---
tag: 0E3G0GRPZ6
kind: concept
name: Differential form
msc: [58A10]
sources:
  - url: https://en.wikipedia.org/wiki/Differential_form
    locator: lead section
same_as:
  wikidata: Q1047080
  wikipedia: Differential form
---

## Summary

A differential form is an object that one can integrate over curves, surfaces, volumes and their higher-dimensional analogues.
A $k$-form assigns to each point an alternating $k$-linear function of tangent vectors. Forms give a coordinate-free approach to multivariable calculus.