Independence of Solutions of Linear Differential Equations, Wronskian; Homogeneous Linear Differential Equations; Exact ,Differential Equations and Equations of S pecial Types; Linear , Equations of Second Order; Ordinary Simultaneous Differential , Equations; T otal Differential Equations (Pfaffian Diff. Equations); , Integration in Series (Method of Frobenius); Singular Solutions; , Picard's Iterative Method, Uniqueness and Existence Theorems; Linear Partial Differential Equations of Order One (Lagrange's Equations); Non-Linear Partial Differential Equations of Order One; Linear Partial Differential Equations; Partial Differential Equations of Second Order: Monge's Methods; Legendre's Equation and Legendre's Functions; Legendre's Functions of Second Kind-Qn(x); Bessel's Equation and Bessel's Functions; Hermite and Lagurree Polynomials; Reccati's equation.