Parametrized curves, curvature of curves; Frenet frames, curves with prescribed curvatures, curves on hypersurfaces; principal, Gaussian, and mean curvatures; surfaces in $\mathbb{R}^3$, triangulation and classification of surfaces, Gauss-Bonnet theorem. Prereq: Grad standing or 2153.01 (254) and either 2568 (568) or 572. Not open to students with credit for 642.
Credit Hours:
3.0
Textbook
Title:
Differential Geometry: Curves, Surfaces, Manifolds
Edition:
2nd
Publisher:
AMS
ISBN:
9780821839881