If your teacher offered you a choice between an intense course or an intensive one, which one would you choose? And would you wonder what his intent was?

Intense means of severe strength or force; having strong feelings. An intense course, then, would be an extremely tough course, such as advanced nuclear science. Intensive means focused on one subject or area for a short time; extremely thorough. So an intensive course would be very focused on one topic and would last short time, as with summer courses. The teacher's intent, his purpose or intention, might be to guide you to the best course for you. Or it might be to fill his summer course.

Searching online, you'll find that in particular intensive is used instead of intense:

Michigan Solar Panel Factory's Labor-Intensive Assembly Tasks

These hiking-intensive trips can, of course, be strenuous.

Implementation can be a time-intensive process in terms of training, data input, data conversion, and down time.

Some dictionaries point out that intense is usually connected with a subjective response, while intensive is generally connected to an objective description. Here are a few examples that get it right:

Intense heat sears Southern California for 4th day

‎Seaton's intent to lie, cheat is as serious as a felony‎

Professional mountain bike rider in intensive care after hit-and-run