The construction of mathematical models to address real-world problems has been one of the most important aspects of each of the branches of science. It is often the case that these mathematical models are formulated in terms of equations involving functions as well as their derivatives. Such equations are called differential equations. If only one independent variable is involved, often time, the equations are called ordinary differential equations. The course will demonstrate the usefulness of ordinary differential equations for modeling physical and other phenomena. Complementary mathematical approaches for their solution will be presented. The topics to be covered are vector algebra with applications to three-dimensional geometry. First order differential equations; applications to integral curves and orthogonal trajectories.  Ordinary linear differential equations with constant coefficients and equation reducible to this type. Simultaneous linear differential equations. Introduction to partial differential equations.