Curvilinear Co-ordinates and Matrices, Orthogonal coordinates, cylindrical coordinatesystems, Spherical polar coordinate systems, orthogonal matrices, Hermiatian matrices and unitary matrices.
Vector spacesTensors, function spaces, Hilbert spaces, orthogonal expansions, operators in infinite dimensional spaces.
Fourier Series and Fourier Transform, Properties, advantages and uses of Fourier series, applications, Gibbs phenomenon, discrete Fourier Transform, transform theorems, momentum representation.
Functions, Dirac-Delta function, legendre functions, Bessel Functions, Laguerre functions, Hermite functions.
Groups and their Representations - Discrete groups, Lie groups and Lie algebra and applications

G B Arfken and H J Weber, Mathematical methods in physics, Academic Press, 2001

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