This book is for physics students interested in the mathematics they use and for mathematics students interested in seeing how some of the ideas of their discipline find realization in an applied setting. The presentation tries to strike a balance between formalism and application, between abstract and concrete. The interconnections among the various topics are clarified both by the use of vector spaces as a central unifying theme, recurring throughout the book, and by putting ideas into their historical context. Enough of the essential formalism is included to make the presentation self-contained.
The book is divided into eight parts: The first covers finite- dimensional vector spaces and the linear operators defined on them. The second is devoted to infinite-dimensional vector spaces, and includes discussions of the classical orthogonal polynomials and of Fourier series and transforms. The third part deals with complex analysis, including complex series and their convergence, the calculus of residues, multivalued functions, and analytic continuation. Part IV treats ordinary differential equations, concentrating on second-order equations and discussing both analytical and numerical methods of solution. The next part deals with operator theory, focusing on integral and Sturm--Liouville operators. Part VI is devoted to Green's functions, both for ordinary differential equations and in multidimensional spaces. Parts VII and VIII contain a thorough discussion of differential geometry and Lie groups and their applications, concluding with Noether's theorem on the relationship between symmetries and conservation laws.
Intended for advanced undergraduates or beginning graduate students, this comprehensive guide should also prove useful as a refresher or reference for physicists and applied mathematicians. Over 300 worked-out examples and more than 800 problems provide valuable learning aids.
Numerous enhancements and revision are incorporated into this new edition. For example, fiber bundle techniques are used to introduce differential geometry. This more elegant and intuitive approach naturally connects differential geometry with not only the general theory of relativity, but also gauge theories of fundamental forces.
Some praise for the previous edition:
PAGEOPH Pure and Applied Geophysics]
Review by Daniel Wojcik, University of Maryland
"This volume should be a welcome addition to any collection. The book is well written and explanations are usually clear. Lives of famous mathematicians and physicists are scattered within the book. They are quite extended, often amusing, making nice interludes. Numerous exercises help the student practice the methods introduced. ... I have recently been using this book for an extended time and acquired a liking for it. Among all the available books treating mathematical methods of physics this one certainly stands out and assuredly it would suit the needs of many physics readers."
ZENTRALBLATT MATH
Review by G.Roepstorff, University of Aachen, Germany
..". Unlike most existing texts with the same emphasis and audience, which are merely collections of facts and formulas, the present book is more systematic, self-contained, with a level of presentation that tends to be more formal and abstract. This entails proving a large number of theorems, lemmas, and corollaries, deferring most of the applications that physics students might be interested in to the example sections in small print. Indeed, there are 350 worked-out examples and about 850 problems. ... A very nice feature is the way the author intertwines the formalism with the life stories and anecdotes of some mathematicians and physicists, leading at their times. As is often the case, the historical view point helps to understand and appreciate the ideas presented in the text. ... For the physics studen
This book is a sequel to the book by the same authors entitled Theory of Groups and Symmetries: Finite Groups, Lie Groups, and Lie Algebras.
The presentation begins with the Dirac notation, which is illustrated by boson and fermion oscillator algebras and also Grassmann algebra. Then detailed account of finite-dimensional representations of groups SL(2, C) and SU(2) and their Lie algebras is presented. The general theory of finite-dimensional irreducible representations of simple Lie algebras based on the construction of highest weight representations is given. The classification of all finite-dimensional irreducible representations of the Lie algebras of the classical series sℓ(n, C), so(n, C) and sp(2r, C) is exposed.
Finite-dimensional irreducible representations of linear groups SL(N, C) and their compact forms SU(N) are constructed on the basis of the Schur-Weyl duality. A special role here is played by the theory of representations of the symmetric group algebra C Sr] (Schur-Frobenius theory, Okounkov-Vershik approach), based on combinatorics of Young diagrams and Young tableaux. Similar construction is given for pseudo-orthogonal groups O(p, q) and SO(p, q), including Lorentz groups O(1, N-1) and SO(1, N-1), and their Lie algebras, as well as symplectic groups Sp(p, q). The representation theory of Brauer algebra (centralizer algebra of SO(p, q) and Sp(p, q) groups in tensor representations) is discussed.
