The Collaborative International Dictionary of English v.0.48:

Course \Course\, v. t. [imp. & p. p. Coursed (k?rst)); p. pr.
   & vb. n. Coursing.]
   1. To run, hunt, or chase after; to follow hard upon; to
      pursue.
      [1913 Webster]

            We coursed him at the heels.          --Shak.
      [1913 Webster]

   2. To cause to chase after or pursue game; as, to course
      greyhounds after deer.
      [1913 Webster]

   3. To run through or over.
      [1913 Webster]

            The bounding steed courses the dusty plain. --Pope.
      [1913 Webster]

The Collaborative International Dictionary of English v.0.48:

Coursing \Cours"ing\ (k?rs"?ng), n.
   The pursuit or running game with dogs that follow by sight
   instead of by scent.
   [1913 Webster]

         In coursing of a deer, or hart, with greyhounds.
                                                  --Bacon
   [1913 Webster]

WordNet (r) 3.0 (2006):

coursing
    n 1: hunting with dogs (usually greyhounds) that are trained to
         chase game (such as hares) by sight instead of by scent