1.Basic concept. 2.Special types of differential equations of the first order. 3.Problems leading to differential equations of the first order. 4.Linear differential equations of order greater than one. 5.Operators and Laplace transforms. 6.Problems leading to linear differential equations of order two. 7.Systems of differential equations linearization of first order systems. 8.Problems giving rise to systems of equations special types of second order linear and nonlinear equations solvable by reducing to systems. 9.Series methods. 10.Numerical methods. 11.Existence and uniqueness theorems for a system of first order differential equations Y1 = f(x,y). Picard’s method. Envelopes. 12.Clairaut equation. 13.Existence and uniqueness theorems for a system of first order differential equations and for linear and nonlinear differential equations of order greater than one wrosnkians.