This book explains how to use the symbolic differentiation system D* for applications in computer games and engineering simulation. The authors describe how to create procedural 3D geometric models, link them together to form multibody physical systems, and simulate and display their physical behavior in real time. The symbolic differentiation capabilities of D* can be used in a wide variety of technical applications, including computer graphics, engineering, and mechanical simulation. Two Lagrangian physics simulation and procedural 3D geometric modeling are developed in great detail.