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Differential forms and cohomology: course

1 Description

 Stokes theorem $$\int_ σ dω = \int_{∂σ} ω$$ Derivative vs boundary

Differential forms provide a modern view of calculus. They also give you a start with algebraic topology in the sense that one can extract topological information about a manifold from its space of differential forms. It's called cohomology.

2 Prerequisites

Just linear algebra, in the sense of theory of vector spaces.

3 Contents

1. Introduction

2. Continuous differential forms

3. de Rham cohomology

4. Cubical differential forms

5. Cubical cohomology

6. Manifolds and differential forms

7. Integration of differential forms

8. Maps

9. From vector calculus to exterior calculus