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: N.U. Prabhu Название: Foundations of Queueing Theory ISBN: 0792399625 ISBN-13(EAN): 9780792399629 Издательство: Springer Рейтинг: Цена: 23757.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: 3 The M 1M IS System with Last Come, First Served 50 3. 6 3. 8 56 4 ERLANGIAN QUEUEING SYSTEMS 59 4. 3 The System E/cl Mil 67 4. 5 Problems for Solution 74 PRIORITY SYSTEMS 79 5 5. 6 Problems for Solution 93 6 QUEUEING NETWORKS 97 6. 3 Closed Networks 103 Open Networks: The Product Formula 104 6. 5 Jackson Networks 111 6.
Автор: Viana Название: Foundations of Ergodic Theory ISBN: 1107126967 ISBN-13(EAN): 9781107126961 Издательство: Cambridge Academ Рейтинг: Цена: 16157.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Rich with examples, applications and over 400 exercises, this textbook provides a coherent and self-contained introduction to ergodic theory, suitable for a variety of one- or two-semester courses. It requires few prerequisites, beginning with elementary material suitable for undergraduate students and gradually building up to more sophisticated topics.
Описание: The book discusses fundamental aspects of Quantum Field Theory and of Gauge theories, with attention to mathematical consistency. Basic issues of the standard model of elementary particles (Higgs mechanism and chiral symmetry breaking in quantum Chromodynamics) are treated without relying on the perturbative expansion and on instanton calculus.
Автор: Landsman, Klaas Название: Foundations of quantum theory ISBN: 3319517767 ISBN-13(EAN): 9783319517766 Издательство: Springer Рейтинг: Цена: 6986.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание:
This book studies the foundations of quantum theory through its relationship to classical physics. This idea goes back to the Copenhagen Interpretation (in the original version due to Bohr and Heisenberg), which the author relates to the mathematical formalism of operator algebras originally created by von Neumann. The book therefore includes comprehensive appendices on functional analysis and C*-algebras, as well as a briefer one on logic, category theory, and topos theory. Matters of foundational as well as mathematical interest that are covered in detail include symmetry (and its "spontaneous" breaking), the measurement problem, the Kochen-Specker, Free Will, and Bell Theorems, the Kadison-Singer conjecture, quantization, indistinguishable particles, the quantum theory of large systems, and quantum logic, the latter in connection with the topos approach to quantum theory.
This book is Open Access under a CC BY licence.
Автор: Yu.V. Egorov; R. Cooke; Yu.V. Egorov; M.A. Shubin; Название: Foundations of the Classical Theory of Partial Differential Equations ISBN: 3540638253 ISBN-13(EAN): 9783540638254 Издательство: Springer Рейтинг: Цена: 14673.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: From the reviews: "...I think the volume is a great success ... a welcome addition to the literature ..." The Mathematical Intelligencer, 1993 "... It is comparable in scope with the great Courant-Hilbert Methods of Mathematical Physics, but it is much shorter, more up to date of course, and contains more elaborate analytical machinery..." The Mathematical Gazette, 1993
Автор: M.A. Picardello Название: Harmonic Analysis and Discrete Potential Theory ISBN: 148992325X ISBN-13(EAN): 9781489923257 Издательство: Springer Рейтинг: Цена: 13974.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This book collects the Proceedings of a Congress held in Frascati (Rome) in the period July 1 -July 10, 1991, on the subject of harmonic analysis and discrete potential theory, and related topics. The Congress was made possible by the financial support of the Italian National Research Council ("Gruppo GNAFA"), the Ministry of University ("Gruppo Analisi Funzionale" of the University of Milano), the University of Rome "Tor Vergata", and was also patronized by the Centro "Vito Volterra" of the University of Rome "Tor Vergata". Financial support for publishing these Proceedings was provided by the University of Rome "Tor Vergata", and by a generous contribution of the Centro "Vito Volterra". I am happy of this opportunity to acknowledge the generous support of all these Institutions, and to express my gratitude, and that of all the participants. A number of distinguished mathematicians took part in the Congress. Here is the list of participants: M. Babillot, F. Choucroun, Th. Coulhon, L. Elie, F. Ledrappier, N. Th. Varopoulos (Paris); L. Gallardo (Brest); Ph. Bougerol, B. Roynette (Nancy); O. Gebuhrer (Strasbourg); G. Ahumada-Bustamante (Mulhouse); A. Valette (Neuchatel); P. Gerl (Salzburg); W. Hansen, H. Leptin (Bielefeld); M. Bozejko, A. Hulanicki, T. Pytlik (Wroclaw); C. Thomassen (Lyngby); P. Sjogren (Goteborg); V. Kaimanovich (Leningrad); A. Nevo (Jerusalem); T. Steger (Chicago); S. Sawyer, M. Taibleson, G. Weiss (St. Louis); J. Cohen, S. S ali ani (Maryland); D. Voiculescu (Berkeley); A. Zemanian (Stony Brook); S. Northshield (Plattsburgh); J. Taylor (Montreal); J.
