# vector fields

(50 minutes to learn)

## Summary

A vector field is a function associating a vector with each point. Common examples include flow fields, force fields, and gradients of functions.

## Context

This concept has the prerequisites:

## Goals

- Understand what a vector field is

- Know some common examples (gradients of functions, force fields, velocity fields)

- Be able to visualize vector fields graphically

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

## -Free-

→ MIT Open Courseware: Multivariable Caclulus (2010)

Video lectures for MIT's introductory multivariable calculus class.

## -Paid-

→ Multivariable Calculus

An introductory multivariable calculus textbook.

Location:
Section 15.1, "Vector fields," pages 1014-1018

Additional dependencies:

- partial derivatives

## See also

- The gradient of a function is a common example of a vector field.
- Some operations which can be applied to vector fields: