# pullback

(45 minutes to learn)

## Summary

Pullback is a mathematical operator which represents functions or differential forms on one space in terms of the corresponding object on another space. They are used to define surface integrals of differential forms.

## Context

This concept has the prerequisites:

- differential forms (Pullback operates on differential forms.)
- exterior derivative (Pullback commutes with the exterior derivative.)
- Chain Rule (The pullback of a differential is given by the chain rule.)
- evaluating multiple integrals: change of variables (When surface integrals are defined in terms of pullback, this is a generalization of the change of variables formula.)

## Goals

- Define the pullback of a function and of a differential form

- Show that the pullback commutes with the exterior derivative

- Be able to manipulate pullback, wedge products, and the exterior derivative algebraically

- Define the surface integral of a differential form in terms of pullback

## Core resources (read/watch one of the following)

## -Paid-

→ Multivariable Mathematics

A textbook on linear algebra and multivariable calculus with proofs.

Location:
Section 8.2.3, "Pullback," pages 342-345

## See also

-No Additional Notes-