Introduction to Differential Geometry.

Catalog description

Calculus methods are applied to the study of curves and surfaces in three dimensional space. After an introduction to the geometry of curves (curvature, torsion, and Frenet's formulas), the course explores the geometry of surfaces. Some of the geometrical properties of a surface that will be investigated are its first and second fundamental forms, its various curvatures (normal, principal, mean, and Gaussian curvatures), and its geodesic curves.