Third Year

Course Capsule: Coordinate Systems: Cartesian, Spherical, cylindrical, Matrices and determinants: Orthogonal Matrices, Hermitian Matrices, Unitary Matrices, Diagonalization of Matrices, Normal Matrices, Eigen values and Eigen vectors. Complex Numbers: Cauchy-Riemann condition, Cauchy’s integral formula for derivatives, Taylor’s expansion, Laurent expansion, Singularity. Infinite Series: Convergence Tests, Alternating Series, Series of Functions, Power Series, Alternative series (Leibnitz test), Asymptotic Series. Differential Equations: Ordinary and Partial differential equations, Riemann Integral Functions. Fourier series: General properties of Fourier series, application of Fourier series, Fourier Transform convolution theorem, Laplace transforms. Special Functions: Hermitian differential operators, orthogonality and completeness of Eigen functions, Legendre polynomials, generating functions, recurrent relations, spherical harmonics.