Why not just use the phrase "Other Courses" as it would inform the user that they are not courses he is teaching.
That said, I would recommend providing an option of a Global search along with a scoped search would allow him to either search across all the courses or just within his courses so that the user can restrict his options.To quote this article
If you’re going to offer your users a scoped search, you should set
the default scope to all sections of the site. This makes it easy for
users to use the global search, which most will prefer. However, those
who want to use a scoped search can still do that. Scoped searches are
much like an advanced search. They’re best suited for users who know
exactly what they want and where to get it. The advantage of the
scoped search is that you don’t see the results for other sections of
the site. This is useful for the expert user, who understands how the
different site sections work. For everyone else, a global search with
scoped search results work best.
Then even if users use the global search you can provide them with answers based upon scope as shown below