I've created roughly 40 videos for an online course and a flipped course in biology, so I've got some experience making videos. I researched the maker of your videos, and he deliberately does NOT reveal his process. So I don't know if this is his method, but I'm comfortable that this would produce something very similar.
Supplies:
- Computer (I use a Windows 7 machine, but Mac should work) with a decent mic
- Presentation software (I use PowerPoint) that has a plain "graph paper" background option
Wacom-style tablet, about $200
Screencast software like Camtasia Studio, about $200
Calculator emulator software. TI makes a $160 one, but this one looks like the one your YouTube guy uses.
Then, his workflow is to build up a powerpoint show with some drawings already made and set to appear when he clicks. He starts the screen cast, narrates, and draws in where needed. He can alt-tab the calculator onto the screen when he wants it (or set it as a picture-in-picture? I've never used one).
After completing the recording, some writing can be speeded up as long as you aren't talking during that part. Export, upload to YouTube.
All you need is money, time, some drawing skill, and the ability to be clear and concise and brisk.
Have I missed any steps?