Local Theory of Plane CurvesIntroductionThe most basic objects in differential geometry are plane curves. This first laboratory examines different ways of presenting plane curves and their geometric properties. We will be especially concerned with local properties of plane curves, which can be defined at a point by considering arbitrarily small neighborhoods of the point. We begin with parametrized plane curves, interpreted as paths traced out by a moving point. Examples of local properties for parametrized curves are speed, velocity and acceleration. |
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Differential geometry is the study of objects of various dimensions, using the tools of differential calculus and linear algebra. In all parts of this course, we will be concerned with the concept of curvature, a notion that describes deviation from straightness or flatness. The structure of the course will emphasize the ways this central concept appears in all dimensions. |
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