It depends on what your own 'real world' is
As a physicist, I use (or at least did before I went towards materials science) quite a lot of maths.

Calculus is really quite useful. Honest, guv.
( K2k6 has a proper job these days, Thu 28 May 2009, 9:50, 2 replies, latest was 16 years ago)

it's more useful
if you use something easier to approximate it

which is what engineering is all about!
( Vipros. clever got me this far, then tricky got me in, Thu 28 May 2009, 9:53, Reply)

One of the good things about science and engineering training
is the ability to estimate quantities with a decent degree of accuracy. You know intuitively your answer is in the right ballpark or not.

Unfortunately, one of my former students hadn't learned this skill, and had made the biggest error I've ever seen in an exam. His answer was wrong by 26 orders of magnitude! He'd made a mistake in the charge on the electron, and said it was 10⁷C instead of 1.6022 x 10^-19C, then used this in his subsequent calculations.

But he didn't notice that his answer was unfeasibly wrong.

To put the error into context, it's roughly the difference between the size of an atom and the size of the observable universe...
( K2k6 has a proper job these days, Thu 28 May 2009, 10:14, Reply)

As a hydrogeologist I find math is a great tool to explain things.
While we will never really have enough data to fully describe/explain/characterize the real physical world (from a geologists point of view), calculus is a nice way to simplify the heterogeneities and allow an approximation of how things might be or might turn out to be depending on what action we take.
(MichaelS wasn't picked again, Thu 28 May 2009, 12:00, Reply)