1.Origin of differential equations. 2.Solutions of differential equations. 3.Equations of first order and first degree. 4.Equations of first order and first degree. Variables separable amd reduction to variables separable. 5.Equations of first order and first Degree- Linear equations and reductions to exact equations. 6.Equations of first order and first Degree – Linear equations and those reducible to that form. 7.Geometric applications. 8.Physical applications. 9.Equations of first order and higher Degree. 10.Singular solutions. 11.Applications of first order and higher Degree equations. 12.Linear equations of order n. 13.Homogeneous linear equations with constant coefficients. 14.Linear equations with constant coefficients. 15.Linear equations with variable coefficients – Variation of parametric, undetermined coefficients. 16.Linear equations with 17.Linear equations with constant coefficients – The Cauchy and Legendre linear equations. 18.Linear equations with variable coefficients – Equations of the second order. 19.Linear equations with variable coefficients – Miscellaneous types. 20.Applications of linear equations. 21.Systems of total and simultaneous equations. 22.Total differential equations. 23.Applications of total and simultaneous equations. 24.Numerical approximations to solutions. 25.Integration in series. 26.Integration in series. 27.The Legendre, Bessel, and Gauss equations. 28.Partial differential equations. 29.Linear partial differential equations of order one. 30.Non-linear partial differential equations of order one. 31.Homogeneous partial differential equations of higher order with constant coefficient. 32.Non-Homogeneous linear equations with constant coefficients. 33.Partial differential equations of order two with constant coefficients.