Finally, the covering groups Spin(p, q) for pseudo-orthogonal groups SO↑(p, q) are studied. For this purpose, Clifford algebras in spaces Rp, q are introduced and representations of these algebras are discussed.
Описание: Generalising Newton's law of gravitation, general relativity is one of the pillars of modern physics. While applications in the beginning were restricted to isolated effects such as a proper understanding of Mercury's orbit, the second half of the twentieth century saw a massive development of applications. These include cosmology, gravitational waves, and even very practical results for satellite based positioning systems as well as different approaches to unite general relativity with another very successful branch of physics – quantum theory. On the occassion of general relativity's centennial, leading scientists in the different branches of gravitational research review the history and recent advances in the main fields of applications of the theory, which was referred to by Lev Landau as “the most beautiful of the existing physical theories”. Contributions from: Andy C. Fabian, AnthonyL. Lasenby, Astrophysical black Holes Neil Ashby, GNSS and other applications of General Relativity Gene Byrd, Arthur Chernin, Pekka Teerikorpi, Mauri Vaaltonen,Observations of general Relativity at strong and weaks limits Ignazio Ciufolini, General Relativity and dragging of inertial frames Carlo Rovelli, The strange world of quantum spacetime
Описание: This is the second, amended edition of the book. In addition to the material of the first edition it contains a derivation of the value of action for each of those Harrington–Shepard calorons/anticalorons that are relevant for the emergence of the thermal ground state, discussions of the caloron center vs. its periphery, of the role of the thermal ground state in U(1) wave propagation, of photonic particle–wave duality, and of calculational intricacies and book-keeping related to one-loop scattering of massless modes in the deconfining phase of an SU(2) Yang–Mills theory. Moreover, a derivation of the temperature–redshift relation of the CMB in deconfining SU(2) Yang–Mills thermodynamics and its application to explaining an apparent early re-ionization of the Universe are given. Finally, a mechanism of mass generation for cosmic neutrinos is proposed.
Описание: This book offers a unified perspective on the study of complex systems with contributions written by leading scientists from various disciplines, including mathematics, physics, computer science, biology, economics and social science. It is written for researchers from a broad range of scientific fields with an interest in recent developments in complex systems.
Автор: Boling Guo, Lixin Tian, Zhenya Yan, Liming Ling, Название: Rogue Waves: Mathematical Theory and Applications in Physics ISBN: 3110469421 ISBN-13(EAN): 9783110469424 Издательство: Walter de Gruyter Рейтинг: Цена: 22305.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This book gives an overview of the theoretical research on rogue waves and discusses solutions to rogue wave formation via the Darboux and bilinear transformations, algebro-geometric reduction, and inverse scattering and similarity transformations. Studies on nonlinear optics are included, making the book a comprehensive reference for researchers in applied mathematics, optical physics, geophysics, and ocean engineering. ContentsThe Research Process for Rogue WavesConstruction of Rogue Wave Solution by the Generalized Darboux TransformationConstruction of Rogue Wave Solution by Hirota Bilinear Method, Algebro-geometric Approach and Inverse Scattering MethodThe Rogue Wave Solution and Parameters Managing in Nonautonomous Physical Model
