I’ve found the book online and will definitrly look into it. It’s going to be my first time with russian math teaching style, i’m really looking forward to it. From what i’ve seen browsing the first chapter it seems very down to earth and straightforward, i really like it. Also, it covers exactly the scope of calculus i want to get better at, so thanks again.

Skimming through Zorich, it looks like it's roughly at the level of an American honors freshman calculus class, i.e. one aimed at math and physics majors. Engineers are unlikely to see any rigorous analysis in undergrad unless they're personally interested in math.