Mathematical Physics
Springer-Verlag New York Inc.
978-0-387-98579-4 (ISBN)
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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.
Sadri Hassani, Department of Physics, Illinois State University, USA
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.
| Erscheint lt. Verlag | 1.2.2002 |
|---|---|
| Zusatzinfo | 114 black & white illustrations, 16 black & white tables |
| Verlagsort | New York, NY |
| Sprache | englisch |
| Maße | 170 x 244 mm |
| Gewicht | 2385 g |
| Einbandart | gebunden |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Angewandte Mathematik |
| Naturwissenschaften ► Physik / Astronomie ► Allgemeines / Lexika | |
| ISBN-10 | 0-387-98579-4 / 0387985794 |
| ISBN-13 | 978-0-387-98579-4 / 9780387985794 |
| Zustand | Neuware |
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