To help engineering graduate students complete their mathematical background necessary in graduate level researches.

Linear algebra and eigenvalue problems, matrix operators, Sturm-Liouville theory, orthogonal functions, power series and Frobenius methods, Legendre polynomials, Associated Legendre polynomials, spherical harmonics, special functions and their orthogonality, Bessel equation, Bessel functions, Laguerre, Hermit, Gegenbauer, Chebyshev, and Gauss equations, theory of complex functions, complex derivative and integral, complex power series, convergence, Cauchy integral and calculation of rezidu, conformal mapping, Schwarts-Kristoffel transformation, Science&engineering applications of the mathematical methods being studied.