There is a particular professor at my math department who is particularly fond of MATLAB and encouraging his students to numerically verify their symbolical evaluations through MATLAB. Over time, his methodology grew on me and it is now something I somewhat find myself propagating. Since I have a strong disliking for the need for proprietary software and prefer the FOSS idealogy, I use NumPy instead of MATLAB. FOSS also guarantees that one can verify the correctness of code implementation from its source whereas with closed-source software, that is impossible.
As mentioned above, I personally think that teaching students to write scripts to quickly test their calculus assertions is a valuable tool in one’s toolkit for the following reasons:
- In this day and age, many tasks can be automated via computers, including generating specific numerical examples for verification purposes in the subject of calculus. This is a task that would otherwise be extremely tedious and unwieldy to do by hand.
- I also find that using programming as a means of numerical verification also tests your understanding of the subject in question, which I personally believe is one great way of seeing if you actually understand something.
Below are some quick examples of NumPy scripts of various topics one encouters in a calculus course. I assume that the user is familiar with the basics of Python and is capable of installing NumPy.
- Evaluation of Limits
- $\varepsilon$-$\delta$ Definition of Limits (TODO)