Math 423/673
Differential Geometry
John Zweck
Lecture Notes
Course Overview
Euclidean Space; Tangent Vectors; Directional
Derivatives
Curves; mappings Between Euclidean Spaces
Inverse Function Theorem and Regular Mappings
Arclength and Vector Fields on Curves
Frenet Formulae
Surfaces
Tangent Spaces
Integration over Surfaces and FTCx4
One Forms
Two-forms, surface integrals and the d-operator
Forms on surfaces and FTC for differential forms
The Shape Operator
Normal Curvature
Gauss and Mean Curvature