Differential Forms

★★★★★Graduate+

📖Definition

Antisymmetric tensor fields enabling coordinate-free integration

📐Formulas

0-form: f
1-form: ω = fᵢ dxⁱ
2-form: ω = f_ij dxⁱ ∧ dx^j
Exterior derivative: d

✏️Examples

예제 1

dx, dy, dz

예제 2

x dy - y dx

예제 3

dx ∧ dy

Applications

Stokes theorem

Electromagnetism

de Rham cohomology

#미분형식#differential#forms#exterior