MAT 471 : Differential Geometry

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Imagine a two-dimensional being inhabiting a curved surface. Would such a being be able to detect or comprehend the "curvature" of its universe ? Differential geometry considers such problems by applying multivariable calculus to the study of curves, surfaces, and their higher-dimensional analogues. Topics include the Frenet-Serret theory of space curves, the first- and second fundamental forms of a surface, Gaussian curvature of surfaces, n-dimensional manifolds, parallel vector fields, geodesics, and Riemannian metrics. Prerequisite: MAT 228 or permission.

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Last modified on Tuesday, January 12, 1999