Revision of Linear Algebra, Linear Transformations, Range and Kernel, Isomorphism, Matrix of transformations
and Change of basis. Series Solutions of ODE and Sturm-Liouville Theory: Power series solutions about
ordinary point, Legendre equation and Legendre polynomials, Solutions about singular points; The method of Frobenius, Bessel equation and Bessel Functions. Sturm-Liouville problem and Generalized Fourier series. Partial Differential Equations: Second order PDEs, Classifications, Formulation and method of solutions of Wave equation, Heat equation and Laplace equation. Tensor Calculus: Line, area and volume integrals, Spaces of N-dimensions, coordinate transformations, covariant and mixed tensors , fundamental operation with tensors, the line element and metric tensor, conjugate tensor, Christoffel’s symbols , covariant derivative.