- Tapa dura: 1026 páginas
- Editor: Springer; Edición: 1st ed. 1999. Corr. 3rd printing 2002 (1 de febrero de 2002)
- Colección: Physics
- Idioma: Inglés
- ISBN-10: 0387985794
- ISBN-13: 978-0387985794
- Valoración media de los clientes: Sé el primero en opinar sobre este producto
- Clasificación en los más vendidos de Amazon: nº124.508 en Libros en idiomas extranjeros (Ver el Top 100 en Libros en idiomas extranjeros)
- Ver el Índice completo
Mathematical Physics: A Modern Introduction to Its Foundations (Inglés) Tapa dura – 1 feb 2002
Hay una nueva edición de este producto:
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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."
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 student in the middle of his training, it will certainly prove to be extremely useful."
Review by Paul Davies, Orion Productions, Adelaide, Australia
"I am pleased to have so many topics collected in a single volume. All the tricks are there of course, but supported by sufficient rigour and substantiation to make the dedicated mathematical physicist sigh with delight."
EMS [EUROPEAN MATHEMATICAL SOCIETY] NEWSLETTER
"This book is a condensed exposition of the mathematics that is met in most parts of physics. The presentation attains a very good balance between the formal introduction of concepts, theorems and proofs on one hand, and the applied approach on the other, with many examples, fully or partially solved problems, and historical remarks. An impressive amount of mathematics is covered. … This book can be warmly recommended as a basic source for the study of mathematics for advanced undergraduates or beginning graduate students in physics and applied mathematics, and also as a reference book for all working mathematicians and physicists."
Reseña del editor
For physics students interested in the mathematics they use, and for math students interested in seeing how some of the ideas of their discipline find realization in an applied setting. The presentation strikes 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.Ver Descripción del producto
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But if you are new to a topic, the book is too formal and terse (for a physicist, at least.) Not much intuition or insight is taught in this book and has to be learned elsewhere.
But if you learn the intuition on the topic elsewhere(IE for Hilbert spaces, take a course using Sakurai or for Lie theory a book like Weinberg I.), I know of no better text to strengthen your formal understanding of the topic.
A new edition is coming out and I'll probably buy that one too.
Hassani first introduces the concept of a vector space and gives numerous examples including the less "intuitive" function spaces and matrix spaces. He quickly builds upon this idea to encompass linear operators, algebras and functions defined in terms of them. Hassani's sweep of basic concepts is comprehensive and thorough while seamlessly weaving in ideas from many different branches of mathematics that provide the edifice for much of modern physics. The side notes enable one to browse through the book and find a particular topic. Interspersing the text with short biographical sketches of mathematicians who made important contributions to the field within the past three centuries adds further interest to the book.
The author has devoted much of the book to those special functions that emerge as solutions to the prototype differential equations of Physics. These functions are presented at a more generalized and rigorous mathematical setting than in many Mathematical Physics books aimed at beginning graduate students while sparing the more tedious proofs all too common in books on Functional Analysis, for example. In particular, his exposition of Green functions and Operator Theory are much more comprehensive and easy to follow than comparable treatment in other texts targeting the same readership.
Hassani continues on through Lie Groups to end this tome with a look at symmetries and conservation laws. The latter are especially relevant in Quantum Field Theory and HEP. Topics given cursory treatment in texts on these subfields of Physics are presented by Hassani in greater detail, again sparing the reader the mathematics that often serve more to sidetrack that edify.
Given the subject matter, it is no easy task to produce such a user-friendly tome, but Hassani has admirably risen to the task. I look forward to more texts by the author, perhaps one with more emphasis on Measure Theoretic approaches?