Автор: Sergei M. Kopeikin Название: Applications and Experiments ISBN: 3110345455 ISBN-13(EAN): 9783110345452 Издательство: Walter de Gruyter Цена: 27884.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Relativistic celestial mechanics – investigating the motion celestial bodies under the influence of general relativity – is a major tool of modern experimental gravitational physics. With a wide range of prominent authors from the field, this two-volume series consists of reviews on a multitude of advanced topics in the area of relativistic celestial mechanics – starting from more classical topics such as the regime of asymptotically-flat spacetime, light propagation and celestial ephemerides, but also including its role in cosmology and alternative theories of gravity as well as modern experiments in this area. This second volume of a two-volume series covers applications of the theory as well as experimental verifications. From tools to determine light travel times in curved space-time to laser ranging between earth and moon and between satellites, and impacts on the definition of time scales and clock comparison techniques, a variety of effects is discussed. On the occasion of his 80-th birthday, these two volumes honor V. A. Brumberg – one of the pioneers in modern relativistic celestial mechanics. Contributions include: J. Simon, A. Fienga: Victor Brumberg and the French school of analytical celestial mechanics T. Fukushima: Elliptic functions and elliptic integrals for celestial mechanics and dynamical astronomy P. Teyssandier: New tools for determining the light travel time in static, spherically symmetric spacetimes beyond the order G2 J. Muller, L. Biskupek, F. Hofmann and E. Mai: Lunar laser ranging and relativity N. Wex: Testing relativistic celestial mechanics with radio pulsars I. Ciufolini et al.: Dragging of inertial frames, fundamental physics, and satellite laser ranging G. Petit, P. Wolf, P. Delva: Atomic time, clocks, and clock comparisons in relativistic spacetime: a review
Автор: Wolfram Название: Applications of Group Theory to Atoms, Molecules, and Solids ISBN: 1107028523 ISBN-13(EAN): 9781107028524 Издательство: Cambridge Academ Рейтинг: Цена: 25502.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Taking a unique, applications-oriented approach, this book helps readers understand the power of group theory and gives them the tools needed to analyze any atomic, molecular, or crystalline solid system. With over 100 end-of-chapter exercises, this book is invaluable for graduate students and researchers in the physical sciences.
This volume presents a collection of problems and solutions in differential geometry with applications. Both introductory and advanced topics are introduced in an easy-to-digest manner, with the materials of the volume being self-contained. In particular, curves, surfaces, Riemannian and pseudo-Riemannian manifolds, Hodge duality operator, vector fields and Lie series, differential forms, matrix-valued differential forms, Maurer-Cartan form, and the Lie derivative are covered.
Readers will find useful applications to special and general relativity, Yang-Mills theory, hydrodynamics and field theory. Besides the solved problems, each chapter contains stimulating supplementary problems and software implementations are also included. The volume will not only benefit students in mathematics, applied mathematics and theoretical physics, but also researchers in the field of differential geometry.
This volume presents a collection of problems and solutions in differential geometry with applications. Both introductory and advanced topics are introduced in an easy-to-digest manner, with the materials of the volume being self-contained. In particular, curves, surfaces, Riemannian and pseudo-Riemannian manifolds, Hodge duality operator, vector fields and Lie series, differential forms, matrix-valued differential forms, Maurer-Cartan form, and the Lie derivative are covered.
Readers will find useful applications to special and general relativity, Yang-Mills theory, hydrodynamics and field theory. Besides the solved problems, each chapter contains stimulating supplementary problems and software implementations are also included. The volume will not only benefit students in mathematics, applied mathematics and theoretical physics, but also researchers in the field of differential geometry.
