I guess I'll rephrase - if you can't understand a transfer function or a probability distribution without opening Matlab, then you've allowed your own expertise to be held hostage. Unfortunately, I know a large number of professionals for whom this is true.
If you're more productive in Matlab, that's fine. But if you're at a loss without it, that's not.
It doesn't belong in the education system or in educational books.
Conversely, if at every step of learning, you're hindered by inferior tools, you'll learn less, and be at a permanent disadvantage to those using superior tools.
If your job will use tool X, learning it well has value. Those not learning it will be at a disadvantage.
Again, no open source software can do what Matlab can. Why ignore this?
One big feature is a massive amount of built-in functionality [1]. You don't have to find various packages, install them, spend a day fighting version issues, or that some author hasn't upgraded to a recent language version, or used a non-standard logging facility, or any of a zillion other time-sinks you face daily with gluing open source packages together. As soon as a professional has been paid to fight open source integration for 1-2 days, it would have been better if the employer had simply bought matlab.
And, here is by far the biggest issue with open source - the numerical accuracy of lots of it is crap. Matlab (and Mathematica, etc.), have employed professional numerical analysists to create numerically stable, robust algorithms, and has had decades (Matlab started in 1970, under academic numerical analyst Cleve Moeller) of refinement to weed out bugs. It's the difference between using BLAS and writing your own linear algebra package - one is likely far more robust.
Sure, some numerical open source packages are decent, and a few are excellent (BLAS and related). But when you need to glue some together, you end up far too often with stuff that's just flakey for production work.
If you've ever coded the quadratic formula as written in high school textbooks and not known all the mess you just made, then you are what most open source developers are. Taking almost any formula from a paper and just typing it in is surely the wrong way to do it numerically, but this is what open source does. A robust engineering platform should have every such formula analyzed for the proper form(s) for implementation to maintain numerical robustness, and it should also avoid allowing users easy ways to do stuff that is not robust. This is the biggest difference between tools like Matlab and Mathematica versus open source projects.
And, like the time spent fiddling with getting open source to work, as soon as you have one engineering task or design fail due to numerical problems, it would have been vastly cheaper to simply use the better tool - Matlab.
Sure, most people don't use it very much, and rarely run into such problems. People using it for serious work in engineering toolchains or production systems cannot rely on instability of opensource.
And those reasons are why things like Matlab still exist, have incredible revenue, and are growing in use.
For example, want to do some work in python? Well, soon you need numpy. Then you might wat pytorch - but crap, it's numpy-ish, but not numpy. So you learn some more nuances on getting the two to play nicely, to get consistent error messages... Then you need some visualization - again, another package (with a host of dependencies), with different conventions, syntax, uses, and god forbid these packages get a little out of sync between releases - then you get to spend a day chasing that down. Now you want some optimization stuff - pull in scikit, but it's not quite consistent with the other libs... so you spend more time making glue functions between the stuff you want to build. Next you need some finite element analysis stuff - oops, pretty much dead compared to the massive amount of toolkits already in Matlab.
Take a moment and look through the list(s) of functions and toolkits standard in matlab [1]. For an incredible amount of engineering work, what you need is there - you spend less time trying to build enough pieces to start to work and you instead get working on the parts you want.
There's a reason python stole a lot of matplotlib ideas from Matlab - it's quite useful.
> As soon as a professional has been paid to fight open source integration for 1-2 days, it would have been better if the employer had simply bought matlab.
I'm a licensed professional, and in my experience it takes 1-2 hours to set up a conda virtualenv with all the packages I need. Whereas if I want Matlab, it takes about a week to talk through the budgeting and licensing options with my employer, find the right number of seats to purchase (other departments might decide to get in on the purchase, so we need to consult broadly), choose which toolboxes we'll pay for, go back and forth on the quotes and POs, and make sure all the licensing really works.
>I'm a licensed professional, and in my experience it takes 1-2 hours to set up a conda virtualenv with all the packages I need.
Yes, there are problems where Python is an easy solution. And many where it is not. And some where it cannot solve the problem without extreme effort.
Having been in dev a long time, this is the simplest, naive works best case path. If this were how setting up Python worked for everyone, there would not be an incredible amount of forum posts, github issues, setup help and problems, easily found on the internet. If you've not had to change underlying code in some python package or even worse recompile underlying C libraries, then you have not faced the kids of problems many (me included) have.
Ever solve a problem like the one I listed? That is not a simple conda install (and I use conda stuff vastly more than matlab/mathematica, so I'm pretty aware of it's use and features). Many problems I can solve in Mathematica (my preferred tool for certain work) cannot be approached by Python at all (or any open source tools I am aware of, and I have tried pretty much all of the things listed as MMA replacements).
>find the right number of seats to purchase (other departments might decide to get in on the purchase
So you're no longer making an apples to apples comparison - you just solved a bigger problem with the Matlab side.
No. Octave claims to support Matlab syntax, and they largely do, but not completely. And they most certainly don't provide all the packages Matlab has, which is where a lot of the use is.
Octave is also unstable, and I doubt any company needing heavy use of a tool like this in production would trust Octave to not puke. It's just simply cheaper to use the polished and vastly more feature rich tool. Download Octave, go find some decently complex matlab code on github, and try to run it. Do that a bit and see how much works as it should.
Octave lists places they see themselves as different, some of which is core pieces that don't work the same. So if you want to replace some engineering tasks with Octave, it's going to be a mess, in the same way OpenOffice is close to MS Office, until the day you send a proposal with a deadline and it pukes because the other end used MS Word instead of an almost clone.
I've used Octave - it's decent. If you cannot afford Matlab, or your school doesn't have it, or you want to learn "matlab" to get marketable skills, then one can learn on Octave. Most serious engineering will not be done on Octave though.
If you're more productive in Matlab, that's fine. But if you're at a loss without it, that's not.
It doesn't belong in the education system or in educational books.