This course introduces the study of ordinary differential equations (ODEs) and their applications.

Emphasis on: linear dependence, the Wronskian, reduction of order, variation of parameters.

Series solutions: power series about ordinary and regular singular points; Frobenius method.

Special functions: Gamma and Beta functions, Bessel functions,

Legendre polynomials, hypergeometric functions.

Laplace transform: solving initial-value problems (IVPs) and applied modelling.