Автор: Vladimir Dobrev Название: Lie Theory and Its Applications in Physics ISBN: 9811096732 ISBN-13(EAN): 9789811096730 Издательство: Springer Рейтинг: Цена: 27950.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Luigi Accardi, Abdessatar Barhoumi, Yun Gang Lu, andMohamed Rhaima: *-Lie Algebras Canonically Associated to Probability Measures on R with All Moments.- Loriano Bonora: Special Conformal Transformations and Contact Terms.- Ivan Dimitrijevic, Branko Dragovich, Jelena Stankovic, Alexey S. Koshelev, and Zoran Rakic: On Nonlocal Modified Gravity and Its Cosmological Solutions.- Malte Henkel: Kinetics of Interface Growth: Physical Ageing and Dynamical Symmetries.- Evgeny Ivanov and Stepan Sidorov: News on SU(21) Supersymmetric Mechanics.- Toshiyuki Kobayashi: Intrinsic Sound of Anti-de Sitter Manifolds.- Efrat Gerchkovitz and Zohar Komargodski: Sphere Partition Functions and the Kahler Metric on the Conformal Manifold.- Mikhail V. Ignatyev, Ivan Penkov, and Joseph A. Wolf: Real Group Orbits on Flag Ind-Varieties of SL(∞, C).- Raul Gomez and Birgit Speh: Derived functors and Intertwining operators for Principal Series Representations of SL2(R).- Ivan Todorov: Hyperlogarithms and Periods in Feynman Amplitudes.- N.I. Stoilova and J. Van der Jeugt: The Parastatistics Fock Space and Explicit Infinite-Dimensional Representations of the Lie Superalgebra osp(2m+12n).- Joseph A. Wolf: Stepwise Square Integrable Representations: the Concept and Some Consequences.- G. Manolakos and G. Zoupanos: Higher-Dimensional Unified Theories with Continuous and Fuzzy Coset Spaces as Extra Dimensions.- Fumihiko Sugino: Higher Genus Amplitudes in SUSY Double-Well Matrix Model for 2D IIA Superstring.- Eduardo Guendelman, Emil Nissimov, Svetlana Pacheva, and Michail Stoilov: Kruskal-Penrose Formalism for Lightlike Thin-Shell Wormholes.- Eduardo Guendelman, Emil Nissimov, and Svetlana Pacheva: Metric-Independent Spacetime Volume-Forms and Dark Energy/Dark Matter Unification.- Hervй Partouche: Large Volume Supersymmetry Breaking without Decompactification Problem.- Lilia Anguelova: Glueball Inflation and Gauge/Gravity Duality.- Ovidiu Cristinel Stoica: Degenerate Metrics and Their Applications to Spacetime.- Denitsa Staicova and Plamen Fiziev: The Heun Functions and Their Applications in Astrophysics.- Chihiro Matsui: Boundary Effects on the Supersymmetric Sine-Gordon Model through Light-cone Lattice Regularization.- Roberto Bondesan and Thomas Quella: Infinite Dimensional Matrix Product States for Long-Range Quantum Spin Models.- Olena Vaneeva, Yuri Karadzhov, and Christodoulos Sophocleous: Group Analysis of a Class of Nonlinear Kolmogorov Equations.- Lachezar S. Georgiev: Thermoelectric Characteristics of Zk Parafermion Coulomb Islands.- Paolo Lorenzoni and Andrea Savoldi: First Order Hamiltonian Operators of Differential-Geometric Type in 2D.- Oksana Kuriksha and Olena Magda: Exact Solutions for Generalized KdV Equations with Variable Coefficients Using the Equivalence Method.- Pavle Pandzic: Classifying Aq(λ) Modules by Their Dirac Cohomology.- Nurit Barnea and Anna Melnikov: B-orbits in Abelian Nilradicals of Types B, C and D: Towards a Conjecture of Panyushev.- Vladimir K. Dobrev and Patrick Moylan: Anti de Sitter Holography via Sekiguchi Decomposition.- Patrick Moylan: Localization and the Canonical Commutation Relations.- Igor Salom and V. Dmitrasinovic: Permutation-Symmetric Three-Body O(6) Hyperspherical Harmonics in Three Spatial Dimensions.- Todor Popov: Quantum Plactic and Pseudo-Plactic Algebras.- Stoimen Stoimenov and Malte Henkel: Conformal Invariance of the 1D Collisionless Boltzmann Equation.- Toshihisa Kubo: On Reducibility Criterions for Scalar Generalized Verma Modules Associated to Maximal Parabolic Subalgebras.-&n
Автор: Wazwaz Abdul-Majid Название: First Course In Integral Equations, A (Second Edition) ISBN: 9814675121 ISBN-13(EAN): 9789814675123 Издательство: World Scientific Publishing Рейтинг: Цена: 6336.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This second edition integrates the newly developed methods with classical techniques to give both modern and powerful approaches for solving integral equations.
ООО "Логосфера " Тел:+7(495) 980-12-10 www.logobook.ru
