and Minkowski diagrams.- Synchronization of clocks.- The Doppler effect.- Relativistic time-dilation.- The relativity of simultaneity.- The Lorentz contraction.- The Lorentz transformation.- The Lorentz invariant interval.- The twin paradox.- Hyperbolic motion.- Energy and mass.- Relativistic increase of mass.- Tachyons.- Magnetism as a relativistic second order effect.- Vectors, tensors and forms.- Vectors.- Four-vectors.- Tangent vector fields and coordinate vectors.- Coordinate transformations.- Structure coefficients.- Tensors.- Transformation of tensor components.- Transformation of basis 1-forms.- The metric tensor.- Forms.- Rotating and accelerated reference frames.- Rotating reference frames.- The spatial metric tensor.- Angular acceleration of the rotating frame.- Gravitational time dilation.- Path of photons emitted from the axis in a rotating frame.- The Sagnac effect.- Uniformly accelerated reference frames.- Covariant differentiation.- Differentiation of forms.- Exterior differentiation.- Covariant derivative.- The Christoffel symbols.- Geodetic curves.- The covariant Euler-Lagrange equations.- Application of the Lagrange formalism to free particles.- Equation of motion from Lagrange’s equations.- Geodesic worldliness in spacetime.- Gravitational Doppler effect.- The Koszul connection.- Connection coefficients and structure coefficients in a Riemannian (torsion free) space.- Covariant differentiation of vectors, forms and tensors.- Covariant differentiation of a vector field in an arbitrary basis.- Covariant differentiation of forms.- Generalization for tensors of higher rank.- The Cartan connection.- Curvature.- The Riemann curvature tensor.- Differential geometry of surfaces.- Surface curvature using the Cartan formalism.- The Ricci identity.- Bianchi’s 1st identity.- Bianchi’s 2nd identity.- Einstein’s field equations.- Energy-momentum conservation.- Newtonian fluid.- Perfect fluids.- Einstein’s curvature tensor.- Einstein’s field equations.- The 'geodesic postulate' as a consequence of the field equations.- The Schwarschild spacetime.- Schwarzschild’s exterior solution.- Radial free fall in Schwarzschild spacetime.- Light cones in Schwarzschild spacetime.- Analytical extension of the Schwarzschild coordinates.- Embedding of the Schwarzschild metric.- Deceleration of light.- Particle trajectories in Schwarzschild 3-space.- Motion in the equatorial plane.- Classical tests of Einstein’s general theory of relativity.- The Hafele-Keating experiment.- Mercury’s perihelion precession.- Deflection of light.- Black holes.- 'Surface gravity': gravitational acceleration on the horizon of a black hole.- Hawking radiation: radiation from a black hole.- Rotating black holes: The Kerr metric.- Zero-angular-momentum-observers.- Does the Kerr space have a horizon?.- Schwarzschild’s interior solution.- Newtonian incompressible star.- The pressure contribution to the gravitational mass of a static, spherically symmetric system.- The Tolman-Oppenheimer-Volkov equation.- An exact solution for incompressible stars – Schwarzschild’s interior solution.- Cosmology.- Comoving coordinate system.- Curvature isotropy – the Robertson-Walker metric.- Cosmic dynamics.- Hubble’s law.- Cosmological redshift of light.- Cosmic fluids.- Isotropic and homogeneous universe models.- Some cosmological models.- Radiation dominated model.- Dust dominated model.- Transition from radiation to matter dominated universe.- Friegmann-Lemaître model.- Inflationary cosmology.- Problems with the Big Bang models.- Cosmic inflation.

