outline: 1.Ordinary differential equations : separable equations, exact differential equation, integrating factors. 2.Ordinary linear differential equations: first-order, second-order, and higher order equations, Euler-Cauchy equations, homogeneous equations. 3.Systems of differential equations: eigenvalues, eigenvectrors. 4.Power series solutions of differential equations: Legendre’s equations and polynomainal, Bessel equations and function, Strum-Liouville problems, orthogonality. 5.Laplace transform: Laplace transform, inverse transform, properties of Laplace transform, convrlution. 6.Linear algebra: introduction to vectors, matrices and determinants.