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In Calculus of Variations, we give up the idea of only optimizing values and start optimizing geometries instead. The unknown is not a single x. It is a whole curve/surface y(x). The object you are minimizing is usually not a simple formula that you can guess. It is an integral that judges the whole shape.In our first lecture, we discuss the famous Brachistochrone problem. You choose two points, turn on gravity and ask a question which almost sounds too simple...which track will allow a bead to
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In Calculus of Variations, we give up the idea of only optimizing values and start optimizing geometries instead. The unknown is not a single x. It is a whole curve/surface y(x). The object you are minimizing is usually not a simple formula that you can guess. It is an integral that judges the whole shape.In our first lecture, we discuss the famous Brachistochrone problem. You choose two points, turn on gravity and ask a question which almost sounds too simple...which track will allow a bead to
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Session 29: Optimization Problems | Single Variable Calculus | Mathematics | MIT OpenCourseWare
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mit.edu
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