"Dynamic Optimization Methods with Applications, Fall 2009"

Abstract:: "This course focuses on dynamic optimization methods, both in discrete and in continuous time. We approach these problems from a dynamic programming and optimal control perspective. We also study the dynamic systems that come from the solutions to these problems. The course will illustrate how these techniques are useful in various applications, drawing on many economic examples. However, the focus will remain on gaining a general command of the tools so that they can be applied later in other classes."

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Michell Trusses

Abstract:: This report summarizes work done as part of the Michell Trusses PFUG under Rice University's VIGRE program. VIGRE is a program of Vertically Integrated Grants for Research and Education in the Mathematical Sciences under the direction of the National Science Foundation. A PFUG is a group of Postdocs, Faculty, Undergraduates and Graduate students formed around the study of a common problem. In this PFUG, we study cost minimizing trusses. We ask what is the structure, constructed of bars and cables, of least cost that will withstand a set of point forces. This work was studied in the Rice University VIGRE class MATH499 in the Spring and Fall of 2008.

Abstract:: 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.

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Abstract:: This report summarizes work done as part of the Calculus of Variations PFUG under Rice University's VIGRE program. VIGRE is a program of Vertically Integrated Grants for Research and Education in the Mathematical Sciences under the direction of the National Science Foundation. A PFUG is a group of Postdocs, Faculty, Undergraduates and Graduate students formed around the study of a common problem. In this PFUG, we study Melzak's Problem, which asks if we can find a polyhedron which minimizes the edge length amongst all polyhedra with unit volume. This work was studied in the Rice University VIGRE class MATH499 in the Fall of 2008.

Abstract:: Introduction to a selection of mathematical topics that are not covered in traditional mechanical engineering curricula, such as differential geometry, integral geometry, discrete computational geometry, graph theory and optimization techniques. Emphasis on basic ideas and on applications in mechanical engineering. Selection will change every year. This course forms an introduction to a selection of mathematical topics that are not covered in traditional mechanical engineering curricula, such as differential geometry, integral geometry, discrete computational geometry, graph theory, optimization techniques, calculus of variations and linear algebra. The topics covered in any particular year depend on the interest of the students and instructor. Emphasis is on basic ideas and on applications in mechanical engineering. This year, the subject focuses on selected topics from linear algebra and the calculus of variations. It is aimed mainly (but not exclusively) at students aiming to study mechanics (solid mechanics, fluid mechanics, energy methods etc.), and the course introduces some of the mathematical tools used in these subjects. Applications are related primarily (but not exclusively) to the microstructures of crystalline solids.