mechgrad
Source: doing this from a mechanical engineering degree this year.
What I did, went and talked to my local university's CS advisor to see how I could pursue a degree in CS and they suggested that instead of a second bachelors I go for a MS.
So if you have a local college you would like to go to or if your alma mater has a degree program that interests you I suggest making an appointment with an advisor to talk about options. Many times you can start off non-degree and switch to degree seeking grad after a set amount of hours.
I specced the MBA with upgraded processor which would definitely be necessary (for CAD) but even the article I linked said it was a little slow with the upgraded processor.
I personally did all my CAD work on campus and MATLAB/programming at home because of computer specs.
I think a macbook is a nicer computer choice if you don't mind doing CAD work at school, or if later down the line you decide to spend ~$500 building a computer (just the computer not monitor, keyboard, os) because working at school is a burden. Though a lot of my CAD projects were group projects, depends more on school though.
The analysis work definitely is processor heavy (I think PRO/E might use CUDA somewhat now) but it just means a slower processor will take longer to run the analysis).
Just running the CAD program usually requires an okay processor and video card but if you google around or ask on forums some other people might have better experience with running solidworks on a MBA.
Here is another experience: https://forum.solidworks.com/thread/70311
We did have some programming in basic excel formula style but that you could run in parallels or virtualbox or what have you.
13" is okay for matlab, you could probably get away with 11" but I think it would be painful.
If you want to run the CAD software like Solidworks a MBP 13" might be the better choice (256GB + 8GB RAM) comes out to cheaper than the MBA 13" equiv with upgraded proc. And could probably run it reasonably well-ish (better than MBA). You usually don't need to do a lot of model analysis in undergrad but sometimes those CAD programs can be a system hog. Especially if you get to complicated model assemblies.
If you don't want to run the CAD software the MBA 13" should be okay it just might take longer to boot up matlab but with the programs you do processing power shouldnt make that much of a difference. If you can hook up an external monitor an 11" might be fine as well.
Heres someones experience with an air and solidworks: http://solidworksonamac.com/using-solidworks-on-a-macbook-ai...
Matlab was what we did all our programming in and that works fine on a Mac.
I feel like a laptop is much nicer choice but 11" is pretty small to get work done on (especially if you're going to try CAD software). And matlab can be screen heavy especially if your classes get into simulink.