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
Автор: Chmutov Название: Introduction to Vassiliev Knot Invariants ISBN: 1107020832 ISBN-13(EAN): 9781107020832 Издательство: Cambridge Academ Рейтинг: Цена: 8094.00 р. 11563.00-30% Наличие на складе: Есть (1 шт.) Описание: This detailed exposition of a relatively recent development in knot theory, namely, the theory of Vassiliev knot invariants, is intended to serve both as a textbook for readers with little background in this area, and as a guide to some of the more advanced material.
Автор: Maria A. Ca?adas-Pinedo; Jos? Luis Flores; Francis Название: Lorentzian Geometry and Related Topics ISBN: 3319662899 ISBN-13(EAN): 9783319662893 Издательство: Springer Рейтинг: Цена: 19564.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание:
This volume contains a collection of research papers and useful surveys by experts in the field which provide a representative picture of the current status of this fascinating area. Based on contributions from the VIII International Meeting on Lorentzian Geometry, held at the University of M laga, Spain, this volume covers topics such as distinguished (maximal, trapped, null, spacelike, constant mean curvature, umbilical...) submanifolds, causal completion of spacetimes, stationary regions and horizons in spacetimes, solitons in semi-Riemannian manifolds, relation between Lorentzian and Finslerian geometries and the oscillator spacetime.
In the last decades Lorentzian geometry has experienced a significant impulse, which has transformed it from just a mathematical tool for general relativity to a consolidated branch of differential geometry, interesting in and of itself. Nowadays, this field provides a framework where many different mathematical techniques arise with applications to multiple parts of mathematics and physics. This book is addressed to differential geometers, mathematical physicists and relativists, and graduate students interested in the field.
Автор: Kostelecky Alan Название: Cpt And Lorentz Symmetry - Proceedings Of The Seventh Meeting ISBN: 9813148497 ISBN-13(EAN): 9789813148499 Издательство: World Scientific Publishing Цена: 19483.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание:
This book contains the Proceedings of the Seventh Meeting on CPT and Lorentz Symmetry, held at Indiana University in Bloomington on June 20-24, 2016. The meeting focused on tests of these fundamental symmetries and on related theoretical issues, including scenarios for possible violations.
Topics covered at the meeting include experimental and observational searches for CPT and Lorentz violation involving: accelerator and collider experiments; astrophysical birefringence, dispersion, and anisotropy; atomic and molecular spectroscopy; clock-comparison measurements; CMB polarization; decays of atoms, nuclei, and particles; equivalence-principle tests with matter and antimatter; exotic atoms, muonium, positronium; gauge and Higgs particles; gravimetry; gravitational waves; high-energy astrophysical observations; hydrogen and antihydrogen; matter interferometry; neutrino oscillations and propagation, neutrino-antineutrino mixing; oscillations and decays of K, B, D mesons; particle-antiparticle comparisons; post-Newtonian gravity in the solar system and beyond; resonant cavities lasers; second and third-generation particles; sidereal and annual time variations, compass asymmetries; space-based missions; spin-polarized matter; spin precession; tests of short-range gravity; and time-of-flight measurements. Theoretical and phenomenological discussions include: physical effects at the level of the Standard Model, General Relativity, and beyond; origins and mechanisms for violations; classical and quantum field theory, gravitation, particle physics, and strings; mathematical foundations; and Finsler geometry.
Автор: Masiello, Antonio Название: Variational Methods in Lorentzian Geometry ISBN: 0367449439 ISBN-13(EAN): 9780367449438 Издательство: Taylor&Francis Рейтинг: Цена: 9492.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This book focuses on the applications of variational methods and critical point theory on infinite dimensional manifolds, to some problems in Lorentzian Geometry which have a variational nature, such as existence and multiplicity results on geodesics.
Автор: Miguel S?nchez; Miguel Ortega; Alfonso Romero Название: Recent Trends in Lorentzian Geometry ISBN: 1489996834 ISBN-13(EAN): 9781489996831 Издательство: Springer Рейтинг: Цена: 16769.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Traditionally, Lorentzian geometry has been used as a necessary tool to understand general relativity, as well as to explore new genuine geometric behaviors, far from classical Riemannian techniques.
Автор: Eisenhart Luther Pfahler Название: Introduction to Differential Geometry ISBN: 0691627460 ISBN-13(EAN): 9780691627465 Издательство: Wiley Рейтинг: Цена: 8712.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание:
Book 3 in the Princeton Mathematical Series.
Originally published in 1950. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.
Автор: V.V. Trofimov Название: Introduction to Geometry of Manifolds with Symmetry ISBN: 0792325613 ISBN-13(EAN): 9780792325611 Издательство: Springer Рейтинг: Цена: 15372.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Provides an introduction to the geometry of manifolds equipped with additional structures connected with the notion of symmetry. This volume presents the elements of differential geometry and is devoted to general topology, part to the theory of smooth manifolds, and the remaining sections deal with manifolds with additional structures.
Описание: In the last years there have been great advances in the applications of topology and differential geometry to problems in condensed matter physics. Concepts drawn from topology and geometry have become essential to the understanding of several phenomena in the area. Physicists have been creative in producing models for actual physical phenomena which realize mathematically exotic concepts and new phases have been discovered in condensed matter in which topology plays a leading role. An important classification paradigm is the concept of topological order, where the state characterizing a system does not break any symmetry, but it defines a topological phase in the sense that certain fundamental properties change only when the system passes through a quantum phase transition. The main purpose of this book is to provide a brief, self-contained introduction to some mathematical ideas and methods from differential geometry and topology, and to show a few applications in condensed matter. It conveys to physicists the basis for many mathematical concepts, avoiding the detailed formality of most textbooks.
Автор: Cutkosky, Steven Dale, Название: Introduction to algebraic geometry / ISBN: 1470435187 ISBN-13(EAN): 9781470435189 Издательство: Mare Nostrum (Eurospan) Рейтинг: Цена: 16929.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This book presents a readable and accessible introductory course in algebraic geometry, with most of the fundamental classical results presented with complete proofs. An emphasis is placed on developing connections between geometric and algebraic aspects of the theory. Differences between the theory in characteristic $0$ and positive characteristic are emphasized. The basic tools of classical and modern algebraic geometry are introduced, including varieties, schemes, singularities, sheaves, sheaf cohomology, and intersection theory. Basic classical results on curves and surfaces are proved. More advanced topics such as ramification theory, Zariski's main theorem, and Bertini's theorems for general linear systems are presented, with proofs, in the final chapters.With more than 200 exercises, the book is an excellent resource for teaching and learning introductory algebraic geometry.
Автор: Giampiero Esposito Название: Quantum Gravity, Quantum Cosmology and Lorentzian Geometries ISBN: 3662149338 ISBN-13(EAN): 9783662149331 Издательство: Springer Рейтинг: Цена: 13060.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Even though the question is not yet settled, this research has led to many interesting, new applications of areas of theoretical and mathematical physics such as twistor theory in flat space, self-adjointness theory, the generalized Riemann zeta-function, and the theory of boundary counterterms in super- gravity.
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