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Curvature and Curve Design Module
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Curvature is applied to the task of aesthetic curve design by using a fairness metric. The student interacts with different aspects of curvature.
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In
this module, simple differential equations are used to study the effects of the
"drag" force which slows the motion of a body moving through a fluid (in this
case: air) and is responsible for the safe landing of the skydiver.
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The problem of creating a vector field as a gradient of a scalar function is illustrated in Electrostatics. Starting from the electostatics of a single point charge, students are led through a series of excercises, to the study of electrostatics of a more complex assembly of point charges and continuous distribution of charges.
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The gradient, its interrelations with other math concepts, and its applications to science and engineering. Rapid-change vector; normal vector to level surface. The gradient and gradient operator in cartesian and other coordinate systems. The gradient as related to differentiability and the directional derivative.
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In
this module, we will explore a variety of concepts related to first-year college level
calculus. We will start by examining a simple see saw model, a model with which should
already be familiar to you. We will then expand this model to include balancing in higher
dimensions and introduce such notions as moment (torque) and centroids.
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info@links.math.rpi.edu ... Last update March 02, 1999