The Resource Mathematical Physics : A Modern Introduction to Its Foundations, by Sadri Hassani, (electronic resource)
Mathematical Physics : A Modern Introduction to Its Foundations, by Sadri Hassani, (electronic resource)
 Summary
 The goal of this book is to expose the reader to the indispensable role that mathematicsoften very abstractplays 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 multidimensional 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."
 Language
 eng
 Edition
 2nd ed. 2013.
 Extent
 XXXI, 1205 p. 160 illus.
 Contents

 Mathematical Preliminaries
 I FiniteDimensional Vector Spaces
 1 Vectors and Linear Maps
 2 Algebras
 3 Operator Algebra
 4 Matrices
 5 Spectral Decomposition
 II InfiniteDimensional 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 SecondOrder 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 SturmLiouville 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
 Isbn
 9783319011950
 Label
 Mathematical Physics : A Modern Introduction to Its Foundations
 Title
 Mathematical Physics
 Title remainder
 A Modern Introduction to Its Foundations
 Statement of responsibility
 by Sadri Hassani
 Language
 eng
 Summary
 The goal of this book is to expose the reader to the indispensable role that mathematicsoften very abstractplays 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 multidimensional 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."
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 0
 Literary form
 non fiction
 Label
 Mathematical Physics : A Modern Introduction to Its Foundations, by Sadri Hassani, (electronic resource)
 Antecedent source
 mixed
 Carrier category
 online resource
 Carrier category code
 cr
 Carrier MARC source
 rdacarrier
 Color
 not applicable
 Content category
 text
 Content type code
 txt
 Content type MARC source
 rdacontent
 Contents
 Mathematical Preliminaries  I FiniteDimensional Vector Spaces  1 Vectors and Linear Maps  2 Algebras  3 Operator Algebra  4 Matrices  5 Spectral Decomposition  II InfiniteDimensional 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 SecondOrder 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 SturmLiouville 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
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 http://library.link/vocab/discovery_link
 {'f': 'http://opac.lib.rpi.edu/record=b3405588'}
 Edition
 2nd ed. 2013.
 Extent
 XXXI, 1205 p. 160 illus.
 File format
 multiple file formats
 Form of item
 electronic
 Isbn
 9783319011950
 Level of compression
 uncompressed
 Media category
 computer
 Media MARC source
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<div class="citation" vocab="http://schema.org/"><i class="fa faexternallinksquare fafw"></i> Data from <span resource="http://link.lib.rpi.edu/portal/MathematicalPhysicsAModernIntroductionto/l5BbnCTxr4Q/" typeof="WorkExample http://bibfra.me/vocab/lite/Item"><span property="name http://bibfra.me/vocab/lite/label"><a href="http://link.lib.rpi.edu/portal/MathematicalPhysicsAModernIntroductionto/l5BbnCTxr4Q/">Mathematical Physics : A Modern Introduction to Its Foundations, by Sadri Hassani, (electronic resource)</a></span>  <span property="offers" typeOf="Offer"><span property="offeredBy" typeof="Library ll:Library" resource="http://link.lib.rpi.edu/"><span property="name http://bibfra.me/vocab/lite/label"><a property="url" href="http://link.lib.rpi.edu/">Rensselaer Libraries</a></span></span></span></span></div>