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This module consists of four units, namely Introduction to Ordinary differential equations, higher order ordinary differential equations, power series solutions and special functions and partial differential equations and their applications. In unit one both first and second order equations are discussed and their solutions obtained with a variety of techniques. in unit two both homogeneous and non-homogeneous higher order equations are considered and a variety of solution techniques are discussed. Some of these techniques include the variation of parameters, the method of undetermined coefficients and the inverse operators. In unit three series solutions of differential equations are discussed. Also discussed special functions of mathematical physics. In unit four we look at partial differential equations and their solution by separation of variables.Other topics discussed are Laplace transforms, Fourier series, Fourier transforms and their applications.