I'd just like to interject for a moment. What you're referring to as calculus, is in fact, real analysis, or as I've recently taken to calling it,

[math]\Bigg(\mathbf{R},+,\times, \leq, |\cdot|,\tau = \{ A\subset \mathbf{R}\hspace{0.1cm} | \hspace{0.1cm}\forall x \in A, \exists \epsilon > 0 ,\hspace{0.1cm} ]x-\epsilon,x+\epsilon[\hspace{0.1cm} \subset A \},\hspace{0.1cm} \displaystyle \bigcap_{\substack{\text{A} \hspace{0.1cm}\sigma-\text{algebra of}\hspace{0.1cm}\mathbf{R}\\

\tau \subset A}}A , \hspace{0.1cm}\mathscr{L}\Bigg) [/math] -analysis. Calculus is not a branch of mathematics unto itself, but rather another application of a fully functioning analysis made useful by topology, measure theory and vital [math]\mathbf{R}[/math]-related properties comprising a full number field as defined by pure mathematics.

Many mathematics students and professors use applications of real analysis every day, without realizing it. Through a peculiar turn of events, the application of real analysis which is widely used today is often called "Calculus", and many of its users are not aware that it is merely a part of real analysis, developed by the Nicolas Bourbaki group.

There is really a calculus, and these people are using it, but it is just a part of the filed they use. Calculus is the computation process: the set of rules and formulae that allow the mathematical mind to derive numerical formulae from other numerical formulae. The computation process is an essential part of a branch of mathematics, but useless by itself; it can only function in the context of a complete number field.

Calculus is normally used in combination with the real number field, its topology and its measured space: the whole system is basically real numbers with analytical methods and properties added, or real analysis.

All the so called calculus problems are really problems of real analysis.