
We start with a graphical explanation and then go into mathematical details.

It uses the theory of "funcoids", a highly abstract thing from topology. This course doesn't include detailed information on funcoids (just their definitions  several equivalent ones), so some proofs may be not understood by you (just believe me), but you can read about funcoids in freely available sources, if you want to check proofs.

You have a detailed article. I am going to split it into smaller parts (while preserving the long artilce, too). Order the course now and receive both existing and ongoing study materials.

Support from Newton, err... the author.

Course certification with simple exam questions will be added. Everybody who will pass receives "Master of discontinuous analysis" certificate!

There are two definitions of generalized limit: an axiomatic one and a concrete one. In usual cases they are equivalent. Choose any of the two. You don't need to remember all the definitions when you just calculate, just follow simple rules.

We take limits on "filters". That's a way to describe limits, upper limits, lower limits, ..., gradients, etc. with the same simple formulas, rather than repeating similar definitions over and over as you see in calculus books. It's not hard to understand.

You learn some of general topology just by the way, without being taught it in a usual boring nonunderstandable way. You learn newest discoveries in general topology and it's easy.

Apply it not only to continuous functions but also to discrete analysis (read: graph theory). Yes, you can apply analysis to graphs. Software developers!