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Book SynopsisIs everything Information? This is a tantalizing question which emerges in modern physics, life sciences, astronomy and in today’s information and technology-driven society. In Powers of Two expert authors undertake a unique expedition - in words and images - throughout the world (and scales) of information. The story resembles, in a way, the classic Powers of Ten journeys through space: from us to the macro and the micro worlds . However, by following Powers of Two through the world of information, a completely different and timely paradigm unfolds. Every power of two, 1, 2, 4, 8…. tells us a different story: starting from the creation of the very first bit at the Big Bang and the evolution of life, through 50 years of computational science, and finally into deep space, describing the information in black holes and even in the entire universe and beyond…. All this to address one question: Is our universe made of information? In this book, we experience the Information Universe in nature and in our society and how information lies at the very foundation of our understanding of the Universe.From the Foreword by Robbert Dijkgraaf: This book is in many ways a vastly extended version of Shannon’s one-page blueprint. It carries us all the way to the total information content of the Universe. And it bears testimony of how widespread the use of data has become in all aspects of life. Information is the connective tissue of the modern sciences. […] Undoubtedly, future generations will look back at this time, so much enthralled by Big Data and quantum computers, as beholden to the information metaphor. But that is exactly the value of this book. With its crisp descriptions and evocative illustrations, it brings the reader into the here and now, at the very frontier of scientific research, including the excitement and promise of all the outstanding questions and future discoveries.Message for the e-reader of the book Powers of Two The book has been designed to be read in two-page spreads in full screen mode. For optimal reader experience in a downloaded .pdf file we strongly recommend you use the following settings in Adobe Acrobat Reader: - Taskbar: View > Page Display > two page view - Taskbar: View > Page Display > Show Cover Page in Two Page View - Taskbar: ^ Preferences > Full Screen > deselect " Fill screen with one page at a time" - Taskbar: View > Full screen mode or ctrl L (cmd L on a Mac) ***** Note: for reading the previews on Spinger link (and on-line reading in a browser), the full screen two-page view only works with these browsers: Firefox - Taskbar: on top of the text, at the uppermost right you will see then >> (which is a drop-down menu) >> even double pages - Fullscreen: F11 or Control+Cmd+F with Mac Edge - Taskbar middle: Two-page view and select show cover page separatelyTrade Review“The book … a very unusual collection of some facts about the relationship between the immaterial world represented by bits and the real physical world described by fundamental physical equations. This book continues the very categorical point of view of J. A. Wheeler … . The book presents short articles on various areas of modern science … in which it is shown that in these areas in some mysterious way there is a connection with the theory of information.” (Vladimir Dzhunushaliev, zbMATH 1479.83004, 2022)Table of ContentsForeword by Robbert DijkgraafChapter 0: IntroductionJoy-riding the Universe – by the authorWorking as an astronomer, data scientist and professor of astro-informatics for nearly fifty years, Edwin Valentijn has witnessed and first-hand engineered the dawn of the era of Big Data in science and society. Throughout his career, he became increasingly aware of the role of information in our world: in computers, in our society, and even in nature and in the Universe itself.The Information UniverseFollowing the increasing powers of two, the story paints a journey through the whole world of information, both in society and in nature. Each step opens a door into a new world: from the first bits with the Big Bang and the dawn of life, going through fifty years of human technology, all the way up to the information content of the whole Universe.What is Information? - Item pageThe basics of information are introduced.Chapter 1: The beginningSpace-time foam – Ti (0 bit: 20 =1)The very first power of two: 20, corresponds to the value one. This identifies the single, eternal, indistinguishable state: the primordial sea from which our Universe emerged – sometimes called the Space-time foam. I call this Ti, the reverse of It. This is one of the miraculous new notions in the story of the Powers of Two.Multiverse: Anthropic principle (Item page)From Ti, the primordial space-time foam, countless universes arise with widely different characteristics: the Multiverse. The Anthropic Principle is a philosophical consideration which states that we, people, will find ourselves in a universe that is suitable for intelligent life to emerge. Therefore, this Principle demonstrates that conditions in our Universe are not “fine-tuned” to the existence of human life and a “creator” doesn’t exist.Big bang (1 bit: 21 =2 states)At the Big Bang the first bit is created. From the indistinguishable unity of the primordial foam Ti, “the zeros were separated from the 1’s”: the first bit corresponds to two possible states. This bit is the first step on our journey to capture the ever-increasing complexity of our expanding Universe in terms of information, through the increasing powers of two.What is a bit? (Item page)The bit is at the core of the concept of information. A bit is any system that can have two states. Humans assign meanings to these states, which are illustrated with the concept of the traffic light: red or green, stop or go. The combination of multiple bits creates an exponentially increasing number of possible states, and hence meanings.Multicellular life (2 bit: 22 =4 states) / (4 bit: 24 =16 states)?Life started with exchanging information between cells. This is fundamental for the evolution of any kind of life. It took at least two billion years for uni-cellular to evolve into multi-cellular organisms around 600 million years ago, and to start the exchange of information between their different cells. By exchanging information, cells collaborate and act as a unified whole: life.The game of life (Item page)The characteristic features of life (or any complex system in the Universe) can be created from information. A simple computer game is all you need to demonstrate this concept. A famous example is Conway's Game of Life, which is full of visuals of living, growing, moving and dying objects. This game was already made on the computers of the early 70's with just a few lines of code.Chapter 2: People's Information UniverseASCII (7 bit: 27 =128 states)There is currently no physical theory how the digital world connects to the human consciousness. In the world of Information Technology (IT) all information exchange is based on agreements between people. For instance, ASCII, a simple list relating each letter of the alphabet to a 7-bit string, connects the digital world to the human consciousness. Machu Picchu (8 bit: 28 =256, 1 byte)The Intiwatana stone, a giant rock carved by the Inca's of ancient Machu Picchu in Peru, can be considered as a first 8-bit hard disk. Why so? As the sunrays lit the different surfaces of this huge rock throughout the year, it triggered the Inca's activities: sowing, harvesting, celebrating and praying.This ancient stone dissolves both the boundaries between heaven and earth, and those between the digital and natural Information Universe. In fact, the stone represents an ultimate picture of the cross-over between the in vivo and the in vitro Information Universe - a main theme of the book. In vitro being the man made technology to handle information and in vivo being the information built in nature, in this case the orbit and the light rays of the sun.First computers (16 bit: 216 =65.536, 2 byte)When computers emerged in the 1970's, astronomers first adopted them to steer their telescopes. Back then, a maximal effort to understand the mathematics of the problem was needed to squeeze the solution into the small computer memory. Nowadays, with large amounts of computing power and machine learning at their disposal, scientists and computer programmers often do the reverse.Star Peace vs. Star Wars (Item page)King Juan Carlos adored the harmony of galaxies as a source of inspiration for people on earth, in those days when Ronald Reagan was promoting his Star-wars programme. With this adoration in mind, in 1985, he gave an inspiring speech at the Royal inauguration of the international astronomical observatory on La Palma, Canary Islands. The inauguration was attended by, for those days, an unprecedented large crowd of European royals and government officials despite the great threat of terrorist attacks by the ETA. (the next and later spreads on facts vs fakes elucidate the relevance of this spread in the story line).Pre-internet Facts and Fakes (Item page)“Edwin Valentijn saved the life of the Dutch Queen Beatrix by catching her just before falling off a cliff at the inauguration on La Palma”, according to the headlines in Dutch newspapers. Fake news-stories are at all times alike and can only be dispelled by tracing links of information to their source, links or associations being a fundamental property of the Information Universe. Later, I discuss the less innocent case of overdrawing attention to terrorist attacks in the past decade.Hard disk (24 bit: 224 =1.6*107, 2 Mb)Only sixty years ago, a 5 MB hard disk weighed over five tons, and had to be loaded onto an aeroplane by using a truck. Now, we carry a thousand times more information in our trouser pocket. This demonstrates the amazing advance of information technology over the past decades. (Picture: first IBM hard disk loaded onto a plane).The telephone (Item page) As a precursor of the Internet, the telephone offered many of the same advantages and dangers, and was heavily discussed at its introduction. Whether telephone or the Internet, it all revolves around communication or copying of information. The telephone, as example of it, is one of the major discoveries of the 20th century. DNA (32 bit: 232 = 4*109, 500 Mb) – Guest author: Charley Lineweaver The information in the DNA creates life. All base pairs of the human DNA can be stored on a 500 Mb drive. How is this information communicated? How does a cell know it has to build part of a liver and not an eye, while they all have the same DNA? Apoptosis and the role of information exchange.Where does biological Information come from? (Item page) – Guest author: Charley Lineweaver Charley Lineweaver, expert on evolutionary biology, exoplanetology and astrobiology, will expand on the role of information in the evolution of life.Lifelines (Item page) – Guest author: Morris SwertzWhat is the role of nature versus that of nurture? A key question in modern health research. In Lifesciences, this question is addressed now using Big Data, like the astronomers who acquire huge data volumes to address the same question on the nature of galaxies. In Lifelines, a cohort of 165.000 people is studied over a period of 30 years using hospital data, blood samples and DNA scans.DVD (33 bit: 233 =9*109, 1 Gb)It’ s amazing how fast the digital image revolution went since 1989.30 years ago, Philips lab approached me since they had made a big discovery: it was possible to store many digital images on a CD. They were chasing me for digital images. While NASA had less than a thousand, I had 32.000 galaxy images obtained by scanning photographic plates from the European Southern Observatory – the first large digital image collection.Human Brain (36 bit: 236 =7*1010, 9 Gb) – Guest author: Katrin Amunts- JulichIn the large EU human brain project, the activities of the human brain are simulated in computers. This is a very difficult mission since the transistors in computers consume 100.000 billion times more energy than the synapsis of neurons. Our brains consist of 1011 neurons, corresponding to 9 Gb of data.Thinking of Karlheinz Meier, coordinator of the Human Brain Project in Heidelberg, Katrin Amunts will author two spreads on the role of information in the human brain.Neuromorphic computing – Guest author: Katrin AmuntsCurrently, it takes a hundred years of a supercomputer’s time to compete with the learning power of only a single day of the human brain. “Neuromorphic computing” researchers design electronic systems inspired by the human brain, in order to make computers many times faster and more energy efficient.CT scan (38 bit: 238 =3*1011, 34 Gb) – Guest author: Anders YnnermanNow it is possible to look inside animal and human bodies on touchscreens. Forensic investigations on, for instance, corpses of victims can be done with touch-screen tables. You can look inside, rotate, scroll and zoom animal and human bodies using tens of gigabytes of CT scan data. Prof. Anders Ynnerman explains how he does it.Terabytes (45 bit: 245 =4.4*1012, 1 Tb) - The largest (astronomical) datasetsDark energy and dark matter: two mysterious constituents of our Universe. How do astronomers get and handle the data from the VLT Survey Telescope on a high mountain top in Chile to shed lights on these ‘still too dark’ topics. This Telescope surveys the sky every hour at night generating Terabytes of astronomical data.Gravity as a lens (Item page) – Guest author: Margot BrouwerWhen light rays are bent by the gravity of a heavy object, this object acts as a lens. This effect can be used to map dark matter, which is invisible but constitutes 80% of the matter in our visible Universe. In 1915, Albert Einstein posed that gravity is equivalent to the curvature of the fabric of space and time itself, leading to the lensing effect.Weak gravitational lensing surveys – Guest author: Margot BrouwerTerabytes of astronomical data are reduced to a few numbers, describing how dark matter behaves and what is its true nature. https://www.youtube.com/watch?v=ZCyYGWqCmFw&t=23sEntering the Petabyte regime (53 bit: 253 =1*1015, 1 Pb)How do we technically acquire and deal with Petabytes of data?Dark Matter maps (Item page)A first dark matter map projected on the night sky. An ultimate encounter between the digital world of modern astronomical observations, and nature: the mysterious dark matter mapped on top of the everyday “night” stellar sky. A visualization that condenses Terabytes of astronomical data to a simple map.Metadata for Peta-data (62 bit: 262 =6*1017, 600 Pb)With pointers, one can connect everything in the Information Universe. Pointers are often inserted in Metadata (data about data) - an ultimate tool for dealing with Big Data. It is possible to create unique pointers to hundreds of Petabytes of data, using a string of less than 64 bits. This is what makes pointers so powerful and indispensable in current and future stages of the big data era; not only for astronomical research, but also for companies like Google, Amazon and Facebook.Downloading the Universe (Item page)The universe can be seen as a spreadsheet, certainly in the way we map it on our computers (in vitro), but also in nature (in vivo). Perceiving the Universe as a spreadsheet links bit to It.Meta data (Item page)A visualisation of the enormous complexity of data models which trace all pointers between data items. (picture: thrilling still from a full dome animation of a data model)Future (astronomical) datasets (item page)While current telescopes collect astronomical datasets of Terabytes, future telescopes such as the LSST and the Euclid satellite, instead, will collect Petabytes. These enormous amounts of data need a whole new approach to data management. For the Euclid satellite my “Universe as a spreadsheet” approach has been adopted.The Euclid satellite (Item page) – Guest author: Margot BrouwerEuclid is ESA’s new space mission to map the Dark Universe. At a distance of 1.5 million kilometres from Earth, this telescope will observe billions of galaxies. Its goal: to shed light on the nature of Dark Matter and Dark Energy, which make up 95% of our Universe. Dr. Margot Brouwer, Dutch scientific communication officer for Euclid, will explain more.The Information Universe (Item page)The resemblance of the overall structure of the real observed Universe (in vivo) with the simulated universe (in vitro), based on the concurrent cosmological model, gave a lot of credit to the latter. When we zoom out the Universe, we see billions of galaxies forming a web-like structure. Amazingly, astronomers can now compute and simulate these structures with very large supercomputers.The lost boy (Item page)Information is timeless, and knows no boundaries. It crosses over the in vivo and the in vitro Information Universe. This concept is well illustrated through daily life stories involving time. At the age of five, a boy loses sight of his older brother on a train in India, and eventually gets lost on the streets of Mumbai. Twenty years later, after being adopted by a family in Australia, he is able to find his natural mother (in vivo) through only searching on Google maps (in vitro).Qbits (50 qbit: 250 =1.1*1015 qbit, 1 Pbit) – Guest author: Lieven VandersypenUsing fundamental particles (quanta, such as electrons) to perform calculations and build computers, is one of the most exciting cross-overs between the in vivo and the in vitro Information Universe. Prof. Lieven Vandersypen, who leads a Quantum Computing group at TU Delft in the Netherlands, will explain how this technology will change the way we compute.Quantum entanglement (Item page) – Guest author: Lieven VandersypenThe states of two particles can be intimately linked (entangled), no matter how far they are separated. What Einstein famously dismissed as “spooky action at a distance”, can now be established on demand at TU Delft in the Netherlands. Prof. Vandersypen will explain how his research group, for the first time ever, both create and apply this entanglement in laboratory.Entanglement (item page) - EVThe Square Kilometre Array (64 bit: 264 =1.3*1018, 1 Eb) – Guest author: TBAThe Square Kilometre Telescope will collect data at the rate of the global internet traffic of 2013, in its endeavour to answer fundamental questions about the origin and evolution of the Universe, and its search for extra-terrestrial life.Cryptography (128 bit: 2128 =3.4*1038) – Guest author Tanja LangeEncrypted messages should not be decoded by adversaries, be they criminals or hostile countries. Cryptography enables secure communications and is one of the few applications which require 128-bit numbers. A guest author will explain more.Chapter 3: Deep spaceThe Desert (128-256 bit) Theoretical physics is not progressing much in the last decennia – some call it a crisis. Likely, an observational breakthrough is out of reach: the highest man-made information density on earth is produced by the high energy accelerators at CERN. But these accelerators have to be 1013 -1015 more powerful to reach the fundamental unit of information, which is probably at the same level of the Planck length. Unfortunately, there is no way to reach this unit of information with these instruments. This enormous gap in reaching all the domains in the Information Universe is illustrated in a figure and in a very sobering, but instructive table in the Appendix.Black holes (128-256 bit?) – Guest author: Manus VisserCan information disappear into a black hole? The Information paradox. Stephen Hawking wondered it and started a field in which space and time are described in terms of information. Dr. Manus Visser, expert on gravity and space-time, will explain more.Observing a Black Hole: Event Horizon Telescope – Guest author: Heino FalckeThe first image of a black hole. Prof. Heino Falcke, chair of the Event Horizon Telescope Science Council, will explain how information from a world-wide network of telescopes was combined using atomic clocks, to create the first ever image of a black hole. (Picture: first image of a black hole)Cogwheels: a deeper level – Guest author: Gerard 't HooftNobel laureate ‘t Hooft explains his views on cogwheels, carrying the fundamental information in the Universe.Gravitational waves – Guest author: Chris van den BroeckLinks: The Universe as a spreadsheetLinks, joins, references, URLs, blockchain, associations and even entanglement in physics are all different words for the same building block, forming the connections in the Information Universe.Cosmic Microwave Background – Guest author: Margot BrouwerParticles of light created in the hot and dense state of the Universe after the Big Bang are still flying through the Universe today. Together, these 1077 photons contain the largest amount of information known in the Universe. This information can still be accessed through telescopes, and brings us invaluable information about the dawn of our Universe.Emergent Gravity – Guest author: Erik VerlindeProf. Erik Verlinde, professor of theoretical physics at the University of Amsterdam, won the Spinoza prize for his new theory explaining gravity. In his theory, all matter, space and time consist of information and are all connected by entanglement. If this theory is correct, the information content of the entire Universe is 2399. This is the highest power described in this book, and actually, in physics.Chapter 4: It from BitOne big information processing machine – Guest author: Gerard 't Hooft (TBC)t Hooftt Hooft: : ““there is something happening at a different level of nature”there is something happening at a different level of nature”..On the origin of physical information. – Guest author: Stefano GottardiThe ear In the ear information is copied a dozen times!The eye – on the visual perception of data- climate change. Links to - facts and fakes- the system of ScienceThe System of ScienceHow does this system work? Discussing Hegel’s system of science, logic, technology, Nature, life, physics, consciousness.Artificial IntelligenceThe machine learning and the data-base oriented communities are still living on different planets. I discuss and revisit Tegmark’s recent book Life 3.0 by comparing 3 crosscuts through the Information Universe: i) the classical computer centric view ii) the data centric view iii) the artificial intelligence view.Information densityThe average information density of the universe can be compared to that of written text.Black Body radiation On the information aspects of the third big physical breakthrough of the 20th century (next to General relativity and quantum mechanics).EntropyDiscussing Shannon’s work and identifying that “Information only exists in relation to its environment”. Examples will be given.Cosmic information, cosmogenesis and dark energy by PadmanabhanCosmic information connects the cosmological constant to cosmogenesisIt from BitIs the Universe one big information processing machine?ConsciousnessVery little is known about the consciousness and I refrain from addressing the consciousness per se. A relevant list of about 5 facts we do know are listed. Any view on the relation between the consciousness and the Information Universe should at least deal with this list.Somnium – Musician Jacco Gardner performing at DOTLiveplanetarium at Eurosonic 2019 show case music festival- Inspired by Kepler’s Somnium – directed by EV The Information UniverseAn overview.Facts and fakesHow is all this related to the current facts and fakes issues on the Internet? How do you make sure that what you are reading is accurate and comes from a reliable source?The link between Open Science, FAIR and reliability of data.

