Mathematical physics: a modern introduction to its foundations/
Sadri Hassani.
- New York: Springer, 1999.
- xxi, 1025 p. : ill. ; 24 cm.
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. Responsibility: Sadri Hassani.