Mathematical Physics
A Modern Introduction to Its Foundations
Published on 1. February 2002
Book
Hardback
XXII, 1026 pages
978-0-387-98579-4 (ISBN)
Description
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.
Reviews / Votes
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."More details
Edition
1st ed. 1999. Corr. 3rd printing 2002
Language
English
Place of publication
NY
United States
Target group
College/higher education
Professional and scholarly
Graduate
Illustrations
16 s/w Tabellen, 114 s/w Abbildungen
114 black & white illustrations, 16 black & white tables
Dimensions
Height: 24.4 cm
Width: 17 cm
Weight
2385 gr
ISBN-13
978-0-387-98579-4 (9780387985794)
Schweitzer Classification
Other editions
New editions
Book
08/2013
2nd Edition
Springer
€90.94
Available immediately
Person
Sadri Hassani, Department of Physics, Illinois State University, USA
Content
Mathematical Preliminaries; I. Finite-Dimensional Vector Spaces: 1. Vectors and Transformations; 2. Operator Algebra; 3. Matrices: Operator Representations; 4. Spectral Decomposition; II. Infinite-Dimnsional Vector Spaces: 5. Hilbert Spaces; 6. Generalized Functions; 7. Classical Orthogonal Polynomials; 8. Fourier Analysis; III. Complex Analysis: 9. Complex Calculus; 10. Calculus of Residues; 11. Complex Analysis: Advanced Topics; IV. Differential Equations: 12. Separation of Variables in Spherical Coordinates; 13. Second-Order Linear Differential Equations; 14. Complex Analysis of SOLDE; 15. Integral Transforms and Differential Equations; V. Operators on Hilbert Spaces: 16. An Introduction to Operator Theory; 17. Integral Equations; 18. Sturm-Liouville Systems: Formalism; 19. Sturm-Liouville Systems: Examples; VI. Green's Functions: 20. Green's Functions in One Dimension; 21. Multi-Dimensional Green's Functions: General Properties; 22. Multi-Dimensional Green's Functions: Applications; VII. Groups and Manifolds: 23. Group Theory; 24. Group Representation Theory; 25. Algebra of Tensors; 26. Analysis of Tensors; VIII. Lie Groups and Their Applications: 27. Lie Groups and Lie Algebras; 28. Differential Geometry; 29. Lie Groups and Differential Equations; 30.Calculus of vVariations, Symmetries, and CConservation Laws; References; IIndex.