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Book SynopsisThis book is a guide to numerical methods for solving fluid dynamics problems. The most widely used discretization and solution methods, which are also found in most commercial CFD-programs, are described in detail. Some advanced topics, like moving grids, simulation of turbulence, computation of free-surface flows, multigrid methods and parallel computing, are also covered. Since CFD is a very broad field, we provide fundamental methods and ideas, with some illustrative examples, upon which more advanced techniques are built. Numerical accuracy and estimation of errors are important aspects and are discussed in many examples. Computer codes that include many of the methods described in the book can be obtained online. This 4th edition includes major revision of all chapters; some new methods are described and references to more recent publications with new approaches are included. Former Chapter 7 on solution of the Navier-Stokes equations has been split into two Chapters to allow for a more detailed description of several variants of the Fractional Step Method and a comparison with SIMPLE-like approaches. In Chapters 7 to 13, most examples have been replaced or recomputed, and hints regarding practical applications are made. Several new sections have been added, to cover, e.g., immersed-boundary methods, overset grids methods, fluid-structure interaction and conjugate heat transfer.Table of ContentsBasic Concepts of Fluid Flow.- Introduction to Numerical Methods.- Finite Difference Methods.- Finite Volume Methods.- Solution of Linear Equation Systems.-Methods for Unsteady Problems.- Solution of the Navier-Stokes Equations.- Complex Geometries.- Turbulent Flows.- Compressible Flows.- Efficiency, Accuracy and Grid Quality.- Special Topics.

