Linear algebra: Review of matrices and linear systems of equations. Vector spaces and subspaces, linear independence, basis and dimensions, linear transformations, orthogonality, Orthogonal basis, Gram Schmidt Process, least-square applications.
Differential equation with series solutions: Legendre’s equation, Legendre’s polynomial Pn(x), Legendre’s function of the second kind [Qn(x)], General solution of Legendre’s equation, Rodrigue’s formula, Legendre polynomials, A generating function of Legendre’s polynomial, Orthogonality of Legendre polynomials, Recurrence formulae for Pn(x) Green's function – Green’s Identities – Generalized functions.
Numerical methods: Solution of systems of equations – iterative methods, method of determining Eigen values and Eigen vectors by Power method. Numerical solution of partial differential equations – Elliptic, parabolic and hyperbolic equations.