# Differential Equations

By
Ekol, G. L. (George L.)
(2010)

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his module consisst of two units, namely Introduction to Ordinary differential equations and higher order differential equations respectively. In unit one both homogeneous and non-homogeneous ordinary differential equations are discussed and their solutions obtained with a variety of techniques.Some of these techniques include the variation of parameters, the method of undetermined coefficients and the inverse operators. In unit two series solutions of differential equations are discussed .Also discussed are partial differential equations and their solution by separation of variables. Other topics discussed are Laplace transforms, Fourier series, Fourier transforms and their applications. Outline: Syllabus Unit 1: Introduction to Ordinary Differential Equations Level 2. Priority A. Calculus 3 is prerequisite. First order differential equations and applications. Second order differential equations. Homogeneous equations with constant coefficients. Equations with variable coefficients. Non-homogeneous equations. Undetermined coefficients. Variations of parameters. Inverse differential operators. Unit 2: Higher Order Differential Equations and Applications Level 2. Priority B. Differential Equations 1 is prerequisite. Series solution of second order linear ordinary differential equations. Special functions. Methods of separation of variables applied to second order partial differential equations. Spherical harmonics. Laplace transform and applications. Fourier series, Fourier transform and applications