Direction Fields

#incomplete

• relabel example graph

Direction Fields, Phase-Plane Direction Fields, Slope Fields, and Vector Fields are a graph of the derivative of a function of multiple variables, , at multiple inputs of and . In other words it is the graph of the slope of at many different points along the graph.

When a function used to generate the direction field is graphed as a solid line on the direction field it is called a phase-plane line. (The blue, red, and green lines above).

Where the slope of the vectors equal 0 for all t given a y it is a equilibrium solution. These are caused by Nullclines, or inputs of t and y where the equation become 0.