000 04929nam a22004695i 4500
001 978-3-319-01195-0
003 DE-He213
005 20160302170921.0
007 cr nn 008mamaa
008 130726s2013 gw | s |||| 0|eng d
020 _a9783319011950
_9978-3-319-01195-0
024 7 _a10.1007/978-3-319-01195-0
_2doi
050 4 _aQC19.2-20.85
072 7 _aPHU
_2bicssc
072 7 _aSCI040000
_2bisacsh
082 0 4 _a530.1
_223
100 1 _aHassani, Sadri.
_eauthor.
245 1 0 _aMathematical Physics
_h[electronic resource] :
_bA Modern Introduction to Its Foundations /
_cby Sadri Hassani.
250 _a2nd ed. 2013.
264 1 _aCham :
_bSpringer International Publishing :
_bImprint: Springer,
_c2013.
300 _aXXXI, 1205 p. 160 illus.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
505 0 _aMathematical 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 Symmetric Group -- VIII Tensors and Manifolds -- 25 Tensors -- 26 Clifford Algebras -- 27 Analysis of Tensors -- IX Lie Groups and Their Applications -- 28 Lie Groups and Lie Algebras -- 28.2 An Outline of Lie Algebra Theory.-�29 Representation of Lie Groups and Lie Algebras -- 30 Representation of Clifford Algebras -- 31 Lie Groups and Differential Equations -- 32 Calculus of Variations, Symmetries, and Conservation Laws -- X Fiber Bundles -- 33 Fiber Bundles and Connections -- 34 Gauge Theories -- 35 Differential Geometry -- 36 Riemannian Geometry.
520 _aThe 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 of historical notes and worked out examples that demonstrate the "unreasonable effectiveness of mathematics" in modern physics. Einstein 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.".
650 0 _aPhysics.
650 0 _aApplied mathematics.
650 0 _aEngineering mathematics.
650 1 4 _aPhysics.
650 2 4 _aTheoretical, Mathematical and Computational Physics.
650 2 4 _aMathematical Methods in Physics.
650 2 4 _aNumerical and Computational Physics.
650 2 4 _aApplications of Mathematics.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783319011943
856 4 0 _uhttp://dx.doi.org/10.1007/978-3-319-01195-0
912 _aZDB-2-PHA
999 _c198267
_d198267