Day: April 19, 2016

Vector Field Diagrams

Vector Field Diagrams

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