Автор: Josef Kral; Jaroslav Lukes; Ivan Netuka; Jiri Vese Название: Potential Theory ISBN: 1461282764 ISBN-13(EAN): 9781461282761 Издательство: Springer Рейтинг: Цена: 6986.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Within the tradition of meetings devoted to potential theory, a conference on potential theory took place in Prague on 19-24, July 1987. The present volume may thus be of intrest to mathematicians speciali- zing in the above-mentioned fields and also to everybody interested in the present state of potential theory as a whole.
Автор: J. Kral Название: Nonlinear Evolution Equations and Potential Theory ISBN: 1461344271 ISBN-13(EAN): 9781461344278 Издательство: Springer Рейтинг: Цена: 12157.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: During . recent years, the Mathematical Institute of the Czechoslovak Academy of Sciences has organized summer schools de- voted to non linear functional analysis and its applications- particularly in the theory of boundary value problems for dif- ferential equations. The main subj ects of the summer school held from 24 to 29 Sep- tember 1973 at Podhradi near Ledec on Sazava were theory of non- linear evolution equations and potential theory. The summer school was attended by more than 60 mathematicians from Czechoslovakia and abroad. The lectures were delivered by Gottfried Anger, Halle (GDR), Viorel Barbu, Ia i (Romania), Haim Brezis, Paris (France), Siegfried nUmmel, Karl-Marx-Stadt (GDR), Jozef Kacur, Bratislava (Czechoslovakia), Josef Kral, Praha (Czechoslovakia), S. N. Kruzkov, Moskva (USSR), Vladimir Lovicar, Praha (Czechoslovakia), Jaroslav Lukes, Praha (Czechoslovakia), Jifi Vesely, Praha (Czechoslovakia), Ivo Vrkoc, Praha (Czechoslovakia). In the present proceedings the text of almost all lectures delivered during the school are collected. Josef Krel Editor September, 1974 DIRECT AND INVERSE PROBLEMS IN POTENTIAL THEORY Gottfried Anger Halle (GDR) The aim of this paper is to sketch the most important direct problems (boundary value problems and initial value problems) of linear elliptic, paraboli"c and hyperbolic differential equations and some inverse problems corresponding to these equations. Both types of problems are divided into two classes. The first one is the class of properly posed problems, the other is the class of improperly posed problems.
Автор: Corneliu Constantinescu; Aurel Cornea Название: Potential Theory on Harmonic Spaces ISBN: 3642654347 ISBN-13(EAN): 9783642654343 Издательство: Springer Рейтинг: Цена: 13275.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: The theory of harmonic spaces, sometimes also called axiomatic theory of harmonic functions, plays a particular role among the above mentioned theories.
Автор: Oliver Dimon Kellogg Название: Foundations of Potential Theory ISBN: 3642867502 ISBN-13(EAN): 9783642867507 Издательство: Springer Рейтинг: Цена: 6986.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: The treatment of the fundamental existence theorems in Chapter XI by means of integral equations meets squarely the difficulties incident to *the discontinuity of the kernel, and the same chapter gives an account of the most recent developments with respect to the Dirichlet problem.
Автор: Kallenberg Olav Название: Foundations of Modern Probability ISBN: 0387953132 ISBN-13(EAN): 9780387953137 Издательство: Springer Рейтинг: Цена: 12577.00 р. Наличие на складе: Поставка под заказ.
Описание: About the first edition: To sum it up, one can perhaps see a distinction among advanced probability books into those which are original and path-breaking in content, such as Levy's and Doob's well-known examples, and those which aim primarily to assimilate known material, such as Loeve's and more recently Rogers and Williams'. Seen in this light, Kallenberg's present book would have to qualify as the assimilation of probability par excellence. It is a great edifice of material, clearly and ingeniously presented, without any non-mathematical distractions. Readers wishing to venture into it may do so with confidence that they are in very capable hands.- Mathematical ReviewsThis new edition contains four new chapters as well as numerous improvements throughout the text. There are new chapters on measure Theory-key results, ergodic properties of Markov processes and large deviations.
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