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Catalog Description:

This course is an introduction to the principles and use of simulation, and suitable software tools, to model the behavior of physical systems in the sciences and engineering. Concepts related to discrete event simulation including random number generation, scheduling and processing are addressed.  Concepts related to continuous simulation including linear, nonlinear, and dynamic systems are studied. Students will design and implement simulations using suitable modeling and simulation software tools.

Prerequisites: 

Calculus-based probability and statistics

Required  Topics (approximate weeks allocated):

• General principles of simulation (2.0)
  • Discrete event, queuing systems, one item inventory control, Monte-Carlo 
• Pseudo-random number generators and expected properties (1.0)
• Random Event Generation and application to queuing systems: Inverse Transformations Method, Convolution, and Acceptance Rejection Methods, Distribution Specific Methods (2.0)
• Introduction to Continuous Simulation.  Simple examples and the Euler algorithm: Accuracy and Stability, Coffee cooling problem, Nuclear decay problem, One and Two-dimensional trajectories, Mini-Solar system (2.0)
• Linear and Nonlinear Systems: Simple Harmonic motion, Dissipative Systems, Electrical circuit oscillation (2.0)
• Chaotic Motion of Dynamical systems: A simple one-dimensional Map, Controlling Chaos, Forced Damped pendulum (2.0)
• Random Processes. Weeks: Introduction to Random Walks, Diffusion Equations, Applications to Polymers (1.0)
• Numerical Integration: Numerical Integration in one-dimension and multi-dimensions, Simple Monte-Carlo Evaluation of Integrals (2.0)
• Time allocated for exams and reviews (1.0)