Gravitomagnetism is a low velocity and weak gravitational field approximation of general relativity. It provides a simple approach to post-Newtonian gravitational phenomena via electromagnetic analogy. Intended for advanced undergraduate students, the present paper applies gravitomagnetism to the quantitative study of the geodetic precession and frame dragging effects, both verified recently in the Gravity Probe B experiment. The result obtained is identical with Schiff's formula. (Contains 2 figures.)