Mathematical Physics [Hardcover]

Sadri Hassani (Author)

Book Description

Publication Date: February 8, 1999 | ISBN-10: 0387985794 | ISBN-13: 978-0387985794 | Edition: 1st

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.

Editorial Reviews

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 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 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 Details

• Hardcover: 1046 pages
• Publisher: Springer; 1st edition (February 8, 1999)
• Language: English
• ISBN-10: 0387985794
• ISBN-13: 978-0387985794
• Product Dimensions: 10.5 x 7.8 x 2.4 inches
• Shipping Weight: 4.1 pounds (View shipping rates and policies)
• Average Customer Review: 4.7 out of 5 stars  See all reviews (9 customer reviews)
• Amazon Best Sellers Rank: #376,936 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews

30 of 31 people found the following review helpful:

4.0 out of 5 stars A pleasure to read, September 12, 2003

By 

Suetonius (England) - See all my reviews

This review is from: Mathematical Physics (Hardcover)

I agree with other reviewers that this book is the first choice if you want to get a handle on mathematical methods of theoretical physics at advanced undergraduate / beginning graduate level. The nearest competitor is Byron & Fuller's "Mathematics of Classical and Quantum Physics" which has been around a long time and has many good points; but having used both I prefer this. The level and philosophy is about the same but the coverage is wider and the presentation clearer and cleaner. It's a pleasure to read.

The book is divided into eight parts, each comprising three or four chapters, on: Finite-dimensional Vector Spaces, Infinite-dimensional Vector Spaces, Complex Analysis, Differential Equations, Operators on Hilbert Spaces, Green's Functions, Groups and Manifolds, Lie Groups and Applications. Fear not: although it isn't designed for freshmen, it emphatically isn't the sort of math book where you have to crack the code to get any benefit.

The layout is excellent, there are many, many worked examples, and I found very few slips or typos. One black mark, the reason I don't give it 5 stars: although there are a massive 850 problems, there are no solutions (just like Byron & Fuller). Unless you're confident in your mathematical ability, you may find that a drawback for self-study. Finally, a word to the wise: check out this title at amazon.co.uk (provided you aren't in a hurry).

17 of 18 people found the following review helpful:

5.0 out of 5 stars First Class Graduate Level Text, January 22, 2006

By 

O. Burak Okan (Cambridge, MA USA) - See all my reviews
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This review is from: Mathematical Physics (Hardcover)

I share the excitement in former reviewers` comments on the overall quality of this book. However, it is important to notice that Hassani does not try to present the material covered in exhaustive detail. This is, however, by no means a criticism given the breadth of topics pertinent to the study of mathematical physics. Therefore, it is impossible to distill such a plethora of material while retaining the full rigor.

The book structures itself around the concept of a vector space, and the author does not shy away from abstractions which involve mathematical structures such as fields, algebras, groups, etc. as well as the topological concepts like completeness, compactness, bounded operators and so on. In this respect, the view toward math is modern and stresses the mutualism between physics and math in the advancement of both.

In general, there is a noticeable trend shift in writing of mathematical physics texts, which was inaugurated by Dennery and Krzywicki`s text and Walter Thirring`s two volume classic as opposed to the Morse and Feshbach variety which mostly focuses on the detailed solutions of certain problems of interest in physics. In this respect, this book is a nice complement and update to both. The quality of writing is reflected on the references and again culling the best of two worlds. Indeed, the references span numerous important fields and approaches to math (Rudin`s Functional Analysis, Bott & Tu`s Differential Forms in Algebraic Topology, Barut & Raczka`s Group Representation Theory...), and this more than compensates the absence or truncation of any ideas/concepts.

The topics that are absent from the text include measure theory, a possible prologue to algebraic geometry, hyper-complex analysis and geometric algebra (except for a short digression on quaternions). However, this does not devalue the book owing to the reasons presented above. I highly recommend this text for anyone who has an appreciation of the strong link between the physical world and its description via mathematical constructions.

17 of 19 people found the following review helpful:

5.0 out of 5 stars Converted to a Hassani fan..., November 27, 2005

By 

Matthew T. Deluca (Jupiter, FL) - See all my reviews
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This review is from: Mathematical Physics (Hardcover)

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.