I am using MATLAB for my research work for the last five years. So I learned MATLAB by solving of my own problems in my research area. Still I have to learn lot more functions in the MATLAB. My suggestion is take some example problems in your subject and start solving by MATLAB, so that it reach effectively to the students.

I have been using Matlab to teaching Control in Electronic Engineering. There are a lot of good sites on the internet about this subject:

http://ctms.engin.umich.edu/CTMS/index.php?example=Introduction§ion=SystemAnalysis

http://nptel.iitm.ac.in/courses/Webcourse-contents/IIT-Delhi/Control%20system%20design%20n%20principles/index2.htm

Well, thank you guys! We are opening the course right now, so we decided to teach Matlab basics (data types, vector and matrix operations, build-in functions, vectorization technique, introduction to GUI etc.). Your advices will be also utilized.

Another interesting question is, if Matlab is the best available environment - e.g. Python (+Spyder) offers almost the same functionality as Matlab (not Simulink), plus it is open source (free of charge).

Check the course on coursera:  https://www.coursera.org/course/matlab. I thought I would follow it but only basics are presented. You might find it useful anyway.

Thank you Petr for your interesting hint! The course you are referring to correspond to approx. one half of our new one-semestral subject on Matlab at CTU in Prague. When we were looking for the potential guideline how to teach Matlab, we found "MathWorks Certified MATLAB Associate Exam", and we try to teach exactly the topics from this certification.

Here is an online course that teaches problem-solving in MATLAB:

https://www.udemy.com/master-matlab-through-guided-problem-solving/?couponCode=MASTERMATLABX_10