Review of linear algebra, applications to networks, structures, and estimation, Lagrange multipliers, differential equations of equilibrium, Laplace's equation and potential flow, boundary-value problems, minimum principles and calculus of variations, Fourier series, discrete Fourier transform, convolution, applications.
Studies the principles of deterministic optimal control. Variational calculus and Pontryagin's maximum principle. Applications of the theory, including optimal feedback control, time-optimal control, and others. Dynamic programming and numerical search algorithms introduced briefly.
Introduction to mathematical modeling, optimization, and simulation, as applied to manufacturing. Specific methods include linear programming, network flow problems, integer and nonlinear programming, discrete-event simulation, heuristics and computer applications for manufacturing processes and systems. Restricted to Leaders for Manufacturing students. One objective of 15.066J is to introduce modeling, optimization and simulation, as it applies to the study and analysis of manufacturing systems for decision support. The introduction of optimization models and algorithms provide a framework to think about a wide range of issues that arise in manufacturing systems. The second objective is to expose students to a wide range of applications for these methods and models, and to integrate this material with their introduction to operations management.
This is a text on elementary multivariable calculus, designed for students who have completed courses in single-variable calculus. The traditional topics are covered: basic vector algebra; lines, planes and surfaces; vector-valued functions; functions of 2 or 3 variables; partial derivatives; optimization; multiple integrals; line and surface integrals.
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