Download or read book Explorations in Mathematical Physics written by Don Koks and published by Springer Science & Business Media. This book was released on 2006-09-15 with total page 549 pages. Available in PDF, EPUB and Kindle. Book excerpt: Have you ever wondered why the language of modern physics centres on geometry? Or how quantum operators and Dirac brackets work? What a convolution really is? What tensors are all about? Or what field theory and lagrangians are, and why gravity is described as curvature? This book takes you on a tour of the main ideas forming the language of modern mathematical physics. Here you will meet novel approaches to concepts such as determinants and geometry, wave function evolution, statistics, signal processing, and three-dimensional rotations. You will see how the accelerated frames of special relativity tell us about gravity. On the journey, you will discover how tensor notation relates to vector calculus, how differential geometry is built on intuitive concepts, and how variational calculus leads to field theory. You will meet quantum measurement theory, along with Green functions and the art of complex integration, and finally general relativity and cosmology. The book takes a fresh approach to tensor analysis built solely on the metric and vectors, with no need for one-forms. This gives a much more geometrical and intuitive insight into vector and tensor calculus, together with general relativity, than do traditional, more abstract methods. Don Koks is a physicist at the Defence Science and Technology Organisation in Adelaide, Australia. His doctorate in quantum cosmology was obtained from the Department of Physics and Mathematical Physics at Adelaide University. Prior work at the University of Auckland specialised in applied accelerator physics, along with pure and applied mathematics.
Download or read book Explorations in Mathematical Physics written by Don Koks and published by Springer. This book was released on 2008-11-01 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Have you ever wondered why the language of modern physics centres on geometry? Or how quantum operators and Dirac brackets work? What a convolution really is? What tensors are all about? Or what field theory and lagrangians are, and why gravity is described as curvature? This book takes you on a tour of the main ideas forming the language of modern mathematical physics. Here you will meet novel approaches to concepts such as determinants and geometry, wave function evolution, statistics, signal processing, and three-dimensional rotations. You will see how the accelerated frames of special relativity tell us about gravity. On the journey, you will discover how tensor notation relates to vector calculus, how differential geometry is built on intuitive concepts, and how variational calculus leads to field theory. You will meet quantum measurement theory, along with Green functions and the art of complex integration, and finally general relativity and cosmology. The book takes a fresh approach to tensor analysis built solely on the metric and vectors, with no need for one-forms. This gives a much more geometrical and intuitive insight into vector and tensor calculus, together with general relativity, than do traditional, more abstract methods. Don Koks is a physicist at the Defence Science and Technology Organisation in Adelaide, Australia. His doctorate in quantum cosmology was obtained from the Department of Physics and Mathematical Physics at Adelaide University. Prior work at the University of Auckland specialised in applied accelerator physics, along with pure and applied mathematics.
Download or read book Mathematical Explorations written by Alan F. Beardon and published by Cambridge University Press. This book was released on 2016-10-13 with total page 129 pages. Available in PDF, EPUB and Kindle. Book excerpt: Provides readers with experience of working on difficult unsolved problems. No deep mathematical background is required.
