{"product_id":"mathematical-physics-a-modern-introduction-to-its-foundations-hardcover","title":"Mathematical Physics: A Modern Introduction to Its Foundations - Hardcover","description":"\u003cdiv\u003e\u003cp style=\"text-align: right;\"\u003e\u003ca href=\"https:\/\/reportcopyrightinfringement.com\/\" target=\"_blank\" rel=\"nofollow\"\u003e\u003cb\u003eReport copyright infringement\u003c\/b\u003e\u003c\/a\u003e\u003c\/p\u003e\u003c\/div\u003e\u003cp\u003eby \u003cb\u003eSadri Hassani\u003c\/b\u003e (Author)\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003eThis 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.\u003c\/p\u003e \u003cp\u003e \u003c\/p\u003e \u003cp\u003eThe 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.\u003c\/p\u003e \u003cp\u003e \u003c\/p\u003e \u003cp\u003eIntended 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.\u003c\/p\u003e \u003cp\u003e \u003c\/p\u003e \u003cp\u003eNumerous 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.\u003c\/p\u003e \u003cp\u003e\u003c\/p\u003e \u003cp\u003eSome praise for the previous edition: \u003c\/p\u003e \u003cp\u003e\u003c\/p\u003e \u003cp\u003ePAGEOPH [Pure and Applied Geophysics]\u003c\/p\u003e \u003cp\u003eReview by Daniel Wojcik, University of Maryland\u003c\/p\u003e \u003cp\u003e\"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.\"\u003c\/p\u003e \u003cp\u003e\u003c\/p\u003e \u003cp\u003eZENTRALBLATT MATH\u003c\/p\u003e \u003cp\u003eReview by G.Roepstorff, University of Aachen, Germany\u003c\/p\u003e \u003cp\u003e\"... 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.\"\u003c\/p\u003e \u003cp\u003e\u003c\/p\u003e \u003cp\u003eTHE PHYSICIST\u003c\/p\u003e \u003cp\u003eReview by Paul Davies, Orion Productions, Adelaide, Australia\u003c\/p\u003e \u003cp\u003e\"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.\"\u003c\/p\u003e \u003cp\u003e\u003c\/p\u003e \u003cp\u003eEMS [EUROPEAN MATHEMATICAL SOCIETY] NEWSLETTER\u003c\/p\u003e \u003cp\u003e\"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.\"\u003c\/p\u003e\u003ch3\u003eBack Jacket\u003c\/h3\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003eThe goal of this book is to expose the reader to the indispensable role that mathematics---often very abstract---plays in modern physics. Starting with the notion of vector spaces, the first half of the book develops topics as diverse as algebras, classical orthogonal polynomials, Fourier analysis, complex analysis, differential and integral equations, operator theory, and multi-dimensional Green's functions. The second half of the book introduces groups, manifolds, Lie groups and their representations, Clifford algebras and their representations, and fiber bundles and their applications to differential geometry and gauge theories.\u003c\/p\u003e\u003cp\u003eThis second edition is a substantial revision of the first one with a complete rewriting of many chapters and the addition of new ones, including chapters on algebras, representation of Clifford algebras and spinors, fiber bundles, and gauge theories. The spirit of the first edition, namely the balance between rigor and physical application, has been maintained, as is the abundance of historical notes and worked out examples that demonstrate the \"unreasonable effectiveness of mathematics\" in modern physics.\u003c\/p\u003e\u003cp\u003eEinstein has famously said, \"The most incomprehensible thing about nature is that it is comprehensible.\" What he had in mind was reiterated in another one of his famous quotes concerning the question of how \" ... mathematics, being after all a product of human thought, is so admirably appropriate to the objects of reality.\" It is a question that comes to everyone's mind when encountering the highly abstract mathematics required for a deep understanding of modern physics. It is the experience that Eugene Wigner so profoundly described as \"the unreasonable effectiveness of mathematics in the natural sciences.\"\u003cbr\u003e\u003c\/p\u003e\u003ch3\u003eAuthor Biography\u003c\/h3\u003e\u003cp\u003eSadri Hassani is Professor Emeritus in the Department of Physics at Illinois State University, USA.\u003c\/p\u003e\n            \u003cdiv\u003e\n\u003cstrong\u003eNumber of Pages:\u003c\/strong\u003e 1205\u003c\/div\u003e\n            \u003cdiv\u003e\n\u003cstrong\u003eDimensions:\u003c\/strong\u003e 2.7 x 10.2 x 7.3 IN\u003c\/div\u003e\n            \u003cdiv\u003e\n\u003cstrong\u003ePublication Date:\u003c\/strong\u003e August 19, 2013\u003c\/div\u003e\n            ","brand":"BooksCloud","offers":[{"title":"Default Title","offer_id":47337007087865,"sku":"9783319011943","price":161.98,"currency_code":"USD","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0789\/2782\/3097\/files\/bnU0aDNYbWJxZ1J3M0FMTWFtd25CZz09.webp?v=1769674537","url":"https:\/\/bookscloud.io\/products\/mathematical-physics-a-modern-introduction-to-its-foundations-hardcover","provider":"BooksCloud Book Dropshipping","version":"1.0","type":"link"}