Vector fields

2D vector field


Examples

$$\myv F(x,y)=-y\uv i +x \uv j$$

Examples

Examples

To do

  • Vector Field Sketches by hand

3D vector field


Examples

Examples

$$\myv F(x,y,z)=z\uv k$$

Mathematica

Download and open "13.1.MticaVectorFields.nb" in the handouts folder...

  • VectorPlot - 2D vector fields
    $$\myv F(x,y)=y\uv i -x\uv j$$

  • VectorPlot3D - 3D vector fields
    $$\myv F(x,y)=y\uv i+z\uv j+x\uv k$$


Use VectorScale $\to$ Automatic if necessary.

To Do

See the Jupyter notebook "vector fields" in your handouts folder on cocalc.com for examples of how to make plots of vector fields in CoCalc.

Sketch these in CoCalc

  • $\myv F(x,y)=x^2 \uv i +x^3 \uv j$
  • $\myv F(x,y)=y^3 \uv i +y^2 \uv j $
  • $\myv F(x,y)=(x+y) \uv i +(x-y) \uv j$

  • $\myv F(x,y,z)=y \uv i + z \uv j + x \uv k$
  • $\myv F(x,y,z)=y\uv i -2 \uv j +x \uv k$
  • $\myv F(x,y,z)=1\uv i -y^2 \uv j +z\uv k$



Image credits