Mathematical Physics_ A Modern Introduction to Its Foundations

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Title:        Mathematical Physics: A Modern Introduction to Its Foundations
Author(s):        Sadri Hassani (auth.)
Publisher:        Springer International Publishing       
Year:        2013        Edition:        2
Language:        English       
Pages (biblio\tech):        1205\1198
ISBN:        978-3-319-01194-3, 978-3-319-01195-0

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.

Table of contents :
Front Matter....Pages I-XXXI
Mathematical Preliminaries....Pages 1-16
Front Matter....Pages 17-17
Vectors and Linear Maps....Pages 19-61
Algebras....Pages 63-100
Operator Algebra....Pages 101-136
Matrices....Pages 137-168
Spectral Decomposition....Pages 169-211
Front Matter....Pages 213-213
Hilbert Spaces....Pages 215-239
Classical Orthogonal Polynomials....Pages 241-263
Fourier Analysis....Pages 265-292
Front Matter....Pages 293-293
Complex Calculus....Pages 295-337
Calculus of Residues....Pages 339-361
Advanced Topics....Pages 363-392
Front Matter....Pages 393-393
Separation of Variables in Spherical Coordinates....Pages 395-415
Second-Order Linear Differential Equations....Pages 417-457
Complex Analysis of SOLDEs....Pages 459-491
Integral Transforms and Differential Equations....Pages 493-507
Front Matter....Pages 509-509
Introductory Operator Theory....Pages 511-541
Integral Equations....Pages 543-561
Sturm-Liouville Systems....Pages 563-602
Front Matter....Pages 603-603
Green’s Functions in One Dimension....Pages 605-634
Front Matter....Pages 603-603
Multidimensional Green’s Functions: Formalism....Pages 635-664
Multidimensional Green’s Functions: Applications....Pages 665-698
Front Matter....Pages 699-699
Group Theory....Pages 701-723
Representation of Groups....Pages 725-760
Representations of the Symmetric Group....Pages 761-777
Front Matter....Pages 779-779
Tensors....Pages 781-827
Clifford Algebras....Pages 829-857
Analysis of Tensors....Pages 859-911
Front Matter....Pages 913-913
Lie Groups and Lie Algebras....Pages 915-951
Representation of Lie Groups and Lie Algebras....Pages 953-985
Representation of Clifford Algebras....Pages 987-1007
Lie Groups and Differential Equations....Pages 1009-1045
Calculus of Variations, Symmetries, and Conservation Laws....Pages 1047-1075
Front Matter....Pages 1077-1077
Fiber Bundles and Connections....Pages 1079-1098
Gauge Theories....Pages 1099-1115
Differential Geometry....Pages 1117-1141
Riemannian Geometry....Pages 1143-1177
Back Matter....Pages 1179-1205

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