Slope Field

Given an ordinary differential equation , the slope field for that differential equation is the vector field that takes a point  to a unit vector with slope . The vectors in a slope field are usually drawn without arrowheads, indicating that they can be followed in either direction. Using a visualization of a slope field, it is easy to graphically trace out solution curves to initial value problems. For example, the illustration above shows the slope field for the equation  together with solution curves for various initial values of .

REFERENCES:

Thomas, G. B. Jr. and Finney, R. L. "Slope Fields and Picard's Theorem." §15.8 in Calculus and Analytic Geometry, 8th ed. Reading, MA: Addison-Wesley, pp. 1088-1089 and 1101, 1992.