This reference describes in detail how to build mathematical simulations of systems that change continuously over time. The topics covered include numerical integration, simulation of stiff systems, simulation of marginally stable systems, simulation of noisy systems, model validation techniques, simulation verification, dynamic nonlinear programming, simulation hardware and software. This highly computer-oriented text introduces numerical methods and algorithms alongside applications and conceptual tools. Homework problems, suggestions for research projects, and open-ended questions conclude each chapter.