rdf-syntax-grammar
mods:
  schema location: http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
  title info:
    title: Mathematical Physics
    sub title: A Modern Introduction to Its Foundations
  name:
    name part: Hassani, Sadri.
    role:
      role term: creator
    role:
      role term: author.
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  origin info:
    place:
      place term: gw
    date issued: 2013
    edition: 2nd ed. 2013.
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: electronic
    form: electronic resource
    reformatting quality: access
    form: remote
    extent: XXXI, 1205 p. 160 illus. online resource.
  abstract: 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 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.".
  table of contents: 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 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.
  note: by Sadri Hassani.
  subject:
    topic: Physics
  subject:
    topic: Applied mathematics
  subject:
    topic: Engineering mathematics
  subject:
    topic: Physics
  subject:
    topic: Theoretical, Mathematical and Computational Physics
  subject:
    topic: Mathematical Methods in Physics
  subject:
    topic: Numerical and Computational Physics
  subject:
    topic: Applications of Mathematics
  classification: QC19.2-20.85
  classification: 530.1
  related item:
    title info:
      title: Springer eBooks
  identifier: 9783319011950
  identifier: http://dx.doi.org/10.1007/978-3-319-01195-0
  record info:
    record creation date: 130726
    record change date: 20170301021137.0
    record identifier: 978-3-319-01195-0