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Book SynopsisThis book is the second edition of an excellent undergraduate-level overview of classical and modern physics, intended for students of physics and related subjects, and also perfectly suited for the education of physics teachers. The twelve-chapter book begins with Newton’s laws of motion and subsequently covers topics such as thermodynamics and statistical physics, electrodynamics, special and general relativity, quantum mechanics and cosmology , the standard model and quantum chromodynamics. The writing is lucid, and the theoretical discussions are easy to follow for anyone comfortable with standard mathematics.An important addition in this second edition is a set of exercises and problems, distributed throughout the book. Some of the problems aim to complement the text, others to provide readers with additional useful tools for tackling new or more advanced topics. Furthermore, new topics have been added in several chapters; for example, the discovery of extra-solar planets from the wobble of their mother stars, a discussion of the Landauer principle relating information erasure to an increase of entropy, quantum logic, first order quantum corrections to the ideal gas equation of state due to the Fermi-Dirac and Bose-Einstein statistics. Both gravitational lensing and the time-correction in geo-positioning satellites are explained as theoretical applications of special and general relativity. The discovery of gravitational waves, one of the most important achievements of physical sciences, is presented as well. Professional scientists, teachers, and researchers will also want to have this book on their bookshelves, as it provides an excellent refresher on a wide range of topics and serves as an ideal starting point for expanding one’s knowledge of new or unfamiliar fields. Readers of this book will not only learn much about physics, they will also learn to love it.Trade ReviewFrom the reviews of the first edition:Selected by Choice magazine as an "Outstanding Academic Title" for 2014“This is a very high-quality presentation. The writing is lucid, and the theoretical discussions are easy to follow for anyone comfortable with the mathematics. … the work is a valuable addition to college libraries. Professionals and researchers will also want it on their bookshelves; it provides an excellent refresher on a wide range of topics and can serve as a good starting point for expanding knowledge of new or unfamiliar subjects. Summing Up: Highly recommended. Lower-division undergraduates and above.” (A. Spero, Choice, Vol. 51 (9), May, 2014)“It describes all the major developments and theories regarding the description of the universe we live on, from the very small to the very large. … I highly recommend this book to any physicist. It will not only be a fun and an easy read but also a useful revision of all the main concepts in physics. Undergraduate and graduate physics students definitely should read it. … appropriate for scientists in other fields who have a genuine interest for physics.” (Monica Pierri-Galvao, Contemporary Physics, April, 2014)Table of ContentsGravitation and Newton Laws.- Entropy, Statistical Physics and Information.- Electromagnetism and Maxwell's Equations.- Electromagnetic Waves.- Special Theory of Relativity.- Atoms and Quantum Theory.- Quantum Electrodynamics.- Fermi-Dirac and Bose-Einstein Statistics.- Four Fundamental Forces.- General Relativity and Cosmology.- Unification of the Forces of Nature.- Physics and Life.

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Book SynopsisThe Laplace transform is a useful mathematical tool encountered by students of physics, engineering, and applied mathematics, within a wide variety of important applications in mechanics, electronics, thermodynamics and more. However, students often struggle with the rationale behind these transforms, and the physical meaning of the transform results. Using the same approach that has proven highly popular in his other Student''s Guides, Professor Fleisch addresses the topics that his students have found most troublesome; providing a detailed and accessible description of Laplace transforms and how they relate to Fourier and Z-transforms. Written in plain language and including numerous, fully worked examples. The book is accompanied by a website containing a rich set of freely available supporting materials, including interactive solutions for every problem in the text, and a series of podcasts in which the author explains the important concepts, equations, and graphs of every section Table of Contents1. The Fourier and Laplace transforms; 2. Laplace transform examples; 3. Properties of the Laplace transform; 4. Applications of the Laplace transform; 5. The Z-transform; References; Index.

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Book SynopsisTrade Review"Stimulating reading" --New ScientistTable of ContentsFundamental principles of theoretical physics; The Gibbs distribution; Ideal gases; Solids; Non-ideal gases; Solutions; Chemical reactions; Fluctuations; Surfaces.

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Book SynopsisThis textbook offers a detailed and self-contained presentation of quantum field theory, suitable for advanced undergraduate and graduate level courses. The author provides full derivations wherever possible and adopts a pedagogical tone without sacrificing rigour. A fully worked solutions manual is available online for instructors.Trade Review'This new and very welcome introduction to quantum field theory takes the reader from the basics of classical physics and the beauty of group theory to the intricacies and elegance of gauge field theories. Students and researchers alike will treasure this fresh approach to one of the foundation stones of modern physics.' Thomas Appelquist, Yale University'I wish this text had been available the last time I taught quantum field theory. The author provides clear, detailed expositions, which serve students with diverse backgrounds for multiple course syllabi.' Steve Gottlieb, Indiana University'The rigorous and logical approach makes this text certainly one to be seriously considered for use in a quantum field theory course. In any case, it is one which practitioners will definitely want to have within easy reach on their bookshelf.' Barry Holstein, University of Massachusetts Amherst'Both as an introductory text and as an excellent single-volume compendium on quantum field theory, this book is highly recommended for students as well as practitioners at all levels.' Wolfram Weise, Technical University of MunichTable of Contents1. Lorentz and Poincare Invariance; 2. Classical Mechanics; 3. Relativistic Classical Fields; 4. Relativistic Quantum Mechanics; 5. Introduction to Particle Physics; 6. Formulation of Quantum Field Theory; 7. Interacting Quantum Field Theories; 8. Symmetries and Renormalization; 9. Nonabelian Gauge Theories.

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Book SynopsisThe book introduces classical mechanics. It does so in an informal style with numerous fresh, modern and inter-disciplinary applications assuming no prior knowledge of the necessary mathematics. The book provides a comprehensive and self-contained treatment of the subject matter up to the forefront of research in multiple areas.Table of ContentsPart I: Newtonian Mechanics 1: Introduction 2: Newton's Three Laws 3: Energy and Work 4: Introductory Rotational Dynamics 5: The Harmonic Oscillator 6: Wave Mechanics & Elements of Mathematical Physics Part II: Langrangian Mechanics 7: Introduction 8: Coordinates & Constraints 9: The Stationary Action Principle 10: Constrained Langrangian Mechanics 11: Point Transformations in Langrangian Mechanics 12: The Jacobi Energy Function 13: Symmetries & Langrangian-Hamiltonian-Jacobi Theory 14: Near-Equilibrium Oscillations 15: Virtual Work & d'Alembert's Principle Part III: Canonical Mechanics 16: Introduction 17: The Hamiltonian & Phase Space 18: Hamiltonian's equations & Routhian Reduction 19: Poisson Brackets & Angular momentum 20: Canonical & Gauge Transformations 21: Hamilton-Jacobi Theory 22: Liouville's Theorem & Classical Statistical Mechanics 23: Constrained Hamiltonian Dynamics 24: Autonomous Geometrical Mehcanics 25: The Structure of Phase Space 26: Near-Integrable Systems Part IV: Classical Field Theory 27: Introduction 28: Langrangian Field Theory 29: Hamiltonian Field Theory 30: Clssical Electromagnetism 31: Neother's Theorem for Fields 32: Classical Path-Integrals Part V: Preliminary Mathematics 33: The (Not so?) Basics 34: Matrices 35: Partial Differentiation 36: Legendre Transformations 37: Vector Calculus 38: Differential equations 39: Calculus of Variations Part VI: Advanced Mathematics 40: Linear Algebra 41: Differential Geometry Part VII: Exam Style Questions Appendix A: Noether's Theorem Explored Appendix B: The Action Principle Explored Appendix C: Useful Relations Appendxi D: Poisson & Nambu Brackets Explored Appendix: Canonical Transformations Explored Appendix F: Action-Angle Variables Explored Appendix G: Statistical Mechanics Explored Appendix H: Biographies

