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