Mathematical Physics

Features

• Cover Type: Hard Cover with 1046 pages
• Published by: Springer
• Edition: 1st Edition February 8, 1999
• Written in: English
• ISBN 10 Number: 0387985794
• ISBN 13 Number: 978-0387985794
• Book Dimensions: 9.3 x 7.4 x 2 inches
• Weighs: 4.1 pounds

Product Review


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 requirements 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 student in the middle of his training, it will certainly prove to be extremely useful."

THE PHYSICIST

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."

Product Description
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.

Reader Reviews
I used this book in a graduate course I recently attended in mathematical physics. At the beginning of the course, I wrestled with this book's treatment of introductory topics such as finite-dimensional vector spaces and operator theory. I struggled with unfamiliar notation and what I felt was a lack of concrete examples. As the course progressed into infinite-dimensional vector spaces however, the unfamiliar notation began to make more sense and I started to appreciate its compactness. I began to understand that the lack of concrete examples was brevity for the sake of completeness. By the end of the course, Hassani's book had become my desktop reference for mathematical physics. The treatment of Green's functions is particularly strong, taking up three solid chapters. Compare this to Arfken's "Mathematical Methods for Physicist" where Green's functions are given only a single subsection. Not to detract from Arfken's book, I just found his coverage of this topic to be weak. Given all of this, I highly recommend a supplementary text for those using this book to learn new material - Arfken and "Mathematics of Classic and Quantum Physics" by Byron and Fuller are both very readable. Those using it as a refresher or reference will find a thorough, compact, and consistent book. Comment | | (Report this)