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Book SynopsisQuantum theory (QT) is the best, most useful physics theory ever invented. For example, ubiquitous are cell phones, laser scanners, medical imagers, all inventions depending on QT. However, there is something deeply wrong with QT. It describes the probabilities of what happens, but it does not give a description of what actually happens. Most (but not all) physicists are not worried about this flaw, the probabilities are good enough for them. Other physicists, the author included, believe that is not good enough. The purpose of physics is to describe reality. To not do so is to abandon ''the great enterprise'' (John Bell). This book shows one way to alter QT so that the new theory does describe what actually happens. This theory, created over three decades ago, has been called the ''Continuous Spontaneous Localization'' (CSL) theory.Many experiments over this period have tested CSL, and so far it is neither confirmed nor refuted. This book shows how CSL works, and discusses its consequTrade ReviewA most welcome addition to the physics literature written with extreme care and covering the objective subject matter in a thorough professional and methodical manner. * Daniel Sudarsky, UNAM, Mexico City *A book of very high quality presenting a way of modifying quantum mechanics to remove some of its most serious problems (especially the measurement problem). * Kelvin McQueen, Chapman University, Orange, California *Pearle is the master of this material and writes with beautiful clarity and well-judged occasional witticisms and side-remarks. His experience as teacher, as well as researcher, shows in the vivid explanations, and the careful and consistent level of detail in the exposition. * Jeremy Butterfield, University of Cambridge *Table of Contents1: Introduction 2: Continuous Spontaneous Localization (CSL) Theory 3: CSL Theory Refinements 4: Non-Relativistic CSL 5: Spontaneous Localization (SL) Theory 6: Some Experiments Testing CSL 7: Interpretational Remarks 8: Supplement to Chapter 1 9: Supplement to Chapter 2 10: Supplement to Chapter 3 11: Supplement to Chapter 4 12: Supplement to Chapter 5 13: Supplement to Chapter 6 14: Supplement to Chapter 7 15: A Stochastic Differential Equation Cookbook 16: CSL Expressed as a Schrodinger Stochastic DE 17: Applying the CSL Stratonovich Equation to the Free Particle Undergoing Collapse in Position 18: Applying the CSL Stratonovich Equation to the Harmonic Oscillator Undergoing Collapse in Position Appendix A: Gaussians Appendix B: Random Walk Appendix C: Brownian Motion/Wiener Process Appendix D: White Noise Appendix E: White Noise Field Appendix F: Density Matrix Appendix G: Theoretical Constraint Calculations

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Book SynopsisA series of seminal technological revolutions has led to a new generation of electronic devices miniaturized to such tiny scales where the strange laws of quantum physics come into play. There is no doubt that, unlike scientists and engineers of the past, technology leaders of the future will have to rely on quantum mechanics in their everyday work. This makes teaching and learning the subject of paramount importance for further progress. Mastering quantum physics is a very non-trivial task and its deep understanding can only be achieved through working out real-life problems and examples. It is notoriously difficult to come up with new quantum-mechanical problems that would be solvable with a pencil and paper, and within a finite amount of time. This book remarkably presents some 700+ original problems in quantum mechanics together with detailed solutions covering nearly 1000 pages on all aspects of quantum science. The material is largely new to the English-speaking audience. The proTrade ReviewIn his Preface, Victor Galitski, Jr. offers something of an apology for preserving an old-school style to the contents. Nice as it is no such apology is called for with such an excellent book. The publisher, OUP, is to be congratulated on the investment of a professional indexer, who has done a good job. * S.W. Lovesey, Contemporary Physics, *An excellent resource for students and teachers seeking a deep understanding of quantum mechanics * Dr David Bowler, UCL *Finally, the reader receives the English translation of this magnificent book, arguably, the best collection of working problems in Quantum Mechanics. My congratulations are going to thousands of students and working physicists who will definitely find here the material for exercises as well as an inspiration in original research. * David Khmelnitskii, Cavendish Laboratory, Cambridge *Most physicists and physics students will affirm that they learned the subject by working the problems. Here is a treasure trove of quantum problems and solutions - a splendid resource for teachers trying to expand the repertoire of their problem sets and for students of all ages trying to deepen their understanding of the heart of modern physics. * William D. Phillips, NIST, Nobel Laureate Physics 1997 *Provides a wide range of opportunities to learn what quantum mechanics does through an impressive collection of solved problems. [...] The result is a gem of old-world craftsmanship, well worth a place alongside the other classic texts of quantum mechanics in any physicist's library. * Physics Today, *This is a must-have book for anybody who wants to gain working knowledge of quantum mechanics. It gives both fundamental physical understanding and concrete knowledge of specific technical methods and approaches. * Eugene Demler, Harvard University *A treasure-trove of insightful problems and solutions, 'Exploring Quantum Mechanics' provides a unique and rare perspective on quantum physics. Spanning a broad range of subfields, it is a testament to the mastery of the original authors, Galitski Sr. et al., and the translator, Galitski Jr. Students and specialists of quantum mechanics in the English speaking science world will greatly benefit from this invaluable collection. * Gil Refael, CalTech *This collection of problems in quantum physics, probably the largest of its kind in the world, gives the reader the unique possibility to learn to feel at home in the world of quantum mechanics. It includes more than seven hundred problems of various difficulty accompanied by detailed solutions, ranging from elementary single-particle quantum mechanics in one dimension to relativistic field theory and advanced aspects of nuclear physics. * Andrey Varlamov, Italian National Research Council *Table of ContentsPreface ; 1. Operators in Quantum Mechanics ; 2. One-Dimensional Motion ; 3. Orbital Angular Momentum ; 4. Motion in a Spherically-symmetric Potential ; 5. Spin ; 6. Time-Dependent Quantum Mechanics ; 7. Motion in a Magnetic Field ; 8. Perturbation Theory; Variational Method; Sudden and Adiabatic Theory ; 9. Quasi-Classical Approximation; 1/N-Expansion in Quantum Mechanics ; 10. Identical particles; Second quantization ; 11. Atoms and Molecules ; 12. Atomic Nucleus ; 13. Particle Collisions ; 14. Quantum Radiation Theory ; 15. Relativistic Wave Equations ; 16. Appendix

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Book SynopsisThis short guide to modern error analysis is primarily intended to be used in undergraduate laboratories in the physical sciences. No prior knowledge of statistics is assumed. The necessary concepts are introduced where needed and illustrated graphically. The book emphasises the use of computers for error calculations and data fitting.Trade ReviewWith the shift from analytic methods to spreadsheet-based techniques, this book will enable students simultaneously to (a) become fluent in the choice and application of appropriate methods (b) understand the underlying principles. * David Saxon, University of Glasgow *This is a rather beautiful little book. * David J. Hand, International Statistical Review *Table of Contents1. Errors in the physical sciences ; 2. Random errors in measurement ; 3. Uncertainties as probabilities ; 4. Error propagation ; 5. Data visualisation and reduction ; 6. Least-squares fitting of complex functions ; 7. Computer minimisation and the error matrix ; 8. Hypothesis testing - how good are our models ; 9. Topics for further summary

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Book SynopsisBased on course material used by the author at Yale University, this practical text addresses the widening gap found between the mathematics required for upper-level courses in the physical sciences and the knowledge of incoming students.Trade Review`Shankar obviously enjoys his mathematics, and his attitude toward mathematics is simultaneously refreshing and contagious....Dirac notation is intriguingly introduced in the discussion of vector spaces. Finally, the book is richly endowed with well-chosen problems.' American Journal of Physics `Consistent with the needs of science students...a sound mathematical reference for anyone studying or practicing in the physical sciences.' Choice Table of ContentsDifferential Calculus of One Variable. Integral Calculus. Calculus of Many Variables. Infinite Series. Complex Numbers. Functions of a Complex Variable. Vector Calculus. Matrices and Determinants. Linear Vector Spaces. Differential Equations. Answers. Index.