Download or read book Microstates Entropy and Quanta written by Don Koks and published by Springer. This book was released on 2019-01-25 with total page 541 pages. Available in PDF, EPUB and Kindle. Book excerpt: Statistical mechanics: the bane of many a physics student, and traditionally viewed as a long parade of ensembles, partition functions, and partial derivatives. But the subject needn't be arcane. When pared back to its underlying concepts and built from the ground up, statistical mechanics takes on a charm of its own, and sheds light on all manner of physical phenomena. This book presents a straightforward introduction to the key concepts in statistical mechanics, following the popular style of the author's highly successful textbook "Explorations in Mathematical Physics". Offering a clear, conceptual approach to the subject matter, the book presents a treatment that is mathematically complete, while remaining very accessible to undergraduates. It commences by asking: why does an ink drop spread out in a bathtub of water? This showcases the importance of counting configurations, which leads naturally to ideas of microstates, energy, entropy, thermodynamics, and physical chemistry. With this foundation, the Boltzmann distribution writes itself in its fullest form, and this opens the door to the Maxwell distribution and related areas of thermal conductivity and viscosity. Quantum ideas then appear: bosons via Einstein's and Debye's theories of heat capacity, and fermions via electrical conduction and low-temperature heat capacity of metals. The text ends with a detailed derivation of blackbody radiation, and uses this to discuss the greenhouse effect, lasers, and cosmology. Suitable for use with core undergraduate courses in statistical mechanics and thermodynamics, this book concentrates on using solid mathematics, while avoiding cumbersome notation. All the necessary mathematical steps are included in the body of the text and in the worked examples. Reviews of Explorations in Mathematical Physics by Don Koks, 2006 "With enjoyable and sometimes surprising excursions along the way, the journey provides a fresh look at many familiar topics, as it takes us from basic linear mathematics to general relativity... look forward to having your geometric intuition nourished and expanded by the author's intelligent commentaries." (Eugen Merzbacher, University of North Carolina) "... an interesting supplement to standard texts for teaching mathematical methods in physics, as it will add alternative views that could serve as additional material." (S. Marcelja, Australian Journal of Physics) "... a tour through the main ideas forming the language of modern mathematical physics ...it is a difficult task for the author to decide what is a good balance between the topics and their presentation, but in this case it has been achieved. ...for those physicists who would like to be exposed to clear motivation and careful explanation of the basics of the present-day apparatus of mathematical physics." (Ivailo Mladenov, Mathematical Reviews).
Download or read book Explorations in Monte Carlo Methods written by Ronald W. Shonkwiler and published by Springer Science & Business Media. This book was released on 2009-08-11 with total page 249 pages. Available in PDF, EPUB and Kindle. Book excerpt: Monte Carlo methods are among the most used and useful computational tools available today, providing efficient and practical algorithims to solve a wide range of scientific and engineering problems. Applications covered in this book include optimization, finance, statistical mechanics, birth and death processes, and gambling systems. Explorations in Monte Carlo Methods provides a hands-on approach to learning this subject. Each new idea is carefully motivated by a realistic problem, thus leading from questions to theory via examples and numerical simulations. Programming exercises are integrated throughout the text as the primary vehicle for learning the material. Each chapter ends with a large collection of problems illustrating and directing the material. This book is suitable as a textbook for students of engineering and the sciences, as well as mathematics.
Download or read book Advanced General Relativity written by John Stewart and published by Cambridge University Press. This book was released on 1993-11-26 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: A self-contained introduction to advanced general relativity.
Download or read book Poetry of the Universe written by Robert Osserman and published by Anchor. This book was released on 2011-04-27 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the bestselling literary tradition of Lewis Thomas's Lives of a Cell and James Watson's The Double Helix, Poetry of the Universe is a delightful and compelling narrative charting the evolution of mathematical ideas that have helped to illuminate the nature of the observable universe. In a richly anecdotal fashion, the book explores teh leaps of imagination and vision in mathematics that have helped pioneer our understanding of the world around us.
Download or read book Mathematical Expeditions written by Frank J. Swetz and published by JHU Press. This book was released on 2012-07-16 with total page 205 pages. Available in PDF, EPUB and Kindle. Book excerpt: "A collection of over 500 culturally and historically diverse mathematical problems carefully chosen to enrich mathematics teaching from middle school through the college level."--Provided by publisher.
