**Vector Field Diagrams** ** ****04/19/16**

A most intuitive way of geometrically representing a solution of equations is through the use of a **Vector field Diagram.** To construct a vector field diagram, take two sets of equations dxdt=f(x,y)and dydt=g(x,y), set them equal to zero, and then isolate the xand y values on opposite sides. These sets of equations will determine the series of ordered pairs in which the **slope is zero **(in the horizontal or vertical direction for the f(x,y)and g(x,y) functions respectively). If one wants to see when the values are greater or less than zero, set the functions to a constant c greater than 0, and then solve with yas an isolate. These new solutions will determine the new slope in the x or y directions. One must combine the horizontal and tangential slopes to make the final value