Week

Topic(s)

1

Parametrized Curves

2

Regular Curves, Arc Length

3

The Local Theory of Curves Parametrized by Arc Length

4

Global Properties of Plane Curves

5

Regular Surfaces, Inverse Images of Regular Values

6

Change of Parameters; Differentiable Functions on Surfaces

7

Diffeomorphism

8

The Tangent Plane and the Differential of a Map

9

The First Fundamental Form; Area

10

Orientation of Surfaces

11

The Definition of Gauss Map and It’s Fundamental Properties

12

The Gauss Map and The Second Fundamental form

13

The Gauss map in local coordinates

14

Continuation to the Gauss map in local coordinates