Mathematical physics: a modern introduction to its foundations

Sadri Hassani0387985794, 9780387985794

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.
FROM THE REVIEWS:
PURE APPLIED GEOPHYSICS “This volume should be a welcome addition to any collection. The book is well written and explanations are usually clear…The typesetting standard is one of the best I have ever seen…The book should already be accessible to advanced undergraduates. It can be used both as a textbook or as a reference book (to some extent)…As a supplementary textbook I believe this book should be sufficient for most physics courses…Among all the available book treating mathematical methods of physics this one certainly stands out and assuredly it would suit the needs of many physics readers.”
LIBRARY OF SCIENCE “MATHEMATICAL PHYSICS will benefit two different classes of readers: first, physics students who are interested in the mathematics they use; and second, math students who are interested in seeing abstract ideas some alive in an applied setting. Unlike many books with the same subject and scope, Hassani’s text manages to strike a successful balance between formalism and application, and between the abstract and the concrete…A further notable feature of the book is its success in exhibiting the interrelations among various topics. Indeed, Hassani uses the underlying theme of a vector space, which surfaces throughout the book, to alert readers to the connection between various seemingly unrelated topics…A further benefit concerns Hassani’s presentation of biographical details of the men and women of mathematics and physics. Doing so defies the current trend of ‘ahistoricism’ in many mathematical and physics texts, and pays fitting tribute to the life stories of the people behind the ideas…Impressive in breadth and scope, [this book] may become the definitive text in this profoundly important area.”