MATH 3370 - Differential Geometry 3 s.h.

Theory of smooth curves: Curvature and torsion, Frenet-Serret formulas, involutes and evolutes, general helix, intrinsic equations. Theory of smooth surfaces: First and second fundamental forms, principal curvatures, Gaussian and mean curvature, lines of curvature, asymptotic lines, conjugate families of curves, Theorema Egregium, fundamental theorem of surfaces, intrinsic geometry, geodesics, Gauss-Bonnet theorem, topological properties of surfaces. Generalizations to higher dimensions: Manifolds, tensors, Stokes’ theorem, Lorentz space, Riemann space. A-E Only.
LA