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Book Synopsis

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Book SynopsisThe second edition of this bestselling book provides an overview of the key topics in undergraduate mathematics, allowing beginning graduate students to fill in any gaps in their knowledge. With numerous examples, exercises and suggestions for further reading, it is a must-have for anyone looking to learn some serious mathematics quickly.Trade Review'Reading Garrity is like talking with your favorite uncle - he tells you the essential stories, in a clear and colorful way, and you get just what you need to explore further. The topics are well chosen (and there are more in this new edition). His points of view enrich the reader - not only do you learn what to know, but how to know it. I wish I had had this book when I started graduate school.' John McCleary, Vassar College'I admired one of the intentions behind the first edition of Garrity's All the Math You Missed: to give students the tools to appreciate the applications of mathematics without painting a simplistic picture of 'Applied Mathematics'. In this second edition, he takes this idea to the next level by introducing four additional chapters, dealing primarily with number theory and category theory.' Robert Kotiuga, Boston University'I felt like I was terribly underprepared for graduate school, and Garrity's book helped me fill in some of those gaps. But far more importantly, the welcoming tone made me see that I wasn't alone in feeling anxious, and it made grad school feel less intimidating.' Daniel Erman, University of Wisconsin, Madison'Incoming graduate students would find the book most useful … this book is designed to provide some useful guidance … The writing is clear and easy to read.' Bill Satzer, MAA ReviewsTable of ContentsOn the structure of mathematics; Brief summaries of topics; 1. Linear Algebra; 2. ε and δ real analysis; 3. Calculus for vector-valued functions; 4. Point set topology; 5. Classical Stokes' theorems; 6. Diff erential forms and Stokes' theorem; 7. Curvature for curves and surfaces; 8. Geometry; 9. Countability and the Axiom of Choice; 10. Elementary number theory; 11. Algebra; 12. Algebraic number theory; 13. Complex analysis; 14. Analytic number theory; 15. Lebesgue integration; 16. Fourier analysis; 17. Diff erential equations; 18. Combinatorics and probability theory; 19. Algorithms; 20. Category theory; Appendix A. Equivalence relations; References; Index.

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Book SynopsisFirst published in 1973, this influential work discusses Einstein''s General Theory of Relativity to show how two of its predictions arise: first, that the ultimate fate of many massive stars is to undergo gravitational collapse to form ''black holes''; and second, that there was a singularity in the past at the beginning of the universe. Starting with a precise formulation of the theory, including the necessary differential geometry, the authors discuss the significance of space-time curvature and examine the properties of a number of exact solutions of Einstein''s field equations. They develop the theory of the causal structure of a general space-time, and use it to prove a number of theorems establishing the inevitability of singularities under certain conditions. A Foreword contributed by Abhay Ashtekar and a new Preface from George Ellis help put the volume into context of the developments in the field over the past fifty years.Trade Review'The book is a masterpiece, written by sure hands.' Science'Certain to rank as an outstanding classic of the current advance of relativity theory.' Contemporary Physics'La parution de ce livre est un événement important …' La Recherche'This special 50th anniversary republication of this famous monograph is well welcome addtion to the community. This text helped lay the groundwork for gravitational research for the next 50 years; inspiring and educating generations of researchers. I recommend this text to anyone who is interested in learning the foundation of gravitational research.' Kymani Tieral Keden Armstrong-Williams, https://physicsbookreviewer.blogspot.com/Table of ContentsForeword to the Anniversary Edition Abhay Ashtekar; Preface to the Anniversary Edition George F. R. Ellis; Preface; 1. The role of gravity; 2. Differential geometry; 3. General relativity; 4. The physical significance of curvature; 5. Exact solutions; 6. Causal structure; 7. The Cauchy problem in General Relativity; 8. Space-time singularities; 9. Gravitational collapse and black holes; 10. The initial singularity in the universe; Appendixes; References; Notation; Index.

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Book SynopsisThere is an explosion of interest in dynamical systems in the mathematical community as well as in many areas of science. The results have been truly exciting: systems which once seemed completely intractable from an analytic point of view can now be understood in a geometric or qualitative sense rather easily. Scientists and engineers realize the power and the beauty of the geometric and qualitative techniques. These techniques apply to a number of important nonlinear problems ranging from physics and chemistry to ecology and economics.Computer graphics have allowed us to view the dynamical behavior geometrically. The appearance of incredibly beautiful and intricate objects such as the Mandelbrot set, the Julia set, and other fractals have really piqued interest in the field.This is text is aimed primarily at advanced undergraduate and beginning graduate students.  Throughout, the author emphasizes the mathematical aspects of the theory of discrete dynamicTable of ContentsI One Dimensional Dynamics1.A Visual and Historical Tour2.Examples of Dynamical Systems3.Elementary Definitions4.Hyperbolicity5.An Example: The Logistic Family6.Symbolic Dynamics7.Topological Conjugacy8.Chaos9.Structural Stability10.Sharkovsky's Theorem11.The Schwarzian Derivative 12.Bifurcations13.Another View of Period Three14.Period-Doubling Route to Chaos15.Homoclinic Points and Bifurcations16.Maps of the Circle17.Morse-Smale DiffeomorphismsII Complex Dynamics18.Quadratic Maps Revisited19.Normal Families and Exceptional Points 20.Periodic Points21.Properties of the Julia Set22.The Geometry of the Julia Sets23.Neutral Periodic Points24.The Mandelbrot Set25.Rational Maps26.The Exponential FamilyIII Higher Dimensional Dynamics27.Dynamics of Linear Maps28.The Smale Horseshoe Map29.Hyperbolic Toral Automorphisms30.Attractors31.The Stable and Unstable Manifold Theorem32.Global Results and Hyperbolic Maps33.The Hopf Bifurcation34.The Herron MapAppendix: Mathematical Preliminaries

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Book SynopsisQuantum Continuous Variables introduces the theory of continuous variable quantum systems, from its foundations based on the framework of Gaussian states to modern developments, including its applications to quantum information and forthcoming quantum technologies. This book addresses the theory of Gaussian states, operations, and dynamics in great depth and breadth, through a novel approach that embraces both the Hilbert space and phase descriptions.The second edition of this book has been revised throughout, and updated to include new topics, such as boson sampling, coherent feedback, nonlinear control, as well as several new solved problems.The volume includes coverage of entanglement theory and quantum information protocols, and their connection with relevant experimental set-ups. General techniques for non-Gaussian manipulations also emerge as the treatment unfolds and are demonstrated with specific case studies.This book willTable of ContentsChapter 1: Introduction. Chapter 2: Quantum Mechanics: Instructions for Use. Chapter 3: Gaussian States of Continuous Variable Systems. Chapter 4: Phase Space Methods. Chapter 5: Gaussian Operations. Chapter 6: Diffusive Dynamics and Continuous Monitoring. Chapter 7: Entanglement of Continuous Variable Systems. Chapter 8: Quantum Information Protocols with Continuous Variables. Chapter 9: A Grand Tour of Continuous Variable Platforms. Appendix A: A Note on Fermions. Appendix B: Some Notable Facts About the Symplectic Group. Appendix C: The Wiener Process. Appendix D: Selected Mathematical Lore on Quantum Channels. Appendix E: Classical and Quantum Estimation Bounds. References. Index.

