Ex: electric and magnetic fields, gravitational and other force fields, wave functions, etc
A field is something with data that varies from point to point
There are scalar fields that vary point to point
Ex: temperature of pressure distributions
Fields like the Newtonian gravitation field are best described by vector fields, which associate a vector to each point
Others, like the electromagnetic field and charge distributions are best modeled by form fields
Some others, like the Einstein field of general relativity, are none of the above
Definition: Vector Field. A vector field on is a function whose input is a point in and whose output is a vector (also in ) emanating from that point.
Vector fields are distinct from functions that return points
The identity function in , takes a point in and returns the same point. But the vectorfield takes a point in and assigns it to a vector starting at that point.
Vector fields are often used to describe the flow of fluids or gases; the vector assigned to each point describes the direction and velocity of the gas at a given point