Download or read book Explorations in Quantum Computing written by Colin P. Williams and published by Springer Science & Business Media. This book was released on 2010-12-07 with total page 724 pages. Available in PDF, EPUB and Kindle. Book excerpt: By the year 2020, the basic memory components of a computer will be the size of individual atoms. At such scales, the current theory of computation will become invalid. "Quantum computing" is reinventing the foundations of computer science and information theory in a way that is consistent with quantum physics - the most accurate model of reality currently known. Remarkably, this theory predicts that quantum computers can perform certain tasks breathtakingly faster than classical computers – and, better yet, can accomplish mind-boggling feats such as teleporting information, breaking supposedly "unbreakable" codes, generating true random numbers, and communicating with messages that betray the presence of eavesdropping. This widely anticipated second edition of Explorations in Quantum Computing explains these burgeoning developments in simple terms, and describes the key technological hurdles that must be overcome to make quantum computers a reality. This easy-to-read, time-tested, and comprehensive textbook provides a fresh perspective on the capabilities of quantum computers, and supplies readers with the tools necessary to make their own foray into this exciting field. Topics and features: concludes each chapter with exercises and a summary of the material covered; provides an introduction to the basic mathematical formalism of quantum computing, and the quantum effects that can be harnessed for non-classical computation; discusses the concepts of quantum gates, entangling power, quantum circuits, quantum Fourier, wavelet, and cosine transforms, and quantum universality, computability, and complexity; examines the potential applications of quantum computers in areas such as search, code-breaking, solving NP-Complete problems, quantum simulation, quantum chemistry, and mathematics; investigates the uses of quantum information, including quantum teleportation, superdense coding, quantum data compression, quantum cloning, quantum negation, and quantum cryptography; reviews the advancements made towards practical quantum computers, covering developments in quantum error correction and avoidance, and alternative models of quantum computation. This text/reference is ideal for anyone wishing to learn more about this incredible, perhaps "ultimate," computer revolution. Dr. Colin P. Williams is Program Manager for Advanced Computing Paradigms at the NASA Jet Propulsion Laboratory, California Institute of Technology, and CEO of Xtreme Energetics, Inc. an advanced solar energy company. Dr. Williams has taught quantum computing and quantum information theory as an acting Associate Professor of Computer Science at Stanford University. He has spent over a decade inspiring and leading high technology teams and building business relationships with and Silicon Valley companies. Today his interests include terrestrial and Space-based power generation, quantum computing, cognitive computing, computational material design, visualization, artificial intelligence, evolutionary computing, and remote olfaction. He was formerly a Research Scientist at Xerox PARC and a Research Assistant to Prof. Stephen W. Hawking, Cambridge University.
Download or read book Mathematics for Physics written by Michael Stone and published by Cambridge University Press. This book was released on 2009-07-09 with total page 821 pages. Available in PDF, EPUB and Kindle. Book excerpt: An engagingly-written account of mathematical tools and ideas, this book provides a graduate-level introduction to the mathematics used in research in physics. The first half of the book focuses on the traditional mathematical methods of physics – differential and integral equations, Fourier series and the calculus of variations. The second half contains an introduction to more advanced subjects, including differential geometry, topology and complex variables. The authors' exposition avoids excess rigor whilst explaining subtle but important points often glossed over in more elementary texts. The topics are illustrated at every stage by carefully chosen examples, exercises and problems drawn from realistic physics settings. These make it useful both as a textbook in advanced courses and for self-study. Password-protected solutions to the exercises are available to instructors at www.cambridge.org/9780521854030.
Download or read book Explorations in Harmonic Analysis written by Steven G. Krantz and published by Springer Science & Business Media. This book was released on 2009-05-24 with total page 367 pages. Available in PDF, EPUB and Kindle. Book excerpt: This self-contained text provides an introduction to modern harmonic analysis in the context in which it is actually applied, in particular, through complex function theory and partial differential equations. It takes the novice mathematical reader from the rudiments of harmonic analysis (Fourier series) to the Fourier transform, pseudodifferential operators, and finally to Heisenberg analysis.
Download or read book Elements of Pure and Applied Mathematics written by Harry Lass and published by Courier Corporation. This book was released on 2009-11-18 with total page 514 pages. Available in PDF, EPUB and Kindle. Book excerpt: Completely self-contained, this survey explores the important topics in pure and applied mathematics. Each chapter can be read independently of the others, and all subjects are unified by cross-references to the complete work. Numerous worked-out examples appear throughout the text, and review questions and references conclude each section. 1957 edition.
Download or read book Mathematics for Physicists written by Alexander Altland and published by Cambridge University Press. This book was released on 2019-02-14 with total page 723 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook is a comprehensive introduction to the key disciplines of mathematics - linear algebra, calculus, and geometry - needed in the undergraduate physics curriculum. Its leitmotiv is that success in learning these subjects depends on a good balance between theory and practice. Reflecting this belief, mathematical foundations are explained in pedagogical depth, and computational methods are introduced from a physicist's perspective and in a timely manner. This original approach presents concepts and methods as inseparable entities, facilitating in-depth understanding and making even advanced mathematics tangible. The book guides the reader from high-school level to advanced subjects such as tensor algebra, complex functions, and differential geometry. It contains numerous worked examples, info sections providing context, biographical boxes, several detailed case studies, over 300 problems, and fully worked solutions for all odd-numbered problems. An online solutions manual for all even-numbered problems will be made available to instructors.
Download or read book Physics of the Impossible written by Michio Kaku and published by Anchor. This book was released on 2008-03-11 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: NATIONAL BESTSELLER • Inspired by the fantastic worlds of Star Trek, Star Wars, and Back to the Future, the renowned theoretical physicist and national bestselling author of The God Equation takes an informed, serious, and often surprising look at what our current understanding of the universe's physical laws may permit in the near and distant future. Teleportation, time machines, force fields, and interstellar space ships—the stuff of science fiction or potentially attainable future technologies? Entertaining, informative, and imaginative, Physics of the Impossible probes the very limits of human ingenuity and scientific possibility.
Download or read book Metamaterials written by Nader Engheta and published by John Wiley & Sons. This book was released on 2006-06-23 with total page 438 pages. Available in PDF, EPUB and Kindle. Book excerpt: Leading experts explore the exotic properties and exciting applications of electromagnetic metamaterials Metamaterials: Physics and Engineering Explorations gives readers a clearly written, richly illustrated introduction to the most recent research developments in the area of electromagnetic metamaterials. It explores the fundamental physics, the designs, and the engineering aspects, and points to a myriad of exciting potential applications. The editors, acknowledged leaders in the field of metamaterials, have invited a group of leading researchers to present both their own findings and the full array of state-of-the-art applications for antennas, waveguides, devices, and components. Following a brief overview of the history of artificial materials, the publication divides its coverage into two major classes of metamaterials. The first half of the publication examines effective media with single (SNG) and double negative (DNG) properties; the second half examines electromagnetic band gap (EBG) structures. The book further divides each of these classes into their three-dimensional (3D volumetric) and two-dimensional (2D planar or surface) realizations. Examples of each type of metamaterial are presented, and their known and anticipated properties are reviewed. Collectively, Metamaterials: Physics and Engineering Explorations presents a review of recent research advances associated with a highly diverse set of electromagnetic metamaterials. Its multifaceted approach offers readers a combination of theoretical, numerical, and experimental perspectives for a better understanding of their behaviors and their potentialapplications in components, devices, and systems. Extensive reference lists provide opportunities to explore individual topics and classes of metamaterials in greater depth. With full-color illustrations throughout to clarify concepts and help visualize actual results, this book provides a dynamic, user-friendly resource for students, engineers, physicists, and other researchers in the areas of electromagnetic materials, microwaves, millimeter waves, and optics. It equips newcomers with a basic understanding of metamaterials and their potential applications. Advanced researchers will benefit from thought-provoking perspectives that will deepen their knowledge and lead them to new areas of investigation.
Download or read book Diverse Topics in Theoretical and Mathematical Physics written by Roman W. Jackiw and published by World Scientific. This book was released on 1995 with total page 528 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this volume, topics are drawn from field theory, especially gauge field theory, as applied to particle, condensed matter and gravitational physics, and concern a variety of interesting subjects. These include geometricalDtopological effects in quantum theory, fractional charge, time travel, relativistic quantized fields in and out of thermal equilibrium and quantum modifications of symmetry in physical systems.Many readers will find this a useful volume, especially theoretical physicists and mathematicians. The material will be of interest to both the expert who will find well-presented novel and stimulating viewpoints of various subjects and the novice who will find complete, detailed and precise descriptions of important topics of current interest, in theoretical and mathematical physics.
Download or read book Methods of Mathematical Physics written by Harold Jeffreys and published by Cambridge University Press. This book was released on 1999-11-18 with total page 734 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a reissue of classic textbook of mathematical methods.