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Book SynopsisQuantum field theory (QFT), the language of particle physics, is crucial to a physicist''s graduate education. Based on lecture notes for courses taught for many years at Radboud University in the Netherlands, this book presents an alternative approach to teaching QFT using Feynman diagrams. A diagrammatic approach to understanding QFT exposes young physicists to an orthogonal introduction to the theory, bringing new ways to understand challenges in the field. Diagrammatic techniques using Feynman diagrams are used didactically, starting from simple discussions in lower dimensions to more complex topics in the Standard Model. Worked examples and exercises, for which solutions are available online, help the reader develop a deep understanding and intuition that enhances their problem-solving skills and understanding of QFT. Classroom-tested, this accessible book is valuable resource for graduate students and researchers.Trade Review'Highly recommended.' E. Kincanon, Choice MagazineTable of ContentsPreface. 1. QFT in zero dimensions; 2. Loop expansion and the effective action; 3. On renormalization; 4. More fields in zero dimensions; 5. QFT in Euclidean spaces; 6. QFT in Minkowski space; 7. Scattering processes; 8. Introduction to loop calculations; 9. More on renormalization; 10. Dirac particles; 11. Helicity techniques for Dirac particles; 12. Vector particles; 13. Quantum electrodynamics; 14. Higher-order effects in QED; 15. Quantum chromodynamics; 16. Higher-order effects in QCD; 17. Electroweak theory; 18. More example computations; Appendices.

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Book SynopsisOvercome your study inertia and polish your knowledge of physics Physics I: 501 Practice Problems For Dummies gives you 501 opportunities to practice solving problems from all the major topics covered you Physics I classin the book and online! Get extra help with tricky subjects, solidify what you've already learned, and get in-depth walk-throughs for every problem with this useful book. These practice problems and detailed answer explanations will help you succeed in this tough-but-required class, no matter what your skill level. Thanks to Dummies, you have a resource to help you put key concepts into practice. Work through practice problems on all Physics I topics covered in school classesStep through detailed solutions to build your understandingAccess practice questions online to study anywhere, any timeImprove your grade and up your study game with practice, practice, practiceThe material presented in Physics I: 501 Practice Problems For Dummies is an excellent resource for students, as well as parents and tutors looking to help supplement Physics I instruction. Physics I: 501 Practice Problems For Dummies (9781119883715) was previously published as Physics I Practice Problems For Dummies (9781118853153). While this version features a new Dummies cover and design, the content is the same as the prior release and should not be considered a new or updated product.Table of ContentsPart 1: The Questions 5 Chapter 1: Reviewing Math Fundamentals and Physics Measurements 7 Chapter 2: Moving along with Kinematics 11 Chapter 3: Moving in a Two-Dimensional World 17 Chapter 4: Pushing and Pulling: The Forces around You 23 Chapter 5: Slipping and Sliding: Motion and Forces 31 Chapter 6: Describing Rotational Motion 39 Chapter 7: Rotating Around in Different Loops 45 Chapter 8: Going with the Flow: Fluids 51 Chapter 9: Getting Some Work Done 57 Chapter 10: Picking Up Some Momentum with Impulse 65 Chapter 11: Rolling Around with Rotational Kinetics and Dynamics 73 Chapter 12: Bouncing with a Spring: Simple Harmonic Motion 87 Chapter 13: Heating Up with Thermodynamics and Heat Transfer 93 Chapter 14: Living in an Ideal World with the Ideal Gas Law 99 Chapter 15: Experiencing the Laws of Thermodynamics 103 Part 2: The Answers 109 Chapter 16: Answers 111 Index 413

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Book SynopsisWill artificial intelligence solve all problems, making scientific formulae redundant? The authors of this book would argue that there is still a vital role in formulating them to make sense of the laws of nature. To derive a formula one needs to follow a series of steps; last of all, check that the result is correct, primarily through the analysis of limiting cases. The book is about unravelling this machinery.Mathematics is the 'queen of all sciences', but students encounter many obstacles in learning the subject — familiarization with the proofs of hundreds of theorems, mysterious symbols, and technical routines for which the usefulness is not obvious upfront. Those interested in the physical sciences could lose motivation, not seeing the wood for the trees.How to Derive a Formula is an attempt to engage these learners, presenting mathematical methods in simple terms, with more of an emphasis on skills as opposed to technical knowledge. Based on intuition and common sense rather than mathematical rigor, it teaches students from scratch using pertinent examples, many taken across the physical sciences.This book provides an interesting new perspective of what a mathematics textbook could be, including historical facts and humour to complement the material.

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Book SynopsisMathematical Models in Science treats General Relativity and Quantum Mechanics in a non-commutative Algebraic Geometric framework.Based on ideas first published in Geometry of Time-Spaces: Non-commutative Algebraic Geometry Applied to Quantum Theory (World Scientific, 2011), Olav Arnfinn Laudal proposes a Toy Model as a Theory of Everything, starting with the notion of the Big Bang in Cosmology, modeled as the non-commutative deformation of a thick point. From this point, the author shows how to extract reasonable models for both General Relativity and Quantum Theory. This book concludes that the universe turns out to be the 6-dimensional Hilbert scheme of pairs of points in affine 3-space. With this in place, one may develop within the model much of the physics known to the reader. In particular, this theory is applicable to the concept of Dark Matter and its effects on our visual universe.Hence, Mathematical Models in Science proves the dependency of deformation theory in Mathematical Physics and summarizes the development of physical applications of pure mathematics developed in the twentieth century.

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Book SynopsisWill artificial intelligence make scientific formulae redundant by eventually solving all current and future physical problems? The authors of this book would argue that there is still a vital role for humans to play in making sense of the laws of nature. To derive a formula one follows a series of steps, only the last of which is to check that the result is correct. The book is about unravelling this machinery.Mathematics is the 'queen of all sciences', but students encounter many obstacles in learning the subject: familiarization with the proofs of hundreds of theorems, mysterious symbols, and technical routines for which the usefulness is not obvious upfront. Learners could lose motivation, not seeing the wood for the trees.This two-volume book How to Derive a Formula is an attempt to engage learners by presenting mathematical methods in as simple terms as possible, with more of an emphasis on skills as opposed to technical knowledge. Based on intuition and common sense rather than mathematical rigour, it teaches students from scratch using pertinent examples, many taken from across the physical sciences to demonstrate the application of the methods taught.This book draws on humour and historical facts to provide an interesting new perspective on what a mathematics textbook could be. The two volumes are presented as an ascent to Everest. Volume 1 covered the necessary basics, taking readers from Base Camp to Camps 1 and 2. This volume moves readers from Camp 2 up to Camps 3 and 4, tackling more advanced methods for deriving formulae. Inevitably, Volume 2 requires readers to tackle more challenging terrain than was experienced in Volume 1 and so is targeted at more advanced students.

