I'm not sure if this a typical case, but the reason I use serious-ish math is my major in physics. When I see a simulation problem calculus comes to mind first.

In my experience there was not a single time calculus was applied in everyday engineering on my projects.

Of course, a lot of people can and do write useful software knowing little to no maths, but then again, I suppose one can build a working bridge based on gut feeling as well.

By "explicit" I mean that e.g. a lot of things I work on for example certainly will use principles that you could write out formally using various mathematical disciplines, but I may or may not have been aware of the underlying maths when writing it, but that does not mean I'm not approaching it in a systematic way.

In a lot of CS papers, even, the use of maths often turns out to be less formal than code, in that I often see maths used to handwave away details you can't get away with not presenting if writing it out as code.