MATH-250 Differential Geometry
Spring for 2008-2009
Not only is the geometry of 2-dimensional surfaces in 3-dimensional space of great practical and theoretical importance in many fields of mathematics and physics, but so is the geometry of n-dimensional surfaces in (n+1)-dimensional space. This course uses and reinforces topics from Multivariable Calculus and Linear Algebra to study the geometry of oriented surfaces in 3-dimensional space, as well as n-dimensional surfaces in the (n+1)-dimensional space. Topics include level surfaces, parametrized surfaces, Vector fields on surfaces, the Gauss map, geodesics, surfaces area, the curvature of surfaces, the exponential map, and the Gauss-Bonnet Theorem.
Prerequisites: Math-137, Math-150, Math-201
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