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Book SynopsisThis book provides a vivid account of the early history of molecular simulation, a new frontier for our understanding of matter that was opened when the demands of theoretical physicists were met by the availability of the modern computers. Since their inception, electronic computers have enormously increased their performance, thus making possible the unprecedented technological revolution that characterizes our present times. This obvious technological advancement has brought with it a silent scientific revolution in the practice of theoretical physics. In particular, in the physics of matter it has opened up a direct route from the microscopic physical laws to observable phenomena. One can now study the time evolution of systems composed of millions of molecules, and simulate the behaviour of macroscopic materials and actually predict their properties. Molecular simulation has provided a new theoretical and conceptual tool that physicists could only dream of when the foundations of statistical mechanics were laid. Molecular simulation has undergone impressive development, both in the size of the scientific community involved and in the range and scope of its applications. It has become the ubiquitous workhorse for investigating the nature of complex condensed matter systems in physics, chemistry, materials and the life sciences. Yet these developments remain largely unknown outside the inner circles of practitioners, and they have so far never been described for a wider public. The main objective of this book is therefore to offer a reasonably comprehensive reconstruction of the early history of molecular simulation addressed to an audience of both scientists and interested non-scientists, describing the scientific and personal trajectories of the main protagonists and discussing the deep conceptual innovations that their work produced.Trade Review“The authors focus mainly on the development of molecular dynamics, in which the motions of many atoms are simultaneously advanced and tracked in small time steps. They explain the scientific evolution of the field; provide biographies— and numerous photographs— of leading characters … . Computer Meets Theoretical Physics should be on the bookshelf of anyone interested in the history of science.” (Christoph Dellago, Physics Today, October, 2021)Table of ContentsA new science.- The origins of simulation.- The growth of molecular dynamics.- Molecular simulation lands in Europe.- CECAM and the development of molecular simulation.- Simulation comes of age.- Quantum systems and critical phenomena.- A first finishing line and some provisional conclusions.

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Book SynopsisThis textbook presents basic and advanced computational physics in a very didactic style. It contains very-well-presented and simple mathematical descriptions of many of the most important algorithms used in computational physics. The first part of the book discusses the basic numerical methods. The second part concentrates on simulation of classical and quantum systems. Several classes of integration methods are discussed including not only the standard Euler and Runge Kutta method but also multi-step methods and the class of Verlet methods, which is introduced by studying the motion in Liouville space. A general chapter on the numerical treatment of differential equations provides methods of finite differences, finite volumes, finite elements and boundary elements together with spectral methods and weighted residual based methods. The book gives simple but non trivial examples from a broad range of physical topics trying to give the reader insight into not only the numerical treatment but also simulated problems. Different methods are compared with regard to their stability and efficiency. The exercises in the book are realised as computer experiments. Trade ReviewFrom the book reviews:“The well-written monograph about computational physics is based on two-semester lecture courses given by the author on a period of several years for undergraduate physics and biophysics students … . convenient for students and practitioners of computer science, chemistry, and mathematics who are interested in applications of numerical methods in physics and engineering sciences. … well-organized book with a concentration to the important ideas of the methods and physical applications including software, examples, illustrations, and references to further reading.” (Georg Hebermehl, zbMATH, Vol. 1303, 2015)Table of ContentsPart I Numerical Methods.- Error Analysis.- Interpolation.- Numerical Differentiation.- Numerical Integration.- Systems of Inhomogeneous Linear Equations.- Roots and Extremal Points.- Fourier Transformation.- Random Numbers and Monte-Carlo Methods.- Eigenvalue Problems.- Data Fitting.- Discretization of Differential Equations.- Equations of Motion.- Part II Simulation of Classical and Quantum Systems.- Rotational Motion.- Molecular Dynamics.- Thermodynamic Systems.- Random Walk and Brownian Motion.- Electrostatics.- Waves.- Diffusion.- Nonlinear Systems.- Simple Quantum Systems.

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Book SynopsisThis textbook introduces modern techniques based on computer simulation to study materials science. It starts from first principles calculations enabling to calculate the physical and chemical properties by solving a many-body Schroedinger equation with Coulomb forces. For the exchange-correlation term, the local density approximation is usually applied. After the introduction of the first principles treatment, tight-binding and classical potential methods are briefly introduced to indicate how one can increase the number of atoms in the system. In the second half of the book, Monte Carlo simulation is discussed in detail. Problems and solutions are provided to facilitate understanding. Readers will gain sufficient knowledge to begin theoretical studies in modern materials research. This second edition includes a lot of recent theoretical techniques in materials research. With the computers power now available, it is possible to use these numerical techniques to study various physical and chemical properties of complex materials from first principles. The new edition also covers empirical methods, such as tight-binding and molecular dynamics.Table of ContentsAb-Initio Methods.- Tight-Binding Methods.- Empirical Methods and Coarse-Graining.- Monte Carlo Methods.- Quantum Monte Carlo (QMC) Methods.

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Book SynopsisThe book covers different aspects of mathematical methods for Physics. It is designed for graduate courses but a part of it can also be used by undergraduate students. The leitmotiv of the book is the search for a common mathematical framework for a wide class of apparently disparate physical phenomena. An important role, within this respect, is provided by a nonconventional formulation of special functions and polynomials. The proposed methods simplify the understanding of the relevant technicalities and yield a unifying view to their applications in Physics as well as other branches of science.The chapters are not organized through the mathematical study of specific problems in Physics, rather they are suggested by the formalism itself. For example, it is shown how the matrix formalism is useful to treat ray Optics, atomic systems evolution, QED, QCD and Feynman diagrams. The methods presented here are simple but rigorous. They allow a fairly substantive tool of analysis for a variety of topics and are useful for beginners as well as the more experienced researchers.

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Book SynopsisThis book gives a concise introduction to Quantum Mechanics with a systematic, coherent, and in-depth explanation of related mathematical methods from the scattering theory and the theory of Partial Differential Equations.The book is aimed at graduate and advanced undergraduate students in mathematics, physics, and chemistry, as well as at the readers specializing in quantum mechanics, theoretical physics and quantum chemistry, and applications to solid state physics, optics, superconductivity, and quantum and high-frequency electronic devices.The book utilizes elementary mathematical derivations. The presentation assumes only basic knowledge of the origin of Hamiltonian mechanics, Maxwell equations, calculus, Ordinary Differential Equations and basic PDEs. Key topics include the Schrödinger, Pauli, and Dirac equations, the corresponding conservation laws, spin, the hydrogen spectrum, and the Zeeman effect, scattering of light and particles, photoelectric effect, electron diffraction, and relations of quantum postulates with attractors of nonlinear Hamiltonian PDEs. Featuring problem sets and accompanied by extensive contemporary and historical references, this book could be used for the course on Quantum Mechanics and is also suitable for individual study.

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Book SynopsisIt is unlikely that today there is a specialist in theoretical physics who has not heard anything about the algebraic Bethe ansatz. Over the past few years, this method has been actively used in quantum statistical physics models, condensed matter physics, gauge field theories, and string theory.This book presents the state-of-the-art research in the field of algebraic Bethe ansatz. Along with the results that have already become classic, the book also contains the results obtained in recent years. The reader will get acquainted with the solution of the spectral problem and more complex problems that are solved using this method. Various methods for calculating scalar products and form factors are described in detail. Special attention is paid to applying the algebraic Bethe ansatz to the calculation of the correlation functions of quantum integrable models. The book also elaborates on multiple integral representations for correlation functions and examples of calculating the long-distance asymptotics of correlations.This text is intended for advanced undergraduate and postgraduate students, and specialists interested in the mathematical methods of studying physical systems that allow them to obtain exact results.

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Book SynopsisBoth a theoretical physicist and mathematician, Ludwig Faddeev is best known for "the Faddeev equations", the first mathematically well-posed formulation of the quantum-mechanical three-body problem, which are foundational in few-body physics. Having made multiple seminal contributions to theoretical physics (Faddeev–Popov ghosts, Faddeev–Senjanovic quantization, Faddeev–Jackiw quantization among others), he was conferred numerous prizes and memberships of prestigious institutions in recognition of the importance of his work. These include the Dannie Heineman Prize, the Dirac Prize, the Max Planck Medal, the Shaw Prize and the Lomonosov Gold Medal among others. A gathering of contributions from some of the biggest names in physics and mathematics, this volume serves as a tribute to this legendary figure in mathematical physics. Volume contributors include: Fields medallist Sir Michael Atiyah, Jürg Fröhlich, Roman Jackiw, Louis Nirenberg, Samson Shatashvili, Vladimir Korepin as well as Nobel laureates Frank Wilczek, C N Yang and Gerard 't Hooft.

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