Is it a good idea to use Octave to teach an Intro to Matlab course? I just discovered GNU Octave, a free open-source alternative to Matlab.

I was wondering if it would be wise to teach an "Intro to Matlab" course using Octave instead of Matlab. My motivations are both idealistic (i.e. I want to support open source software) and financial (I want to save my university some money on licensing fees). 

My concerns are that if Octave is too different from Matlab, it would be difficult to find textbooks and other teaching resources, and that when my students make it out into the real world they will most likely have to use Matlab and so they may be disadvantaged if they learned Octave instead. 

Does anyone familiar with Octave have any insight?

EDIT: Since a few of the initial comments and answers are focusing on the name of the course, I want to clarify that there is no issue changing the name (and I probably will if I use Octave). Nevertheless, I want my students to have the skills to be able to use Matlab after passing my course, and my question is about whether they will possess those skills if I teach the course using Octave.
As suggested also by SiXUlm in a comment, if you want to avoid being committed to a specific software, rename the course, e.g.,


  Introduction to scientific computing


or 


  Introduction to scientific computing with Octave/Matlab


During the course, outline possible syntax and library differences.


  when my students make it out into the real world they will most likely have to use Matlab


Most of your students will likely not use Matlab at all in the real world. A few of them will, but they would be able to fill the gaps by themselves.