Contents:

The following notes are referenced from "First Steps in Differential Geometry" Chapter3.

3.1 Derivatives and Linear Approximation

3.2 Geometric Definition of Tangent Space

3.3 Analytical Definition of Tangent Space

3.4 Diffeomorphism

3.5 Vector field, Vector Field & Flow

The following notes are referenced from "First Steps in Differential Geometry" Chapter4.

4.1 Alternating form and its opertation

4.2 Differential form and its operatation

4.3 Integrating Differential Forms