Basic concepts and classifying differential equations -- Solutions of first-order differential equations -- Applications of first-order differential equations -- Linear differential equations : theory of solutions -- Solutions of linear homogeneous differential equations with constant coefficients -- Solutions of linear nonhomogeneous equations and initial-value problems -- Applications of second-order linear differential equations -- Laplace transforms and inverse Laplace transforms -- Solutions by Laplace transforms -- Matrices and the matrix exponential -- Solutions of linear differential equations with constant coefficients by matrix methods -- Power series solutions -- Gamma and Bessel functions -- Numerical methods -- Boundary-value problems and Fourier series -- Laplace transforms.