Mathematical Physics : A Modern Introduction to Its Foundations. 2nd ed. 2013

種類:

電子ブック

責任表示:

by Sadri Hassani

出版情報:

Cham : Springer International Publishing : Imprint: Springer, 2013

著者名:

• Hassani, Sadri.
• SpringerLink (Online service)

ISBN:

9783319011950 [3319011952]    

注記:

Mathematical Preliminaries -- I Finite-Dimensional Vector Spaces -- 1 Vectors and Linear Maps -- 2 Algebras -- 3 Operator Algebra -- 4 Matrices -- 5 Spectral Decomposition -- II Infinite-Dimensional Vector Spaces -- 6 Hilbert Spaces.- 7 Classical Orthogonal Polynomials -- 8 Fourier Analysis -- III Complex Analysis -- 9 Complex Calculus -- 10 Calculus of Residues -- 11 Advanced Topics -- IV Differential Equations -- 12 Separation of Variables in Spherical Coordinates -- 13 Second-Order Linear Differential Equations -- 14 Complex Analysis of SOLDEs -- 15 Integral Transforms and Differential Equations.- V Operators on Hilbert Spaces -- 16 Introductory Operator Theory -- 17 Integral Equations.- 18 Sturm-Liouville Systems -- VI Green's Functions -- 19 Green's Functions in One Dimension -- 20 Multidimensional Green's Functions: Formalism -- 21 Multidimensional Green's Functions: Applications -- VII Groups and Their Representations -- 22 Group Theory -- 23 Representation of Groups -- 24 Representations of the Symmet
The 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. This 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

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