Vector Fields

1
Vector Fields

• A brief introduction

2
Functions---The Big Picture
3
Our Function zoo

• We have been concentrating mostly on functions
  with two or three input (real) variables and one
  output (real) variable. In Calc A and Calc B we
  study functions with one real input variable and
  one real output variable.
• These are called Scalar Fields.

4
Scalar Fields
A scalar field is one whose output values are
real numbers
5
Scalar Fields in Higher Dimensions
Harder to picture Examples?
6
Vector Fields

• Functions in which the inputs are real numbers of
  vectors and the outputs are also vectors are
  called vector fields.
• We will still concentrate on vectors with 2 or 3
  coordinates to make these things easier to
  picture. But really we can work in any
  dimension.

7
Some special CasesParametrically Defined Curves
In the plane
In 3-dimensional space
8
Trajectories in 3-dimensional spaceAn Example
4 world records Tallest, Longest, Fastest and
Greatest Drop.
Steel Dragon Nagashima Spaland, Japan
9
Vector Fields
A vector field is one whose output values are
vectors.
Examples?
10
Vector Fields
A vector field is one whose output values are
vectors.
Direction field---if we care only about direction
and not magnitude