Differential Geometry

Metric spaces, Curves in Euclidian 3 space (E3): Curvature, torsion, fundamental theorem of ordinary differential equations, fundamental existence theorem for space curves. Surfaces in E3: geometry on a surface, Inverse Function Theorem, Implicit Function Theorem, and Gauss curvature. Coordinate charts, Fubini's Theorem, orientation and an introduction to Riemannian Geometry. PREREQ: MAT 226, MAT 313, and MAT 320.

Fall, Spring

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