This course is intended to give graduate and senior-level undergraduate engineering students a foundation in the theory and methods for numerical  solution of ordinary (ODEs) and partial differential (PDEs) equations. Topics include Runge-Kutta and multistep methods for single and systems of ODEs, shooting and finite difference methods for boundary value problems, numerical solution of linear second-order PDEs (Laplace, Poisson, heat and wave equations), advection and Burger's equations. Particular emphasis will be set on differences in solution methods for explicit and implicit numerical schemes as well as on establishing connection between their order, stability and convergence properties. Different relevant models from physics and engineering will be introduced and numerically solved.