A great many real, live engineers that I know would object to anyone calling themselves an engineer without a lot of study of the big three: statics, dynamics, and thermodynamics; not just general mathematics. It's one of the reasons I don't call myself an engineer. (But I do get to harsh on them a bit about not being professional programmers---their code isn't pretty.)

The other reason, of course, is that the "software engineer" term comes from a group of people who really wanted the respect that comes with "engineer" but realized that the big three don't get very far, software-wise. (And coincidentally didn't want to do all that icky math stuff. Not to mention much of the icky programming stuff.)