This was my first honors course at Texas A&M. An honors course is supposed to cover the same material as the regular course, but go into more depth. What exactly this means is left for the instructor to figure out.
The regular course covers some standard integral calculus material, but rarely do we spend much time on the proofs. That is one avenue I chose to distinguish the honors course from the regular course; cover the proofs. While I often went over the basics of the proofs in my regular section as well, I expected honors students to be able to recreate the more straightforward proofs on the exams.
One of the two lab days is devoted to learning the basics of MATLAB, a computer algebra system. MATLAB is often the most hated part of the course. Understanding how to use and program MATLAB is potentially one of the most useful skills taught in the course. I have extensive experience teaching MATLAB from my Mathematical Modeling course. I decided to do my best to teach my students the fundamentals of programming: using if statements, for and while loops. We would learn the basics of data manipulation, and how to make graphs of functions. We would implement the basic techniques of numeric integration. We would do some numeric evaluation of the accuracy of the various algorithms for numeric integration.
Last, I realized one thing that students always struggle with is abstraction. When parameters in equations are not given as numbers, but are left as letters (especially the scary looking Greek ones), students struggle. So the final pillar of my honors course was to, whenever possible, replace numbers with letters and do the computations in a more abstract setting.