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Mathematical physics : a modern introduction to its foundations /

"This book is for physics students interested in the mathematics they use and for mathematics students interested in seeing how some of the ideas of their discipline find realization in an applied setting. The presentation tries to strike a balance between formalism and application, between abs...

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Bibliographic Details
Main Author: Hassani, Sadri.
Corporate Author: SpringerLink (Online service)
Format: Online Book
Published: Cham: Springer, [2013]
Edition:Second edition.
Online Access:Online version
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Table of Contents:
  • Mathematical preliminaries
  • Vectors and transformations
  • Operator algebra
  • Matrices : operator representations
  • Spectral decomposition
  • Hilbert spaces
  • Generalized functions
  • Classical orthogonal polynomials
  • Fourier analysis
  • Complex calculus
  • Calculus of residues
  • Complex analysis : advanced topics
  • Separation of variables in spherical coordinates
  • Second-oder linear differential equations
  • Complex analysis of SOLDEs
  • Integral transforms and differential equations
  • An introduction to operator theory
  • t Integral equations
  • Sturm-Liouville systems : formalism
  • Sturm-Liouville systems : examples
  • Green's functions in one dimension
  • Multidimensional Green's functions : applications
  • Group theory
  • Group reprensentation theory
  • Algebra of tensors
  • Analysis of tensors
  • Lie groups and lie algebras
  • Differential geometry
  • Lie groups and differential equations
  • Calculus of variations, symmetries, and conservation laws.