Linear systems of ODEs. Solving methods of linear systems of ODEs (elimination method, methods using eigenvalues and eigenvectors of a matrix). Series solutions of linear differential equations. Laplace transform for solving linear ODEs and systems of ODEs. Boundary value problems. Sturm-Liouville problems. Integral equations of Fredholm and Volterra type. Solving Fredholm integral equations whose kernel is a Green function of a homogeneous Sturm Liouville problem and Volterra integral equations with convolution type kernel. Applications of systems of ODEs and integral equations.